diff --git a/dev/.documenter-siteinfo.json b/dev/.documenter-siteinfo.json new file mode 100644 index 00000000..d5421aa6 --- /dev/null +++ b/dev/.documenter-siteinfo.json @@ -0,0 +1 @@ +{"documenter":{"julia_version":"1.9.3","generation_timestamp":"2023-10-29T15:58:37","documenter_version":"1.1.2"}} \ No newline at end of file diff --git a/dev/api/index.html b/dev/api/index.html index 49ff999b..8b1f0c8a 100644 --- a/dev/api/index.html +++ b/dev/api/index.html @@ -1,22 +1,22 @@ -API · OnlineStats Documentation
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API

OnlineStats.ADAGRAD — Type
ADAGRAD()

A variation of SGD with element-wise weights generated by the average of the squared gradients.

  • Reference: https://ruder.io/optimizing-gradient-descent/
  • Note: ADAGRAD uses a learning rate in OnlineStats, which differs from how it is typically presented. See https://www.seqstat.com/post/adagrad/ for details.
source
OnlineStats.ADAM — Type
ADAM(β1 = .99, β2 = .999)

A variant of SGD with element-wise learning rates generated by exponentially weighted first and second moments of the gradient.

  • Reference: https://ruder.io/optimizing-gradient-descent/
source
OnlineStats.ADAMAX — Type
ADAMAX(η, β1 = .9, β2 = .999)

ADAMAX with momentum parameters β1, β2. ADAMAX is an extension of ADAM.

  • Reference: https://ruder.io/optimizing-gradient-descent/
source
OnlineStats.Ash — Type
Ash(h::Union{KHist, Hist, ExpandingHist})
+
API
OnlineStats.ADAGRAD — Type
ADAGRAD()
A variation of SGD with element-wise weights generated by the average of the squared gradients.
  • Reference: https://ruder.io/optimizing-gradient-descent/
  • Note: ADAGRAD uses a learning rate in OnlineStats, which differs from how it is typically presented. See https://www.seqstat.com/post/adagrad/ for details.
source
OnlineStats.ADAM — Type
ADAM(β1 = .99, β2 = .999)
A variant of SGD with element-wise learning rates generated by exponentially weighted first and second moments of the gradient.
  • Reference: https://ruder.io/optimizing-gradient-descent/
source
OnlineStats.ADAMAX — Type
ADAMAX(η, β1 = .9, β2 = .999)
ADAMAX with momentum parameters β1, β2.  ADAMAX is an extension of ADAM.
  • Reference: https://ruder.io/optimizing-gradient-descent/
source
OnlineStats.Ash — Type
Ash(h::Union{KHist, Hist, ExpandingHist})
 Ash(h::Union{KHist, Hist, ExpandingHist}, m::Int, kernel::Function)
Create an Average Shifted Histogram using h as the base histogram with smoothing parameter m and kernel function kernel.  Built-in kernels are available in the OnlineStats.Kernels module.
Example
using OnlineStats, Plots
 
 o = fit!(Ash(ExpandingHist(1000)), randn(10^6))
 
 plot(o)
 plot(o, 20)
-plot(o, OnlineStats.Kernels.epanechnikov, 4)
source
OnlineStats.AutoCov — Type
AutoCov(b, T = Float64; weight=EqualWeight())
Calculate the auto-covariance/correlation for lags 0 to b for a data stream of type T.
Example
y = cumsum(randn(100))
+plot(o, OnlineStats.Kernels.epanechnikov, 4)
source
OnlineStats.AutoCov — Type
AutoCov(b, T = Float64; weight=EqualWeight())
Calculate the auto-covariance/correlation for lags 0 to b for a data stream of type T.
Example
y = cumsum(randn(100))
 o = AutoCov(5)
 fit!(o, y)
 autocov(o)
-autocor(o)
source
OnlineStats.BiasVec — Type
BiasVec(x)
Lightweight wrapper of a vector which adds a bias/intercept term at the end.
Example
BiasVec(rand(5))
source
OnlineStats.Bootstrap — Type
Bootstrap(o::OnlineStat, nreps = 100, d = [0, 2])
Calculate an online statistical bootstrap of nreps replicates of o.  For each call to fit!, any given replicate will be updated rand(d) times (default is double or nothing).
Example
o = Bootstrap(Variance())
+autocor(o)
source
OnlineStats.BiasVec — Type
BiasVec(x)
Lightweight wrapper of a vector which adds a bias/intercept term at the end.
Example
BiasVec(rand(5))
source
OnlineStats.Bootstrap — Type
Bootstrap(o::OnlineStat, nreps = 100, d = [0, 2])
Calculate an online statistical bootstrap of nreps replicates of o.  For each call to fit!, any given replicate will be updated rand(d) times (default is double or nothing).
Example
o = Bootstrap(Variance())
 fit!(o, randn(1000))
-confint(o, .95)
source
OnlineStats.CCIPCA — Type
CCIPCA(outdim::Int, indim; l::Int)
Online PCA with the CCIPCA (Candid Covariance-free Incremental PCA) algorithm, where indim is the length of incoming vectors, outdim is the number of dimension to project to, and l is the level of amnesia. Give values of l in the range 2-4 if you want old vectors to be gradually less important, i.e. latest vectors added get more weight.
If no indim is specified it will be set later, on first call to fit. After that it is fixed and cannot change.
The CCIPCA is a very fast, simple, and online approximation of PCA. It can be used for Dimensionality Reduction to project high-dimensional vectors into a low-dimensional (typically 2D or 3D) space. This algorithm has shown very good properties in comparative studies; it is both fast and give a good approximation to (batch) PCA.
Example
o = CCIPCA(2, 10)                # Project 10-dimensional vectors into 2D
+confint(o, .95)
source
OnlineStats.CCIPCA — Type
CCIPCA(outdim::Int, indim; l::Int)
Online PCA with the CCIPCA (Candid Covariance-free Incremental PCA) algorithm, where indim is the length of incoming vectors, outdim is the number of dimension to project to, and l is the level of amnesia. Give values of l in the range 2-4 if you want old vectors to be gradually less important, i.e. latest vectors added get more weight.
If no indim is specified it will be set later, on first call to fit. After that it is fixed and cannot change.
The CCIPCA is a very fast, simple, and online approximation of PCA. It can be used for Dimensionality Reduction to project high-dimensional vectors into a low-dimensional (typically 2D or 3D) space. This algorithm has shown very good properties in comparative studies; it is both fast and give a good approximation to (batch) PCA.
Example
o = CCIPCA(2, 10)                # Project 10-dimensional vectors into 2D
 u1 = rand(10)
 fit!(o, u1)                      # Fit to u1
 u2 = rand(10)
@@ -27,8 +27,8 @@
 OnlineStats.fittransform!(o, u4) # Fit u4 and then project u4 into the space
 sort!(o)                         # Sort from high to low eigenvalues
 o[1]                             # Get primary (1st) eigenvector
-OnlineStats.relativevariances(o)         # Get the variation (explained) "by" each eigenvector
source
OnlineStats.CallFun — Type
CallFun(o::OnlineStat, f::Function)
Call f(o) every time the OnlineStat o gets updated.
Example
o = CallFun(Mean(), println)
-fit!(o, [0,0,1,1])
source
OnlineStats.CountMinSketch — Type
CountMinSketch(T = Number; nhash=50, hashlength=1000, storagetype=Int)
Create a Count-Min Sketch with nhash hash functions of width hashlength.  Counts in the sketch will be stored as storagetype.
This lets you calculate an upper bound on the number of occurrences of some value x in a data stream via value(count_min_sketch, x).  For details and error bounds, please see the references section.
Example
o = CountMinSketch()
+OnlineStats.relativevariances(o)         # Get the variation (explained) "by" each eigenvector
source
OnlineStats.CallFun — Type
CallFun(o::OnlineStat, f::Function)
Call f(o) every time the OnlineStat o gets updated.
Example
o = CallFun(Mean(), println)
+fit!(o, [0,0,1,1])
source
OnlineStats.CountMinSketch — Type
CountMinSketch(T = Number; nhash=50, hashlength=1000, storagetype=Int)
Create a Count-Min Sketch with nhash hash functions of width hashlength.  Counts in the sketch will be stored as storagetype.
This lets you calculate an upper bound on the number of occurrences of some value x in a data stream via value(count_min_sketch, x).  For details and error bounds, please see the references section.
Example
o = CountMinSketch()
 
 y = rand(1:100, 10^6)
 
@@ -36,7 +36,7 @@
 
 value(o, 1)
 
-sum(y .== 1)
References
  • https://florian.github.io/count-min-sketch/
source
OnlineStats.DPMM — Type
DPMM(comp_mu::Real,
+sum(y .== 1)
References
  • https://florian.github.io/count-min-sketch/
source
OnlineStats.DPMM — Type
DPMM(comp_mu::Real,
      comp_lambda::Real,
      comp_alpha::Real,
      comp_beta::Real,
@@ -72,29 +72,29 @@
 o    = DPMM(μ, λ, α, β, α_dp; comp_birth_thres=0.5,
             comp_death_thres=1e-2, n_comp_max=10) 
 p = MixtureModel([ Normal(-2.0, 0.5), Normal(3.0, 1.0) ], [0.7, 0.3])
-o = fit!(o, rand(p, 1000))
source
OnlineStats.DWDLoss — Type
DWDLoss(q)(y, xβ)
Distance-weighted discrimination loss function (smoothed l1hingeloss) with smoothing parameter q.  Loss is calculated between a boolean response y ∈ {-1, 1} and linear predictor xβ.
source
OnlineStats.Diff — Type
Diff(T::Type = Float64)
Track the difference and the last value.
Example
o = Diff()
+o = fit!(o, rand(p, 1000))
source
OnlineStats.DWDLoss — Type
DWDLoss(q)(y, xβ)
Distance-weighted discrimination loss function (smoothed l1hingeloss) with smoothing parameter q.  Loss is calculated between a boolean response y ∈ {-1, 1} and linear predictor xβ.
source
OnlineStats.Diff — Type
Diff(T::Type = Float64)
Track the difference and the last value.
Example
o = Diff()
 fit!(o, [1.0, 2.0])
 last(o)
-diff(o)
source
OnlineStats.ElasticNet — Type
ElasticNet(α)
Weighted average of Ridge (abs) and LASSO (abs2) penalty functions.
$(1 - α) * Ridge + α * LASSO$
source
OnlineStats.ExpandingHist — Type
ExpandingHist(nbins)
An adaptive histogram where the bin edges keep doubling in size in order to contain every observation. nbins must be an even number.  Bins are left-closed and the rightmost bin is closed, e.g.
  • [a, b), [b, c), [c, d]
Example
o = fit!(ExpandingHist(200), randn(10^6))
+diff(o)
source
OnlineStats.ElasticNet — Type
ElasticNet(α)
Weighted average of Ridge (abs) and LASSO (abs2) penalty functions.
$(1 - α) * Ridge + α * LASSO$
source
OnlineStats.ExpandingHist — Type
ExpandingHist(nbins)
An adaptive histogram where the bin edges keep doubling in size in order to contain every observation. nbins must be an even number.  Bins are left-closed and the rightmost bin is closed, e.g.
  • [a, b), [b, c), [c, d]
Example
o = fit!(ExpandingHist(200), randn(10^6))
 
 using Plots
 plot(o)
Details
How ExpandingHist works is best understood through example.  Suppose we start with a histogram of edges/counts as follows:
|1|2|5|3|2|
  • Now we observe a data point that is not contained in the bin edges:
|1|2|5|3|2|       *
  • In order to contain the point, the range of the edges doubles in the direction of the new data point and adjacent bins merge their counts:
|1|2|5|3|2|       *
  \ / \ / \ /      ↓
   ↓   ↓   ↓       ↓
-| 3 | 8 | 2 | 0 | 1 |
  • Note that multiple iterations of bin-doubling may occur until the new point is contained by the bin edges.
source
OnlineStats.FastForest — Type
FastForest(p, nkeys=2; stat=FitNormal(), kw...)
Calculate a random forest where each variable is summarized by stat.
Keyword Arguments
  • nt=100): Number of trees in the forest
  • b=floor(Int, sqrt(p)): Number of random features for each tree to receive
  • maxsize=1000: Maximum size for any tree in the forest
  • splitsize=5000: Number of observations in any given node before splitting
  • λ = .05: Probability that each tree is updated on a new observation
Example
x, y = randn(10^5, 10), rand(1:2, 10^5)
+| 3 | 8 | 2 | 0 | 1 |
  • Note that multiple iterations of bin-doubling may occur until the new point is contained by the bin edges.
source
OnlineStats.FastForest — Type
FastForest(p, nkeys=2; stat=FitNormal(), kw...)
Calculate a random forest where each variable is summarized by stat.
Keyword Arguments
  • nt=100): Number of trees in the forest
  • b=floor(Int, sqrt(p)): Number of random features for each tree to receive
  • maxsize=1000: Maximum size for any tree in the forest
  • splitsize=5000: Number of observations in any given node before splitting
  • λ = .05: Probability that each tree is updated on a new observation
Example
x, y = randn(10^5, 10), rand(1:2, 10^5)
 
 o = fit!(FastForest(10), zip(eachrow(x),y))
 
-classify(o, x[1,:])
source
OnlineStats.FastTree — Type
FastTree(p::Int, nclasses=2; stat=FitNormal(), maxsize=5000, splitsize=1000)
Calculate a decision tree of p predictors variables and classes 1, 2, …, nclasses. Nodes split when they reach splitsize observations until maxsize nodes are in the tree. Each variable is summarized by stat, which can be FitNormal() or Hist(nbins).
Example
x = randn(10^5, 10)
+classify(o, x[1,:])
source
OnlineStats.FastTree — Type
FastTree(p::Int, nclasses=2; stat=FitNormal(), maxsize=5000, splitsize=1000)
Calculate a decision tree of p predictors variables and classes 1, 2, …, nclasses. Nodes split when they reach splitsize observations until maxsize nodes are in the tree. Each variable is summarized by stat, which can be FitNormal() or Hist(nbins).
Example
x = randn(10^5, 10)
 y = rand([1,2], 10^5)
 
 o = fit!(FastTree(10), zip(eachrow(x),y))
 
 xi = randn(10)
-classify(o, xi)
source
OnlineStats.FitBeta — Type
FitBeta(; weight)
Online parameter estimate of a Beta distribution (Method of Moments).
Example
o = fit!(FitBeta(), rand(1000))
source
OnlineStats.FitCauchy — Type
FitCauchy(b=500)
Approximate parameter estimation of a Cauchy distribution.  Estimates are based on approximated quantiles.  See Quantile and ExpandingHist for details on how the distribution is estimated.
Example
o = fit!(FitCauchy(), randn(1000))
source
OnlineStats.FitGamma — Type
FitGamma(; weight)
Online parameter estimate of a Gamma distribution (Method of Moments).
Example
using Random
-o = fit!(FitGamma(), randexp(10^5))
source
OnlineStats.FitLogNormal — Type
FitLogNormal()
Online parameter estimate of a LogNormal distribution (MLE).
Example
o = fit!(FitLogNormal(), exp.(randn(10^5)))
source
OnlineStats.FitMultinomial — Type
FitMultinomial(p)
Online parameter estimate of a Multinomial distribution.  The sum of counts does not need to be consistent across observations.  Therefore, the n parameter of the Multinomial distribution is returned as 1.
Example
x = [1 2 3; 4 8 12]
-fit!(FitMultinomial(3), x)
source
OnlineStats.FitMvNormal — Type
FitMvNormal(d)
Online parameter estimate of a d-dimensional MvNormal distribution (MLE).
Example
y = randn(100, 2)
-o = fit!(FitMvNormal(2), eachrow(y))
source
OnlineStats.FitNormal — Type
FitNormal()
Calculate the parameters of a normal distribution via maximum likelihood.
Example
o = fit!(FitNormal(), randn(1000))
source
OnlineStats.GeometricMean — Type
GeometricMean(T = Float64)
Calculate the geometric mean of a data stream, stored as type T.
Example
o = fit!(GeometricMean(), 1:100)
source
OnlineStats.FitBeta — Type
FitBeta(; weight)
Online parameter estimate of a Beta distribution (Method of Moments).
Example
o = fit!(FitBeta(), rand(1000))
source
OnlineStats.FitCauchy — Type
FitCauchy(b=500)
Approximate parameter estimation of a Cauchy distribution.  Estimates are based on approximated quantiles.  See Quantile and ExpandingHist for details on how the distribution is estimated.
Example
o = fit!(FitCauchy(), randn(1000))
source
OnlineStats.FitGamma — Type
FitGamma(; weight)
Online parameter estimate of a Gamma distribution (Method of Moments).
Example
using Random
+o = fit!(FitGamma(), randexp(10^5))
source
OnlineStats.FitLogNormal — Type
FitLogNormal()
Online parameter estimate of a LogNormal distribution (MLE).
Example
o = fit!(FitLogNormal(), exp.(randn(10^5)))
source
OnlineStats.FitMultinomial — Type
FitMultinomial(p)
Online parameter estimate of a Multinomial distribution.  The sum of counts does not need to be consistent across observations.  Therefore, the n parameter of the Multinomial distribution is returned as 1.
Example
x = [1 2 3; 4 8 12]
+fit!(FitMultinomial(3), x)
source
OnlineStats.FitMvNormal — Type
FitMvNormal(d)
Online parameter estimate of a d-dimensional MvNormal distribution (MLE).
Example
y = randn(100, 2)
+o = fit!(FitMvNormal(2), eachrow(y))
source
OnlineStats.FitNormal — Type
FitNormal()
Calculate the parameters of a normal distribution via maximum likelihood.
Example
o = fit!(FitNormal(), randn(1000))
source
OnlineStats.GeometricMean — Type
GeometricMean(T = Float64)
Calculate the geometric mean of a data stream, stored as type T.
Example
o = fit!(GeometricMean(), 1:100)
source
OnlineStats.HeatMap — Type
Heatmap(xedges, yedges; left = true, closed = true)
 Heatmap(itr; left = true, closed = true)
Create a two dimensional histogram with the bin partition created by xedges and yedges. When fitting a new observation, the first value will be associated with X, the second with Y.
  • If left, the bins will be left-closed.
  • If closed, the bins on the ends will be closed.  See Hist.
Example
using Plots
 
 xy = zip(randn(10^6), randn(10^6))
@@ -104,7 +104,7 @@
 xy = zip(1 .+ randn(10^6) ./ 10, randn(10^6))
 o = HeatMap(xy)
 plot(o, marginals=false)
-plot(o)
source
OnlineStats.Hist — Type
Hist(edges; left = true, closed = true)
Create a histogram with bin partition defined by edges.
  • If left, the bins will be left-closed.
  • If closed, the bin on the end will be closed.
    • E.g. for a two bin histogram $[a, b), [b, c)$ vs. $[a, b), [b, c]$
Example
o = fit!(Hist(-5:.1:5), randn(10^6))
+plot(o)
source
OnlineStats.Hist — Type
Hist(edges; left = true, closed = true)
Create a histogram with bin partition defined by edges.
  • If left, the bins will be left-closed.
  • If closed, the bin on the end will be closed.
    • E.g. for a two bin histogram $[a, b), [b, c)$ vs. $[a, b), [b, c]$
Example
o = fit!(Hist(-5:.1:5), randn(10^6))
 
 # approximate statistics
 using Statistics
@@ -114,7 +114,7 @@
 std(o)
 quantile(o)
 median(o)
-extrema(o)
source
OnlineStats.HyperLogLog — Type
HyperLogLog(T = Number)
 HyperLogLog{P}(T = Number)
Approximate count of distinct elements of a data stream of type T, using 2 ^ P "registers".  P must be an integer between 4 and 16 (default).
By default it returns the improved HyperLogLog cardinality estimator as defined by [1].
The original HyperLogLog estimator [2] can be retrieved with the option original_estimator=true.
Example
o = HyperLogLog()
 fit!(o, rand(1:100, 10^6))
 
@@ -125,12 +125,12 @@
 # by default the improved estimator is returned:
 value(o)
 # the original HyperLogLog estimator can be retrieved via:
-value(o; original_estimator=true)
References
[1] Improved estimator: Otmar Ertl. New cardinality estimation algorithms for HyperLogLog sketches. https://arxiv.org/abs/1702.01284
[2] Original estimator: P. Flajolet, Éric Fusy, O. Gandouet, and F. Meunier. Hyperloglog: The analysis of a near-optimal cardinality estimation algorithm. In Analysis of Algorithms (AOFA), pages 127–146, 2007.
source
OnlineStats.IndexedPartition — Type
IndexedPartition(T, stat, b=100)
Summarize data with stat over a partition of size b where the data is indexed by a variable of type T.
Example
x, y = randn(10^5), randn(10^6)
+value(o; original_estimator=true)
References
[1] Improved estimator: Otmar Ertl. New cardinality estimation algorithms for HyperLogLog sketches. https://arxiv.org/abs/1702.01284
[2] Original estimator: P. Flajolet, Éric Fusy, O. Gandouet, and F. Meunier. Hyperloglog: The analysis of a near-optimal cardinality estimation algorithm. In Analysis of Algorithms (AOFA), pages 127–146, 2007.
source
OnlineStats.IndexedPartition — Type
IndexedPartition(T, stat, b=100)
Summarize data with stat over a partition of size b where the data is indexed by a variable of type T.
Example
x, y = randn(10^5), randn(10^6)
 o = IndexedPartition(Float64, KHist(10))
 fit!(o, zip(x, y))
 
 using Plots
-plot(o)
source
OnlineStats.KHist — Type
KHist(k::Int)
Estimate the probability density of a univariate distribution at k approximately equally-spaced points.
Ref: https://www.jmlr.org/papers/volume11/ben-haim10a/ben-haim10a.pdf
A difference from the above reference is that the minimum and maximum values are not allowed to merge into another bin.
Example
o = fit!(KHist(25), randn(10^6))
 
 # Approximate statistics
 using Statistics
@@ -141,52 +141,52 @@
 median(o)
 
 using Plots
-plot(o)
source
OnlineStats.KIndexedPartition — Type
KIndexedPartition(T, stat_init, k=100)
Similar to IndexedPartition, but indexes the first variable by centroids (like KHist) rather than intervals.
  • Note: stat_init must be a function e.g. () -> Mean()
Example
using Plots
+plot(fit!(KHist2D(), zip(x, y)))
source
OnlineStats.KIndexedPartition — Type
KIndexedPartition(T, stat_init, k=100)
Similar to IndexedPartition, but indexes the first variable by centroids (like KHist) rather than intervals.
  • Note: stat_init must be a function e.g. () -> Mean()
Example
using Plots
 
 o = KIndexedPartition(Float64, () -> KHist(10))
 
 fit!(o, zip(randn(10^6), randn(10^6)))
 
-plot(o)
source
OnlineStats.KMeans — Type
KMeans(k; rate=LearningRate(.6))
Approximate K-Means clustering of k clusters.
Example
x = [randn() + 5i for i in rand(Bool, 10^6), j in 1:2]
+plot(o)
source
OnlineStats.KMeans — Type
KMeans(k; rate=LearningRate(.6))
Approximate K-Means clustering of k clusters.
Example
x = [randn() + 5i for i in rand(Bool, 10^6), j in 1:2]
 
 o = fit!(KMeans(2, 2), eachrow(x))
 
 sort!(o; rev=true)  # Order clusters by number of observations
 
-classify(o, x[1])  # returns index of cluster closest to x[1]
source
OnlineStats.KahanMean — Type
KahanMean(; T=Float64, weight=EqualWeight())
Track a univariate mean. Uses a compensation term for the update.
#Note
This should be more accurate as Mean in most cases but the guarantees of KahanSum do not apply. merge! can have some accuracy issues.
Update
$μ = (1 - γ) * μ + γ * x$
Example
@time fit!(KahanMean(), randn(10^6))
source
OnlineStats.KahanSum — Type
KahanSum(T::Type = Float64)
Track the overall sum. Includes a compensation term that effectively doubles precision, see Wikipedia for details.
Example
fit!(KahanSum(Float64), fill(1, 100))
source
OnlineStats.KahanVariance — Type
KahanVariance(; T=Float64, weight=EqualWeight())
Track the univariate variance. Uses compensation terms for a higher accuracy.
#Note
This should be more accurate as Variance in most cases but the guarantees of KahanSum do not apply. merge! can have accuracy issues.
Example
o = fit!(KahanVariance(), randn(10^6))
+classify(o, x[1])  # returns index of cluster closest to x[1]
source
OnlineStats.KahanMean — Type
KahanMean(; T=Float64, weight=EqualWeight())
Track a univariate mean. Uses a compensation term for the update.
#Note
This should be more accurate as Mean in most cases but the guarantees of KahanSum do not apply. merge! can have some accuracy issues.
Update
$μ = (1 - γ) * μ + γ * x$
Example
@time fit!(KahanMean(), randn(10^6))
source
OnlineStats.KahanSum — Type
KahanSum(T::Type = Float64)
Track the overall sum. Includes a compensation term that effectively doubles precision, see Wikipedia for details.
Example
fit!(KahanSum(Float64), fill(1, 100))
source
OnlineStats.KahanVariance — Type
KahanVariance(; T=Float64, weight=EqualWeight())
Track the univariate variance. Uses compensation terms for a higher accuracy.
#Note
This should be more accurate as Variance in most cases but the guarantees of KahanSum do not apply. merge! can have accuracy issues.
Example
o = fit!(KahanVariance(), randn(10^6))
 mean(o)
 var(o)
-std(o)
source
OnlineStats.Lag — Type
Lag(T, b::Int)
Store the last b values for a data stream of type T.  Values are stored as
$v(t), v(t-1), v(t-2), …, v(t-b+1)$
so that value(o::Lag)[1] is the most recent observation and value(o::Lag)[end] is the b-th most recent observation.
Example
o = fit!(Lag(Int, 10), 1:12)
+std(o)
source
OnlineStats.Lag — Type
Lag(T, b::Int)
Store the last b values for a data stream of type T.  Values are stored as
$v(t), v(t-1), v(t-2), …, v(t-b+1)$
so that value(o::Lag)[1] is the most recent observation and value(o::Lag)[end] is the b-th most recent observation.
Example
o = fit!(Lag(Int, 10), 1:12)
 o[1]
-o[end]
source
OnlineStats.LinReg — Type
LinReg()
Linear regression, optionally with element-wise ridge regularization.
Example
x = randn(100, 5)
+o[end]
source
OnlineStats.LinReg — Type
LinReg()
Linear regression, optionally with element-wise ridge regularization.
Example
x = randn(100, 5)
 y = x * (1:5) + randn(100)
 o = fit!(LinReg(), zip(eachrow(x),y))
 coef(o)
 coef(o, .1)
-coef(o, [0,0,0,0,Inf])
source
OnlineStats.LinRegBuilder — Type
LinRegBuilder(p)
Create an object from which any variable can be regressed on any other set of variables, optionally with element-wise ridge regularization.  The main function to use with LinRegBuilder is coef:
coef(o::LinRegBuilder, λ = 0; y=1, x=[2,3,...], bias=true, verbose=false)
Return the coefficients of a regressing column y on columns x with ridge (abs2 penalty) parameter λ.  An intercept (bias) term is added by default.
Examples
x = randn(1000, 10)
+coef(o, [0,0,0,0,Inf])
source
OnlineStats.LinRegBuilder — Type
LinRegBuilder(p)
Create an object from which any variable can be regressed on any other set of variables, optionally with element-wise ridge regularization.  The main function to use with LinRegBuilder is coef:
coef(o::LinRegBuilder, λ = 0; y=1, x=[2,3,...], bias=true, verbose=false)
Return the coefficients of a regressing column y on columns x with ridge (abs2 penalty) parameter λ.  An intercept (bias) term is added by default.
Examples
x = randn(1000, 10)
 o = fit!(LinRegBuilder(), eachrow(x))
 
 coef(o; y=3, verbose=true)
 
-coef(o; y=7, x=[2,5,4])
source
OnlineStats.MSPI — Type
MSPI()
Majorized Stochastic Proximal Iteration.
  • Reference: https://repository.lib.ncsu.edu/handle/1840.20/34945
source
OnlineStats.Mosaic — Type
Mosaic(T::Type, S::Type)
Data structure for generating a mosaic plot, a comparison between two categorical variables.
Example
using OnlineStats, Plots
+log(sum(exp.(x))) # should be very close
source
OnlineStats.MSPI — Type
MSPI()
Majorized Stochastic Proximal Iteration.
  • Reference: https://repository.lib.ncsu.edu/handle/1840.20/34945
source
OnlineStats.Mosaic — Type
Mosaic(T::Type, S::Type)
Data structure for generating a mosaic plot, a comparison between two categorical variables.
Example
using OnlineStats, Plots
 x = [rand() > .8 for i in 1:10^5]
 y = rand([1,2,2,3,3,3], 10^5)
 o = fit!(Mosaic(Bool, Int), zip(x, y))
-plot(o)
source
OnlineStats.MovingTimeWindow — Type
MovingTimeWindow{T<:TimeType, S}(window::Dates.Period)
 MovingTimeWindow(window::Dates.Period; valtype=Float64, timetype=Date)
Fit a moving window of data based on time stamps.  Each observation must be a Tuple, NamedTuple, or Pair where the first item is <: Dates.TimeType.  Observations with a timestamp NOT in the range
now() - window ≤ timestamp ≤ now()
are discarded on every fit!.
Example
using Dates
 dts = Date(2010):Day(1):Date(2011)
 y = rand(length(dts))
 
 o = MovingTimeWindow(Day(4); timetype=Date, valtype=Float64)
-fit!(o, zip(dts, y))
source
OnlineStats.MovingWindow — Type
MovingWindow(b, T)
 MovingWindow(T, b)
Track a moving window of b items of type T.  Also known as a circular buffer.
Example
o = MovingWindow(10, Int)
-fit!(o, 1:14)
source
OnlineStats.NBClassifier — Type
NBClassifier(p::Int, T::Type; stat = Hist(15))
Calculate a naive bayes classifier for classes of type T and p predictors.  For each class K, predictor variables are summarized by the stat.
Example
x, y = randn(10^4, 10), rand(Bool, 10^4)
+fit!(o, 1:14)
source
OnlineStats.NBClassifier — Type
NBClassifier(p::Int, T::Type; stat = Hist(15))
Calculate a naive bayes classifier for classes of type T and p predictors.  For each class K, predictor variables are summarized by the stat.
Example
x, y = randn(10^4, 10), rand(Bool, 10^4)
 
 o = fit!(NBClassifier(10, Bool), zip(eachrow(x),y))
 collect(keys(o))
@@ -194,32 +194,32 @@
 
 xi = randn(10)
 predict(o, xi)
-classify(o, xi)
source
OnlineStats.OMAP — Type
OMAP()
Online MM via Averaged Parameter.
  • Reference: https://repository.lib.ncsu.edu/handle/1840.20/34945
source
OnlineStats.OMAS — Type
OMAS()
Online MM via Averaged Surrogate.
  • Reference: https://repository.lib.ncsu.edu/handle/1840.20/34945
source
OnlineStats.OrderStats — Type
OrderStats(b::Int, T::Type = Float64; weight=EqualWeight())
Average order statistics with batches of size b.
Example
o = fit!(OrderStats(100), randn(10^5))
+classify(o, xi)
source
OnlineStats.OMAP — Type
OMAP()
Online MM via Averaged Parameter.
  • Reference: https://repository.lib.ncsu.edu/handle/1840.20/34945
source
OnlineStats.OMAS — Type
OMAS()
Online MM via Averaged Surrogate.
  • Reference: https://repository.lib.ncsu.edu/handle/1840.20/34945
source
OnlineStats.OrderStats — Type
OrderStats(b::Int, T::Type = Float64; weight=EqualWeight())
Average order statistics with batches of size b.
Example
o = fit!(OrderStats(100), randn(10^5))
 quantile(o, [.25, .5, .75])
 
 f = ecdf(o)
-f(0)
source
OnlineStats.Partition — Type
Partition(stat)
 Partition(stat, nparts)
Split a data stream into nparts (default 100) where each part is summarized by stat.
Example
o = Partition(Extrema())
 fit!(o, cumsum(randn(10^5)))
 
 using Plots
-plot(o)
source
OnlineStats.ProbMap — Type
ProbMap(T::Type; weight=EqualWeight())
 ProbMap(A::AbstractDict{T, Float64}; weight=EqualWeight())
Track a dictionary that maps unique values to its probability.  Similar to CountMap, but uses a weighting mechanism.
Example
o = ProbMap(Int)
 fit!(o, rand(1:10, 1000))
-probs(o)
source
OnlineStats.Quantile — Type
Quantile(q::Vector{Float64} = [0, .25, .5, .75, 1]; b=500)
Calculate (approximate) quantiles from a data stream.  Internally uses ExpandingHist to estimate the distribution, for which b is the number of histogram bins.  Setting b to a larger number will increase accuracy at the cost of speed.
Example
q = [.25, .5, .75]
+probs(o)
source
OnlineStats.Quantile — Type
Quantile(q::Vector{Float64} = [0, .25, .5, .75, 1]; b=500)
Calculate (approximate) quantiles from a data stream.  Internally uses ExpandingHist to estimate the distribution, for which b is the number of histogram bins.  Setting b to a larger number will increase accuracy at the cost of speed.
Example
q = [.25, .5, .75]
 x = randn(10^6)
 
 o = fit!(Quantile(q, b=1000), randn(10^6))
 value(o)
 
-quantile(x, q)
source
OnlineStats.RMSPROP — Type
RMSPROP(α = .9)
A Variation of ADAGRAD that uses element-wise weights generated by an exponentially weighted mean of the squared gradients.
  • Reference: https://ruder.io/optimizing-gradient-descent/
source
OnlineStats.ReservoirSample — Type
ReservoirSample(k::Int, T::Type = Float64)
Create a sample without replacement of size k.  After running through n observations, the probability of an observation being in the sample is 1 / n.
Example
fit!(ReservoirSample(100, Int), 1:1000)
source
OnlineStats.SGD — Type
SGD()
Stochastic Gradient Descent.
  • Reference: https://ruder.io/optimizing-gradient-descent/
source
OnlineStats.StatLag — Type
StatLag(stat, b)
Track a moving window (previous b copies) of stat.
Example
fit!(StatLag(Mean(), 10), 1:20)
source
OnlineStats.StatLearn — Type
StatLearn(args...; penalty=zero, rate=LearningRate())
Fit a model (via stochastic approximation) that is linear in the parameters.  The (offline) objective function that StatLearn approximately minimizes is
$(1/n) ∑ᵢ f(yᵢ, xᵢ'β) + ∑ⱼ λⱼ g(βⱼ),$
where $fᵢ$ are loss functions of a response variable and linear predictor, $λⱼ$s are nonnegative regularization parameters, and $g$ is a penalty function.
Use StatLearn with caution, as stochastic approximation algorithms are inherently noisy.
Arguments
  • loss = OnlineStats.l2regloss: The loss function to be (approximately) minimized.
    • Regression Losses:
      • l2regloss: Squared error loss
      • l1regloss: Absolute error loss
    • Classification (y ∈ {-1, 1}) Losses:
      • logisticloss: Logistic regression
      • l1hingeloss: Loss function used in Support Vector Machines.
      • DWDLoss(q): Generalized Distance Weighted Discrimination (smoothed l1hingeloss)
  • algorithm = MSPI(): The stochastic approximation method to be used.
    • Algorithms based on Stochastic gradient:
      • SGD(): Stochastic Gradient Descent
      • ADAGRAD(): AdaGrad (adaptive version of SGD)
      • RMSPROP(): RMSProp (adaptive version of SGD)
    • Algorithms based on Majorization-Minimization Principle:
      • MSPI(): Majorized Stochastic Proximal Iteration
      • OMAS(): Online MM via Averaged Surrogate
      • OMAP(): Online MM via Averaged Parameter
  • λ = 0.0: The hyperparameter(s) used for the penalty function
    • User can provide elementwise penalty hyperparameters (Vector{Float64}) or single hyperparameter (Float64).
Keyword Arguments
  • penalty: The regularization function used.
    • zero: no penalty (default)
    • abs: (LASSO) parameters penalized by their absolute value
    • abs2: (Ridge) parameters penalized by their squared value
    • ElasticNet(α): α * (abs penalty) + (1-α) * (abs2 penalty)
  • rate = LearningRate(.6)
Example
x = randn(1000, 5)
+quantile(x, q)
source
OnlineStats.RMSPROP — Type
RMSPROP(α = .9)
A Variation of ADAGRAD that uses element-wise weights generated by an exponentially weighted mean of the squared gradients.
  • Reference: https://ruder.io/optimizing-gradient-descent/
source
OnlineStats.ReservoirSample — Type
ReservoirSample(k::Int, T::Type = Float64)
Create a sample without replacement of size k.  After running through n observations, the probability of an observation being in the sample is 1 / n.
Example
fit!(ReservoirSample(100, Int), 1:1000)
source
OnlineStats.SGD — Type
SGD()
Stochastic Gradient Descent.
  • Reference: https://ruder.io/optimizing-gradient-descent/
source
OnlineStats.StatLag — Type
StatLag(stat, b)
Track a moving window (previous b copies) of stat.
Example
fit!(StatLag(Mean(), 10), 1:20)
source
OnlineStats.StatLearn — Type
StatLearn(args...; penalty=zero, rate=LearningRate())
Fit a model (via stochastic approximation) that is linear in the parameters.  The (offline) objective function that StatLearn approximately minimizes is
$(1/n) ∑ᵢ f(yᵢ, xᵢ'β) + ∑ⱼ λⱼ g(βⱼ),$
where $fᵢ$ are loss functions of a response variable and linear predictor, $λⱼ$s are nonnegative regularization parameters, and $g$ is a penalty function.
Use StatLearn with caution, as stochastic approximation algorithms are inherently noisy.
Arguments
  • loss = OnlineStats.l2regloss: The loss function to be (approximately) minimized.
    • Regression Losses:
      • l2regloss: Squared error loss
      • l1regloss: Absolute error loss
    • Classification (y ∈ {-1, 1}) Losses:
      • logisticloss: Logistic regression
      • l1hingeloss: Loss function used in Support Vector Machines.
      • DWDLoss(q): Generalized Distance Weighted Discrimination (smoothed l1hingeloss)
  • algorithm = MSPI(): The stochastic approximation method to be used.
    • Algorithms based on Stochastic gradient:
      • SGD(): Stochastic Gradient Descent
      • ADAGRAD(): AdaGrad (adaptive version of SGD)
      • RMSPROP(): RMSProp (adaptive version of SGD)
    • Algorithms based on Majorization-Minimization Principle:
      • MSPI(): Majorized Stochastic Proximal Iteration
      • OMAS(): Online MM via Averaged Surrogate
      • OMAP(): Online MM via Averaged Parameter
  • λ = 0.0: The hyperparameter(s) used for the penalty function
    • User can provide elementwise penalty hyperparameters (Vector{Float64}) or single hyperparameter (Float64).
Keyword Arguments
  • penalty: The regularization function used.
    • zero: no penalty (default)
    • abs: (LASSO) parameters penalized by their absolute value
    • abs2: (Ridge) parameters penalized by their squared value
    • ElasticNet(α): α * (abs penalty) + (1-α) * (abs2 penalty)
  • rate = LearningRate(.6)
Example
x = randn(1000, 5)
 y = x * range(-1, stop=1, length=5) + randn(1000)
 
 o = fit!(StatLearn(MSPI()), zip(eachrow(x), y))
 coef(o)
 
 o = fit!(StatLearn(OnlineStats.l1regloss, ADAGRAD()), zip(eachrow(x), y))
-coef(o)
source
OnlineStats.Trace — Type
Trace(stat, b=500, f=value)
Wrapper around an OnlineStat that stores b "snapshots" (a fixed copy of the OnlineStat).  The snapshots are taken at approximately equally-spaced intervals between 0 and the current nobs.  The main use case is visualizing state changes as observations are added.
Example
using OnlineStats, Plots
+coef(o)
source
OnlineStats.Trace — Type
Trace(stat, b=500, f=value)
Wrapper around an OnlineStat that stores b "snapshots" (a fixed copy of the OnlineStat).  The snapshots are taken at approximately equally-spaced intervals between 0 and the current nobs.  The main use case is visualizing state changes as observations are added.
Example
using OnlineStats, Plots
 
 o = Trace(Mean(), 10)
 
@@ -227,10 +227,10 @@
 
 OnlineStats.snapshots(o)
 
-plot(o)
source
Base.sort! — Method
sort!(o::CCIPCA)
Sort eigenvalues and their eigenvectors of o so highest ones come first. Useful before visualising since it ensures most variation is on the first (X) axis.
source
OnlineStats.fittransform! — Method
fittransform!(o::CCIPCA, u::Vector{Float64})
First fit! and then transform the vector u into the PCA space represented by o.
source
OnlineStats.l1hingeloss — Method
l1hingeloss(y, xβ)
Loss function between boolean response y ∈ {-1, 1} and linear predictor xβ for support vector machines:
$max(1 - y * xβ, 0)$
source
OnlineStats.l1regloss — Method
l1regloss(y, xβ)
Loss function between continuous response y and linear predictor xβ based on the $L_1$ norm:
$|y - xβ|$
source
OnlineStats.l2regloss — Method
l2regloss(y, xβ)
Loss function between continuous response y and linear predictor xβ based on the $L_2$ norm:
$.5 * (y - xβ) ^ 2$
source
OnlineStats.logisticloss — Method
logisticloss(y, xβ)
Loss function between boolean response y ∈ {-1, 1} and linear predictor xβ for logistic regression:
$log(1 + exp(-y * xβ))$
source
OnlineStats.reconstruct — Method
reconstruct(o::CCIPCA, uproj::AbstractArray{Float64})
Reconstruct the (projected) vector uproj back to the original space from which o has been fitted.
source
OnlineStats.relativevariances — Method
relativevariances(o::CCIPCA)
Get the relative variance (explained) in the direction of each eigenvector. Returns a vector of zeros if no vectors have yet been fitted. Note that this does not inclue the residual variance that is not captured in the eigenvectors.
source
OnlineStatsBase.value — Method
value(o::DPMM)
Realize the mixture model where each component is the marginal predictive distribution obtained as
q(x; mₖ, lₖ, aₖ, bₖ)
+plot(o)
source
Base.sort! — Method
sort!(o::CCIPCA)
Sort eigenvalues and their eigenvectors of o so highest ones come first. Useful before visualising since it ensures most variation is on the first (X) axis.
source
OnlineStats.fittransform! — Method
fittransform!(o::CCIPCA, u::Vector{Float64})
First fit! and then transform the vector u into the PCA space represented by o.
source
OnlineStats.l1hingeloss — Method
l1hingeloss(y, xβ)
Loss function between boolean response y ∈ {-1, 1} and linear predictor xβ for support vector machines:
$max(1 - y * xβ, 0)$
source
OnlineStats.l1regloss — Method
l1regloss(y, xβ)
Loss function between continuous response y and linear predictor xβ based on the $L_1$ norm:
$|y - xβ|$
source
OnlineStats.l2regloss — Method
l2regloss(y, xβ)
Loss function between continuous response y and linear predictor xβ based on the $L_2$ norm:
$.5 * (y - xβ) ^ 2$
source
OnlineStats.logisticloss — Method
logisticloss(y, xβ)
Loss function between boolean response y ∈ {-1, 1} and linear predictor xβ for logistic regression:
$log(1 + exp(-y * xβ))$
source
OnlineStats.reconstruct — Method
reconstruct(o::CCIPCA, uproj::AbstractArray{Float64})
Reconstruct the (projected) vector uproj back to the original space from which o has been fitted.
source
OnlineStats.relativevariances — Method
relativevariances(o::CCIPCA)
Get the relative variance (explained) in the direction of each eigenvector. Returns a vector of zeros if no vectors have yet been fitted. Note that this does not inclue the residual variance that is not captured in the eigenvectors.
source
OnlineStatsBase.value — Method
value(o::DPMM)
Realize the mixture model where each component is the marginal predictive distribution obtained as
q(x; mₖ, lₖ, aₖ, bₖ)
     = ∫ N(x; μₖ, sqrt(1/τₖ)) q(μₖ | τₖ; mₖ, lₖ) q(τₖ; aₖ, bₖ) dμₖ dτₖ
     = ∫ N(x; mₖ, sqrt(1/τₖ + 1/(lₖ*τₖ))) Gamma(τₖ; aₖ, bₖ) dμₖ dτₖ
-    = TDist( 2*aₖ, mₖ, sqrt(bₖ/aₖ*(lₖ+1)/lₖ) )
source
StatsAPI.confint — Function
confint(b::Bootstrap, coverageprob = .95)
Return a confidence interval for a Bootstrap b.
source
StatsBase.transform — Method
transform(o::CCIPCA, u::AbstractArray{Float64})
Transform (i.e. project) the vector u into the PCA space represented by o.
source
OnlineStatsBase.CircBuff — Type
CircBuff(T, b; rev=false)
Create a fixed-length circular buffer of b items of type T.
  • rev=false: o[1] is the oldest.
  • rev=true: o[end] is the oldest.
Example
a = CircBuff(Int, 5)
+    = TDist( 2*aₖ, mₖ, sqrt(bₖ/aₖ*(lₖ+1)/lₖ) )
source
StatsAPI.confint — Function
confint(b::Bootstrap, coverageprob = .95)
Return a confidence interval for a Bootstrap b.
source
StatsBase.transform — Method
transform(o::CCIPCA, u::AbstractArray{Float64})
Transform (i.e. project) the vector u into the PCA space represented by o.
source
OnlineStatsBase.CircBuff — Type
CircBuff(T, b; rev=false)
Create a fixed-length circular buffer of b items of type T.
  • rev=false: o[1] is the oldest.
  • rev=true: o[end] is the oldest.
Example
a = CircBuff(Int, 5)
 b = CircBuff(Int, 5, rev=true)
 
 fit!(a, 1:10)
@@ -239,7 +239,7 @@
 a[1] == b[end] == 1
 a[end] == b[1] == 10
 
-value(o; ordered=false)  # Retrieve values (no copy) without ordering
OnlineStatsBase.CountMap — Type
CountMap(T::Type)
 CountMap(dict::AbstractDict{T, Int})
Track a dictionary that maps unique values to its number of occurrences.  Similar to StatsBase.countmap.
Counts can be incremented by values other than one (and decremented) using the fit!(::CountMap{T}, ::Pair{T,Int}) method, e.g.
o = fit!(CountMap(String), ["A", "B"])
 fit!(o, "A" => 5)
 fit!(o, "A" => -1)
Example
o = fit!(CountMap(Int), rand(1:10, 1000))
@@ -248,30 +248,30 @@
 OnlineStats.pdf(o, 1)
 collect(keys(o))
 sort!(o)
-delete!(o, 1)
OnlineStatsBase.CountMissing — Type
CountMissing(stat)
Calculate a stat along with the count of missing values.  
Example
o = CountMissing(Mean())
-fit!(o, [1, missing, 3])
OnlineStatsBase.Counter — Type
Counter(T=Number)
Count the number of items in a data stream with elements of type T.
Example
fit!(Counter(Int), 1:100)
OnlineStatsBase.CountMissing — Type
CountMissing(stat)
Calculate a stat along with the count of missing values.  
Example
o = CountMissing(Mean())
+fit!(o, [1, missing, 3])
source
OnlineStatsBase.Counter — Type
Counter(T=Number)
Count the number of items in a data stream with elements of type T.
Example
fit!(Counter(Int), 1:100)
source
OnlineStatsBase.CovMatrix — Type
CovMatrix(p=0; weight=EqualWeight())
 CovMatrix(::Type{T}, p=0; weight=EqualWeight())
Calculate a covariance/correlation matrix of p variables.  If the number of variables is unknown, leave the default p=0.
Example
o = fit!(CovMatrix(), randn(100, 4) |> eachrow)
 cor(o)
 cov(o)
 mean(o)
-var(o)
OnlineStatsBase.Extrema — Type
Extrema(T::Type = Float64)
 Extrema(min_init::T, max_init::T)
Maximum and minimum (and number of occurrences for each) for a data stream of type T.
Example
Extrema(Float64) == Extrema(Inf, -Inf)
 
 o = fit!(Extrema(), rand(10^5))
 extrema(o)
 maximum(o)
-minimum(o)
OnlineStatsBase.ExtremeValues — Type
ExtremeValues(T = Float64, b=25)
Track the b smallest and largest values of a data stream (as well as how many times that value occurred).
Example
o = ExtremeValues(Int, 3)
+minimum(o)
source
OnlineStatsBase.ExtremeValues — Type
ExtremeValues(T = Float64, b=25)
Track the b smallest and largest values of a data stream (as well as how many times that value occurred).
Example
o = ExtremeValues(Int, 3)
 
 fit!(o, 1:100)
 
 value(o).lo  # [1 => 1, 2 => 1, 3 => 1]
 
-value(o).hi  # [98 => 1, 99 => 1, 100 => 1]
OnlineStatsBase.FilterTransform — Type
FilterTransform(stat::OnlineStat{S}, T = S; filter = x->true, transform = identity)
 FilterTransform(T => filter => transform => stat)
Wrapper around an OnlineStat that the filters and transforms its input.  Note that, depending on  your transformation, you may need to specify the type of a single observation (T).
Examples
o = FilterTransform(Mean(), Union{Missing,Number}, filter=!ismissing)
 fit!(o, [1, missing, 3])
 
 o = FilterTransform(String => (x->true) => (x->parse(Int,x)) => Mean())
-fit!(o, "1")
OnlineStatsBase.Group — Type
Group(stats::OnlineStat...)
 Group(; stats...)
 Group(collection)
Create a vector-input stat from several scalar-input stats.  For a new observation y, y[i] is sent to stats[i].
Examples
x = randn(100, 2)
 
@@ -280,37 +280,37 @@
 
 o = fit!(Group(m1 = Mean(), m2 = Mean()), eachrow(x))
 o.stats.m1
-o.stats.m2
OnlineStatsBase.GroupBy — Type
GroupBy(T, stat)
Update stat for each group (of type T).  A single observation is either a (named) tuple with two elements or a Pair.
Example
x = rand(Bool, 10^5)
+o.stats.m2
source
OnlineStatsBase.GroupBy — Type
GroupBy(T, stat)
Update stat for each group (of type T).  A single observation is either a (named) tuple with two elements or a Pair.
Example
x = rand(Bool, 10^5)
 y = x .+ randn(10^5)
-fit!(GroupBy(Bool, Series(Mean(), Extrema())), zip(x,y))
OnlineStatsBase.Mean — Type
Mean(T = Float64; weight=EqualWeight())
Track a univariate mean, stored as type T.
Example
@time fit!(Mean(), randn(10^6))
OnlineStatsBase.Moments — Type
Moments(; weight=EqualWeight())
First four non-central moments.
Example
o = fit!(Moments(), randn(1000))
+fit!(GroupBy(Bool, Series(Mean(), Extrema())), zip(x,y))
source
OnlineStatsBase.Mean — Type
Mean(T = Float64; weight=EqualWeight())
Track a univariate mean, stored as type T.
Example
@time fit!(Mean(), randn(10^6))
source
OnlineStatsBase.Moments — Type
Moments(; weight=EqualWeight())
First four non-central moments.
Example
o = fit!(Moments(), randn(1000))
 mean(o)
 var(o)
 std(o)
 skewness(o)
-kurtosis(o)
OnlineStatsBase.RepeatingRange — Type
RepeatingRange(rng)
Range that repeats forever. e.g.
r = OnlineStatsBase.RepeatingRange(1:2)
-r[1:5] == [1, 2, 1, 2, 1]
OnlineStatsBase.Series — Type
Series(stats)
 Series(stats...)
 Series(; stats...)
Track a collection stats for one data stream.
Example
s = Series(Mean(), Variance())
-fit!(s, randn(1000))
OnlineStatsBase.SkipMissing — Type
SkipMissing(stat)
Wrapper around an OnlineStat that will skip over missing values.
Example
o = SkipMissing(Mean())
+fit!(s, randn(1000))
source
OnlineStatsBase.SkipMissing — Type
SkipMissing(stat)
Wrapper around an OnlineStat that will skip over missing values.
Example
o = SkipMissing(Mean())
 
-fit!(o, [1, missing, 3])
OnlineStatsBase.Sum — Type
Sum(T::Type = Float64)
Track the overall sum.
Example
fit!(Sum(Int), fill(1, 100))
OnlineStatsBase.TryCatch — Type
TryCatch(stat; error_limit=1000, error_message_limit=90)
Wrap each call to fit! in a try-catch block and track the errors encountered (via CountMap).   Only error_limit unique errors will be included in the CountMap.  If a new error occurs after  error_limit has been reached, it will be included in the CountMap as "Other".  Only the first  error_message_limit characters of each error message will be recorded.
Example
o = TryCatch(Mean())
+fit!(o, [1, missing, 3])
source
OnlineStatsBase.TryCatch — Type
TryCatch(stat; error_limit=1000, error_message_limit=90)
Wrap each call to fit! in a try-catch block and track the errors encountered (via CountMap).   Only error_limit unique errors will be included in the CountMap.  If a new error occurs after  error_limit has been reached, it will be included in the CountMap as "Other".  Only the first  error_message_limit characters of each error message will be recorded.
Example
o = TryCatch(Mean())
 
 fit!(o, [1, missing, 3])
 
-OnlineStatsBase.errors(o)
OnlineStatsBase.Variance — Type
Variance(T = Float64; weight=EqualWeight())
Univariate variance, tracked as type T.
Example
o = fit!(Variance(), randn(10^6))
+OnlineStatsBase.errors(o)
source
OnlineStatsBase.Variance — Type
Variance(T = Float64; weight=EqualWeight())
Univariate variance, tracked as type T.
Example
o = fit!(Variance(), randn(10^6))
 mean(o)
 var(o)
-std(o)
Base.merge! — Method
merge!(a, b)
Merge OnlineStat b into a (supported by most OnlineStat types).
Example
a = fit!(Mean(), 1:10)
+std(o)
source
Base.merge! — Method
merge!(a, b)
Merge OnlineStat b into a (supported by most OnlineStat types).
Example
a = fit!(Mean(), 1:10)
 b = fit!(Mean(), 11:20)
-merge!(a, b)
OnlineStatsBase.smooth — Method
smooth(a, b, γ)
Weighted average of a and b with weight γ.
$(1 - γ) * a + γ * b$
OnlineStatsBase.smooth_syr! — Method
smooth_syr!(A::AbstractMatrix, x, γ::Number)
Weighted average of symmetric rank-1 update.  Updates the upper triangle of:
A = (1 - γ) * A + γ * x * x'
OnlineStatsBase.value — Method
value(stat::OnlineStat)
Calculate the value of stat from its "sufficient statistics".
StatsAPI.fit! — Method
fit!(stat1::OnlineStat, stat2::OnlineStat)
Alias for merge!. Merges stat2 into stat1.
Useful for reductions of OnlineStats using fit!.
Example
julia> v = [reduce(fit!, [1, 2, 3], init=Mean()) for _ in 1:3]
+merge!(a, b)
source
OnlineStatsBase.smooth_syr! — Method
smooth_syr!(A::AbstractMatrix, x, γ::Number)
Weighted average of symmetric rank-1 update.  Updates the upper triangle of:
A = (1 - γ) * A + γ * x * x'
source
StatsAPI.fit! — Method
fit!(stat1::OnlineStat, stat2::OnlineStat)
Alias for merge!. Merges stat2 into stat1.
Useful for reductions of OnlineStats using fit!.
Example
julia> v = [reduce(fit!, [1, 2, 3], init=Mean()) for _ in 1:3]
 3-element Vector{Mean{Float64, EqualWeight}}:
 Mean: n=3 | value=2.0
 Mean: n=3 | value=2.0
 Mean: n=3 | value=2.0
 
 julia> reduce(fit!, v, init=Mean())
-Mean: n=9 | value=2.0
StatsAPI.fit! — Method
fit!(stat::OnlineStat, data)
Update the "sufficient statistics" of a stat with more data.   If typeof(data) is not the type of a single observation for the provided stat, fit! will attempt to iterate through and fit! each item in data.  Therefore, fit!(Mean(), 1:10) translates roughly to:
o = Mean()
+Mean: n=9 | value=2.0
source
StatsAPI.fit! — Method
fit!(stat::OnlineStat, data)
Update the "sufficient statistics" of a stat with more data.   If typeof(data) is not the type of a single observation for the provided stat, fit! will attempt to iterate through and fit! each item in data.  Therefore, fit!(Mean(), 1:10) translates roughly to:
o = Mean()
 
 for x in 1:10
     fit!(o, x)
-end

+end
source
diff --git a/dev/assets/documenter.js b/dev/assets/documenter.js index 6adfbbbf..f5311607 100644 --- a/dev/assets/documenter.js +++ b/dev/assets/documenter.js @@ -1,15 +1,16 @@ // Generated by Documenter.jl requirejs.config({ paths: { - 'highlight-julia': 'https://cdnjs.cloudflare.com/ajax/libs/highlight.js/11.5.1/languages/julia.min', + 'highlight-julia': 'https://cdnjs.cloudflare.com/ajax/libs/highlight.js/11.8.0/languages/julia.min', 'headroom': 'https://cdnjs.cloudflare.com/ajax/libs/headroom/0.12.0/headroom.min', - 'jqueryui': 'https://cdnjs.cloudflare.com/ajax/libs/jqueryui/1.12.1/jquery-ui.min', - 'katex-auto-render': 'https://cdnjs.cloudflare.com/ajax/libs/KaTeX/0.13.24/contrib/auto-render.min', - 'jquery': 'https://cdnjs.cloudflare.com/ajax/libs/jquery/3.6.0/jquery.min', + 'jqueryui': 'https://cdnjs.cloudflare.com/ajax/libs/jqueryui/1.13.2/jquery-ui.min', + 'minisearch': 'https://cdn.jsdelivr.net/npm/minisearch@6.1.0/dist/umd/index.min', + 'katex-auto-render': 'https://cdnjs.cloudflare.com/ajax/libs/KaTeX/0.16.8/contrib/auto-render.min', + 'jquery': 'https://cdnjs.cloudflare.com/ajax/libs/jquery/3.7.0/jquery.min', 'headroom-jquery': 'https://cdnjs.cloudflare.com/ajax/libs/headroom/0.12.0/jQuery.headroom.min', - 'katex': 'https://cdnjs.cloudflare.com/ajax/libs/KaTeX/0.13.24/katex.min', - 'highlight': 'https://cdnjs.cloudflare.com/ajax/libs/highlight.js/11.5.1/highlight.min', - 'highlight-julia-repl': 'https://cdnjs.cloudflare.com/ajax/libs/highlight.js/11.5.1/languages/julia-repl.min', + 'katex': 'https://cdnjs.cloudflare.com/ajax/libs/KaTeX/0.16.8/katex.min', + 'highlight': 'https://cdnjs.cloudflare.com/ajax/libs/highlight.js/11.8.0/highlight.min', + 'highlight-julia-repl': 'https://cdnjs.cloudflare.com/ajax/libs/highlight.js/11.8.0/languages/julia-repl.min', }, shim: { "highlight-julia": { @@ -70,13 +71,90 @@ $(document).ready(function() { hljs.highlightAll(); }) +}) +//////////////////////////////////////////////////////////////////////////////// +require(['jquery'], function($) { + +let timer = 0; +var isExpanded = true; + +$(document).on("click", ".docstring header", function () { + let articleToggleTitle = "Expand docstring"; + + debounce(() => { + if ($(this).siblings("section").is(":visible")) { + $(this) + .find(".docstring-article-toggle-button") + .removeClass("fa-chevron-down") + .addClass("fa-chevron-right"); + } else { + $(this) + .find(".docstring-article-toggle-button") + .removeClass("fa-chevron-right") + .addClass("fa-chevron-down"); + + articleToggleTitle = "Collapse docstring"; + } + + $(this) + .find(".docstring-article-toggle-button") + .prop("title", articleToggleTitle); + $(this).siblings("section").slideToggle(); + }); +}); + +$(document).on("click", ".docs-article-toggle-button", function () { + let articleToggleTitle = "Expand docstring"; + let navArticleToggleTitle = "Expand all docstrings"; + + debounce(() => { + if (isExpanded) { + $(this).removeClass("fa-chevron-up").addClass("fa-chevron-down"); + $(".docstring-article-toggle-button") + .removeClass("fa-chevron-down") + .addClass("fa-chevron-right"); + + isExpanded = false; + + $(".docstring section").slideUp(); + } else { + $(this).removeClass("fa-chevron-down").addClass("fa-chevron-up"); + $(".docstring-article-toggle-button") + .removeClass("fa-chevron-right") + .addClass("fa-chevron-down"); + + isExpanded = true; + articleToggleTitle = "Collapse docstring"; + navArticleToggleTitle = "Collapse all docstrings"; + + $(".docstring section").slideDown(); + } + + $(this).prop("title", navArticleToggleTitle); + $(".docstring-article-toggle-button").prop("title", articleToggleTitle); + }); +}); + +function debounce(callback, timeout = 300) { + if (Date.now() - timer > timeout) { + callback(); + } + + clearTimeout(timer); + + timer = Date.now(); +} + }) //////////////////////////////////////////////////////////////////////////////// require([], function() { function addCopyButtonCallbacks() { for (const el of document.getElementsByTagName("pre")) { const button = document.createElement("button"); - button.classList.add("copy-button", "fas", "fa-copy"); + button.classList.add("copy-button", "fa-solid", "fa-copy"); + button.setAttribute("aria-label", "Copy this code block"); + button.setAttribute("title", "Copy"); + el.appendChild(button); const success = function () { @@ -85,7 +163,7 @@ function addCopyButtonCallbacks() { }; const failure = function () { - button.classList.add("error", "fa-times"); + button.classList.add("error", "fa-xmark"); button.classList.remove("fa-copy"); }; @@ -94,7 +172,7 @@ function addCopyButtonCallbacks() { setTimeout(function () { button.classList.add("fa-copy"); - button.classList.remove("success", "fa-check", "fa-times"); + button.classList.remove("success", "fa-check", "fa-xmark"); }, 5000); }); } @@ -138,29 +216,418 @@ require(['jquery', 'headroom', 'headroom-jquery'], function($, Headroom) { // Manages the top navigation bar (hides it when the user starts scrolling down on the // mobile). window.Headroom = Headroom; // work around buggy module loading? -$(document).ready(function() { - $('#documenter .docs-navbar').headroom({ - "tolerance": {"up": 10, "down": 10}, +$(document).ready(function () { + $("#documenter .docs-navbar").headroom({ + tolerance: { up: 10, down: 10 }, }); +}); + }) +//////////////////////////////////////////////////////////////////////////////// +require(['jquery', 'minisearch'], function($, minisearch) { + +// In general, most search related things will have "search" as a prefix. +// To get an in-depth about the thought process you can refer: https://hetarth02.hashnode.dev/series/gsoc + +let results = []; +let timer = undefined; + +let data = documenterSearchIndex["docs"].map((x, key) => { + x["id"] = key; // minisearch requires a unique for each object + return x; +}); + +// list below is the lunr 2.1.3 list minus the intersect with names(Base) +// (all, any, get, in, is, only, which) and (do, else, for, let, where, while, with) +// ideally we'd just filter the original list but it's not available as a variable +const stopWords = new Set([ + "a", + "able", + "about", + "across", + "after", + "almost", + "also", + "am", + "among", + "an", + "and", + "are", + "as", + "at", + "be", + "because", + "been", + "but", + "by", + "can", + "cannot", + "could", + "dear", + "did", + "does", + "either", + "ever", + "every", + "from", + "got", + "had", + "has", + "have", + "he", + "her", + "hers", + "him", + "his", + "how", + "however", + "i", + "if", + "into", + "it", + "its", + "just", + "least", + "like", + "likely", + "may", + "me", + "might", + "most", + "must", + "my", + "neither", + "no", + "nor", + "not", + "of", + "off", + "often", + "on", + "or", + "other", + "our", + "own", + "rather", + "said", + "say", + "says", + "she", + "should", + "since", + "so", + "some", + "than", + "that", + "the", + "their", + "them", + "then", + "there", + "these", + "they", + "this", + "tis", + "to", + "too", + "twas", + "us", + "wants", + "was", + "we", + "were", + "what", + "when", + "who", + "whom", + "why", + "will", + "would", + "yet", + "you", + "your", +]); + +let index = new minisearch({ + fields: ["title", "text"], // fields to index for full-text search + storeFields: ["location", "title", "text", "category", "page"], // fields to return with search results + processTerm: (term) => { + let word = stopWords.has(term) ? null : term; + if (word) { + // custom trimmer that doesn't strip @ and !, which are used in julia macro and function names + word = word + .replace(/^[^a-zA-Z0-9@!]+/, "") + .replace(/[^a-zA-Z0-9@!]+$/, ""); + } + + return word ?? null; + }, + // add . as a separator, because otherwise "title": "Documenter.Anchors.add!", would not find anything if searching for "add!", only for the entire qualification + tokenize: (string) => string.split(/[\s\-\.]+/), + // options which will be applied during the search + searchOptions: { + boost: { title: 100 }, + fuzzy: 2, + processTerm: (term) => { + let word = stopWords.has(term) ? null : term; + if (word) { + word = word + .replace(/^[^a-zA-Z0-9@!]+/, "") + .replace(/[^a-zA-Z0-9@!]+$/, ""); + } + + return word ?? null; + }, + tokenize: (string) => string.split(/[\s\-\.]+/), + }, +}); + +index.addAll(data); + +let filters = [...new Set(data.map((x) => x.category))]; +var modal_filters = make_modal_body_filters(filters); +var filter_results = []; + +$(document).on("keyup", ".documenter-search-input", function (event) { + // Adding a debounce to prevent disruptions from super-speed typing! + debounce(() => update_search(filter_results), 300); +}); + +$(document).on("click", ".search-filter", function () { + if ($(this).hasClass("search-filter-selected")) { + $(this).removeClass("search-filter-selected"); + } else { + $(this).addClass("search-filter-selected"); + } + + // Adding a debounce to prevent disruptions from crazy clicking! + debounce(() => get_filters(), 300); +}); + +/** + * A debounce function, takes a function and an optional timeout in milliseconds + * + * @function callback + * @param {number} timeout + */ +function debounce(callback, timeout = 300) { + clearTimeout(timer); + timer = setTimeout(callback, timeout); +} + +/** + * Make/Update the search component + * + * @param {string[]} selected_filters + */ +function update_search(selected_filters = []) { + let initial_search_body = ` +
Type something to get started!
+ `; + + let querystring = $(".documenter-search-input").val(); + + if (querystring.trim()) { + results = index.search(querystring, { + filter: (result) => { + // Filtering results + if (selected_filters.length === 0) { + return result.score >= 1; + } else { + return ( + result.score >= 1 && selected_filters.includes(result.category) + ); + } + }, + }); + + let search_result_container = ``; + let search_divider = `
`; + + if (results.length) { + let links = []; + let count = 0; + let search_results = ""; + + results.forEach(function (result) { + if (result.location) { + // Checking for duplication of results for the same page + if (!links.includes(result.location)) { + search_results += make_search_result(result, querystring); + count++; + } + + links.push(result.location); + } + }); + + let result_count = `
${count} result(s)
`; + + search_result_container = ` +
+ ${modal_filters} + ${search_divider} + ${result_count} +
+ ${search_results} +
+
+ `; + } else { + search_result_container = ` +
+ ${modal_filters} + ${search_divider} +
0 result(s)
+
+
No result found!
+ `; + } + + if ($(".search-modal-card-body").hasClass("is-justify-content-center")) { + $(".search-modal-card-body").removeClass("is-justify-content-center"); + } + + $(".search-modal-card-body").html(search_result_container); + } else { + filter_results = []; + modal_filters = make_modal_body_filters(filters, filter_results); + + if (!$(".search-modal-card-body").hasClass("is-justify-content-center")) { + $(".search-modal-card-body").addClass("is-justify-content-center"); + } + + $(".search-modal-card-body").html(initial_search_body); + } +} + +/** + * Make the modal filter html + * + * @param {string[]} filters + * @param {string[]} selected_filters + * @returns string + */ +function make_modal_body_filters(filters, selected_filters = []) { + let str = ``; + + filters.forEach((val) => { + if (selected_filters.includes(val)) { + str += `${val}`; + } else { + str += `${val}`; + } + }); + + let filter_html = ` +
+ Filters: + ${str} +
+ `; + + return filter_html; +} + +/** + * Make the result component given a minisearch result data object and the value of the search input as queryString. + * To view the result object structure, refer: https://lucaong.github.io/minisearch/modules/_minisearch_.html#searchresult + * + * @param {object} result + * @param {string} querystring + * @returns string + */ +function make_search_result(result, querystring) { + let search_divider = `
`; + let display_link = + result.location.slice(Math.max(0), Math.min(50, result.location.length)) + + (result.location.length > 30 ? "..." : ""); // To cut-off the link because it messes with the overflow of the whole div + + if (result.page !== "") { + display_link += ` (${result.page})`; + } + + let textindex = new RegExp(`\\b${querystring}\\b`, "i").exec(result.text); + let text = + textindex !== null + ? result.text.slice( + Math.max(textindex.index - 100, 0), + Math.min( + textindex.index + querystring.length + 100, + result.text.length + ) + ) + : ""; // cut-off text before and after from the match + + let display_result = text.length + ? "..." + + text.replace( + new RegExp(`\\b${querystring}\\b`, "i"), // For first occurrence + '$&' + ) + + "..." + : ""; // highlights the match + + let in_code = false; + if (!["page", "section"].includes(result.category.toLowerCase())) { + in_code = true; + } + + // We encode the full url to escape some special characters which can lead to broken links + let result_div = ` + +
+
${result.title}
+
${result.category}
+
+

+ ${display_result} +

+
+ ${display_link} +
+ + ${search_divider} + `; + + return result_div; +} + +/** + * Get selected filters, remake the filter html and lastly update the search modal + */ +function get_filters() { + let ele = $(".search-filters .search-filter-selected").get(); + filter_results = ele.map((x) => $(x).text().toLowerCase()); + modal_filters = make_modal_body_filters(filters, filter_results); + update_search(filter_results); +} }) //////////////////////////////////////////////////////////////////////////////// require(['jquery'], function($) { // Modal settings dialog -$(document).ready(function() { - var settings = $('#documenter-settings'); - $('#documenter-settings-button').click(function(){ - settings.toggleClass('is-active'); +$(document).ready(function () { + var settings = $("#documenter-settings"); + $("#documenter-settings-button").click(function () { + settings.toggleClass("is-active"); }); // Close the dialog if X is clicked - $('#documenter-settings button.delete').click(function(){ - settings.removeClass('is-active'); + $("#documenter-settings button.delete").click(function () { + settings.removeClass("is-active"); }); // Close dialog if ESC is pressed - $(document).keyup(function(e) { - if (e.keyCode == 27) settings.removeClass('is-active'); + $(document).keyup(function (e) { + if (e.keyCode == 27) settings.removeClass("is-active"); }); }); @@ -168,151 +635,242 @@ $(document).ready(function() { //////////////////////////////////////////////////////////////////////////////// require(['jquery'], function($) { +let search_modal_header = ` +
+
+

+ + + + +

+
+
+ +
+
+`; + +let initial_search_body = ` +
Type something to get started!
+`; + +let search_modal_footer = ` + +`; + +$(document.body).append( + ` + + ` +); + +document.querySelector(".docs-search-query").addEventListener("click", () => { + openModal(); +}); + +document.querySelector(".close-search-modal").addEventListener("click", () => { + closeModal(); +}); + +$(document).on("click", ".search-result-link", function () { + closeModal(); +}); + +document.addEventListener("keydown", (event) => { + if ((event.ctrlKey || event.metaKey) && event.key === "/") { + openModal(); + } else if (event.key === "Escape") { + closeModal(); + } + + return false; +}); + +// Functions to open and close a modal +function openModal() { + let searchModal = document.querySelector("#search-modal"); + + searchModal.classList.add("is-active"); + document.querySelector(".documenter-search-input").focus(); +} + +function closeModal() { + let searchModal = document.querySelector("#search-modal"); + let initial_search_body = ` +
Type something to get started!
+ `; + + searchModal.classList.remove("is-active"); + document.querySelector(".documenter-search-input").blur(); + + if (!$(".search-modal-card-body").hasClass("is-justify-content-center")) { + $(".search-modal-card-body").addClass("is-justify-content-center"); + } + + $(".documenter-search-input").val(""); + $(".search-modal-card-body").html(initial_search_body); +} + +document + .querySelector("#search-modal .modal-background") + .addEventListener("click", () => { + closeModal(); + }); + +}) +//////////////////////////////////////////////////////////////////////////////// +require(['jquery'], function($) { + // Manages the showing and hiding of the sidebar. -$(document).ready(function() { +$(document).ready(function () { var sidebar = $("#documenter > .docs-sidebar"); - var sidebar_button = $("#documenter-sidebar-button") - sidebar_button.click(function(ev) { + var sidebar_button = $("#documenter-sidebar-button"); + sidebar_button.click(function (ev) { ev.preventDefault(); - sidebar.toggleClass('visible'); - if (sidebar.hasClass('visible')) { + sidebar.toggleClass("visible"); + if (sidebar.hasClass("visible")) { // Makes sure that the current menu item is visible in the sidebar. $("#documenter .docs-menu a.is-active").focus(); } }); - $("#documenter > .docs-main").bind('click', function(ev) { + $("#documenter > .docs-main").bind("click", function (ev) { if ($(ev.target).is(sidebar_button)) { return; } - if (sidebar.hasClass('visible')) { - sidebar.removeClass('visible'); + if (sidebar.hasClass("visible")) { + sidebar.removeClass("visible"); } }); -}) +}); // Resizes the package name / sitename in the sidebar if it is too wide. // Inspired by: https://github.com/davatron5000/FitText.js -$(document).ready(function() { +$(document).ready(function () { e = $("#documenter .docs-autofit"); function resize() { - var L = parseInt(e.css('max-width'), 10); + var L = parseInt(e.css("max-width"), 10); var L0 = e.width(); - if(L0 > L) { - var h0 = parseInt(e.css('font-size'), 10); - e.css('font-size', L * h0 / L0); + if (L0 > L) { + var h0 = parseInt(e.css("font-size"), 10); + e.css("font-size", (L * h0) / L0); // TODO: make sure it survives resizes? } } // call once and then register events resize(); $(window).resize(resize); - $(window).on('orientationchange', resize); + $(window).on("orientationchange", resize); }); // Scroll the navigation bar to the currently selected menu item -$(document).ready(function() { +$(document).ready(function () { var sidebar = $("#documenter .docs-menu").get(0); var active = $("#documenter .docs-menu .is-active").get(0); - if(typeof active !== 'undefined') { + if (typeof active !== "undefined") { sidebar.scrollTop = active.offsetTop - sidebar.offsetTop - 15; } -}) +}); }) //////////////////////////////////////////////////////////////////////////////// require(['jquery'], function($) { -function set_theme(theme) { - var active = null; - var disabled = []; - for (var i = 0; i < document.styleSheets.length; i++) { - var ss = document.styleSheets[i]; - var themename = ss.ownerNode.getAttribute("data-theme-name"); - if(themename === null) continue; // ignore non-theme stylesheets - // Find the active theme - if(themename === theme) active = ss; - else disabled.push(ss); - } - if(active !== null) { - active.disabled = false; - if(active.ownerNode.getAttribute("data-theme-primary") === null) { - document.getElementsByTagName('html')[0].className = "theme--" + theme; - } else { - document.getElementsByTagName('html')[0].className = ""; - } - disabled.forEach(function(ss){ - ss.disabled = true; - }); - } - - // Store the theme in localStorage - if(typeof(window.localStorage) !== "undefined") { - window.localStorage.setItem("documenter-theme", theme); - } else { - console.error("Browser does not support window.localStorage"); - } -} - // Theme picker setup -$(document).ready(function() { +$(document).ready(function () { // onchange callback - $('#documenter-themepicker').change(function themepick_callback(ev){ - var themename = $('#documenter-themepicker option:selected').attr('value'); - set_theme(themename); + $("#documenter-themepicker").change(function themepick_callback(ev) { + var themename = $("#documenter-themepicker option:selected").attr("value"); + if (themename === "auto") { + // set_theme(window.matchMedia('(prefers-color-scheme: dark)').matches ? 'dark' : 'light'); + window.localStorage.removeItem("documenter-theme"); + } else { + // set_theme(themename); + window.localStorage.setItem("documenter-theme", themename); + } + // We re-use the global function from themeswap.js to actually do the swapping. + set_theme_from_local_storage(); }); // Make sure that the themepicker displays the correct theme when the theme is retrieved // from localStorage - if(typeof(window.localStorage) !== "undefined") { - var theme = window.localStorage.getItem("documenter-theme"); - if(theme !== null) { - $('#documenter-themepicker option').each(function(i,e) { - e.selected = (e.value === theme); - }) - } else { - $('#documenter-themepicker option').each(function(i,e) { - e.selected = $("html").hasClass(`theme--${e.value}`); - }) + if (typeof window.localStorage !== "undefined") { + var theme = window.localStorage.getItem("documenter-theme"); + if (theme !== null) { + $("#documenter-themepicker option").each(function (i, e) { + e.selected = e.value === theme; + }); } } -}) +}); }) //////////////////////////////////////////////////////////////////////////////// require(['jquery'], function($) { // update the version selector with info from the siteinfo.js and ../versions.js files -$(document).ready(function() { +$(document).ready(function () { // If the version selector is disabled with DOCUMENTER_VERSION_SELECTOR_DISABLED in the // siteinfo.js file, we just return immediately and not display the version selector. - if (typeof DOCUMENTER_VERSION_SELECTOR_DISABLED === 'boolean' && DOCUMENTER_VERSION_SELECTOR_DISABLED) { + if ( + typeof DOCUMENTER_VERSION_SELECTOR_DISABLED === "boolean" && + DOCUMENTER_VERSION_SELECTOR_DISABLED + ) { return; } var version_selector = $("#documenter .docs-version-selector"); var version_selector_select = $("#documenter .docs-version-selector select"); - version_selector_select.change(function(x) { - target_href = version_selector_select.children("option:selected").get(0).value; + version_selector_select.change(function (x) { + target_href = version_selector_select + .children("option:selected") + .get(0).value; window.location.href = target_href; }); // add the current version to the selector based on siteinfo.js, but only if the selector is empty - if (typeof DOCUMENTER_CURRENT_VERSION !== 'undefined' && $('#version-selector > option').length == 0) { - var option = $(""); + if ( + typeof DOCUMENTER_CURRENT_VERSION !== "undefined" && + $("#version-selector > option").length == 0 + ) { + var option = $( + "" + ); version_selector_select.append(option); } - if (typeof DOC_VERSIONS !== 'undefined') { + if (typeof DOC_VERSIONS !== "undefined") { var existing_versions = version_selector_select.children("option"); - var existing_versions_texts = existing_versions.map(function(i,x){return x.text}); - DOC_VERSIONS.forEach(function(each) { - var version_url = documenterBaseURL + "/../" + each; + var existing_versions_texts = existing_versions.map(function (i, x) { + return x.text; + }); + DOC_VERSIONS.forEach(function (each) { + var version_url = documenterBaseURL + "/../" + each + "/"; var existing_id = $.inArray(each, existing_versions_texts); // if not already in the version selector, add it as a new option, // otherwise update the old option with the URL and enable it if (existing_id == -1) { - var option = $(""); + var option = $( + "" + ); version_selector_select.append(option); } else { var option = existing_versions[existing_id]; @@ -326,6 +884,6 @@ $(document).ready(function() { if (version_selector_select.children("option").length > 0) { version_selector.toggleClass("visible"); } -}) +}); }) diff --git a/dev/assets/search.js b/dev/assets/search.js deleted file mode 100644 index c133f741..00000000 --- a/dev/assets/search.js +++ /dev/null @@ -1,267 +0,0 @@ -// Generated by Documenter.jl -requirejs.config({ - paths: { - 'lunr': 'https://cdnjs.cloudflare.com/ajax/libs/lunr.js/2.3.9/lunr.min', - 'lodash': 'https://cdnjs.cloudflare.com/ajax/libs/lodash.js/4.17.21/lodash.min', - 'jquery': 'https://cdnjs.cloudflare.com/ajax/libs/jquery/3.6.0/jquery.min', - } -}); -//////////////////////////////////////////////////////////////////////////////// -require(['jquery', 'lunr', 'lodash'], function($, lunr, _) { - -$(document).ready(function() { - // parseUri 1.2.2 - // (c) Steven Levithan - // MIT License - function parseUri (str) { - var o = parseUri.options, - m = o.parser[o.strictMode ? "strict" : "loose"].exec(str), - uri = {}, - i = 14; - - while (i--) uri[o.key[i]] = m[i] || ""; - - uri[o.q.name] = {}; - uri[o.key[12]].replace(o.q.parser, function ($0, $1, $2) { - if ($1) uri[o.q.name][$1] = $2; - }); - - return uri; - }; - parseUri.options = { - strictMode: false, - key: ["source","protocol","authority","userInfo","user","password","host","port","relative","path","directory","file","query","anchor"], - q: { - name: "queryKey", - parser: /(?:^|&)([^&=]*)=?([^&]*)/g - }, - parser: { - strict: /^(?:([^:\/?#]+):)?(?:\/\/((?:(([^:@]*)(?::([^:@]*))?)?@)?([^:\/?#]*)(?::(\d*))?))?((((?:[^?#\/]*\/)*)([^?#]*))(?:\?([^#]*))?(?:#(.*))?)/, - loose: /^(?:(?![^:@]+:[^:@\/]*@)([^:\/?#.]+):)?(?:\/\/)?((?:(([^:@]*)(?::([^:@]*))?)?@)?([^:\/?#]*)(?::(\d*))?)(((\/(?:[^?#](?![^?#\/]*\.[^?#\/.]+(?:[?#]|$)))*\/?)?([^?#\/]*))(?:\?([^#]*))?(?:#(.*))?)/ - } - }; - - $("#search-form").submit(function(e) { - e.preventDefault() - }) - - // list below is the lunr 2.1.3 list minus the intersect with names(Base) - // (all, any, get, in, is, only, which) and (do, else, for, let, where, while, with) - // ideally we'd just filter the original list but it's not available as a variable - lunr.stopWordFilter = lunr.generateStopWordFilter([ - 'a', - 'able', - 'about', - 'across', - 'after', - 'almost', - 'also', - 'am', - 'among', - 'an', - 'and', - 'are', - 'as', - 'at', - 'be', - 'because', - 'been', - 'but', - 'by', - 'can', - 'cannot', - 'could', - 'dear', - 'did', - 'does', - 'either', - 'ever', - 'every', - 'from', - 'got', - 'had', - 'has', - 'have', - 'he', - 'her', - 'hers', - 'him', - 'his', - 'how', - 'however', - 'i', - 'if', - 'into', - 'it', - 'its', - 'just', - 'least', - 'like', - 'likely', - 'may', - 'me', - 'might', - 'most', - 'must', - 'my', - 'neither', - 'no', - 'nor', - 'not', - 'of', - 'off', - 'often', - 'on', - 'or', - 'other', - 'our', - 'own', - 'rather', - 'said', - 'say', - 'says', - 'she', - 'should', - 'since', - 'so', - 'some', - 'than', - 'that', - 'the', - 'their', - 'them', - 'then', - 'there', - 'these', - 'they', - 'this', - 'tis', - 'to', - 'too', - 'twas', - 'us', - 'wants', - 'was', - 'we', - 'were', - 'what', - 'when', - 'who', - 'whom', - 'why', - 'will', - 'would', - 'yet', - 'you', - 'your' - ]) - - // add . as a separator, because otherwise "title": "Documenter.Anchors.add!" - // would not find anything if searching for "add!", only for the entire qualification - lunr.tokenizer.separator = /[\s\-\.]+/ - - // custom trimmer that doesn't strip @ and !, which are used in julia macro and function names - lunr.trimmer = function (token) { - return token.update(function (s) { - return s.replace(/^[^a-zA-Z0-9@!]+/, '').replace(/[^a-zA-Z0-9@!]+$/, '') - }) - } - - lunr.Pipeline.registerFunction(lunr.stopWordFilter, 'juliaStopWordFilter') - lunr.Pipeline.registerFunction(lunr.trimmer, 'juliaTrimmer') - - var index = lunr(function () { - this.ref('location') - this.field('title',{boost: 100}) - this.field('text') - documenterSearchIndex['docs'].forEach(function(e) { - this.add(e) - }, this) - }) - var store = {} - - documenterSearchIndex['docs'].forEach(function(e) { - store[e.location] = {title: e.title, category: e.category, page: e.page} - }) - - $(function(){ - searchresults = $('#documenter-search-results'); - searchinfo = $('#documenter-search-info'); - searchbox = $('#documenter-search-query'); - searchform = $('.docs-search'); - sidebar = $('.docs-sidebar'); - function update_search(querystring) { - tokens = lunr.tokenizer(querystring) - results = index.query(function (q) { - tokens.forEach(function (t) { - q.term(t.toString(), { - fields: ["title"], - boost: 100, - usePipeline: true, - editDistance: 0, - wildcard: lunr.Query.wildcard.NONE - }) - q.term(t.toString(), { - fields: ["title"], - boost: 10, - usePipeline: true, - editDistance: 2, - wildcard: lunr.Query.wildcard.NONE - }) - q.term(t.toString(), { - fields: ["text"], - boost: 1, - usePipeline: true, - editDistance: 0, - wildcard: lunr.Query.wildcard.NONE - }) - }) - }) - searchinfo.text("Number of results: " + results.length) - searchresults.empty() - results.forEach(function(result) { - data = store[result.ref] - link = $(''+data.title+'') - link.attr('href', documenterBaseURL+'/'+result.ref) - if (data.category != "page"){ - cat = $('('+data.category+', '+data.page+')') - } else { - cat = $('('+data.category+')') - } - li = $('
  • ').append(link).append(" ").append(cat) - searchresults.append(li) - }) - } - - function update_search_box() { - querystring = searchbox.val() - update_search(querystring) - } - - searchbox.keyup(_.debounce(update_search_box, 250)) - searchbox.change(update_search_box) - - // Disable enter-key form submission for the searchbox on the search page - // and just re-run search rather than refresh the whole page. - searchform.keypress( - function(event){ - if (event.which == '13') { - if (sidebar.hasClass('visible')) { - sidebar.removeClass('visible'); - } - update_search_box(); - event.preventDefault(); - } - } - ); - - search_query_uri = parseUri(window.location).queryKey["q"] - if(search_query_uri !== undefined) { - search_query = decodeURIComponent(search_query_uri.replace(/\+/g, '%20')) - searchbox.val(search_query) - } - update_search_box(); - }) -}) - -}) diff --git a/dev/assets/themes/documenter-dark.css b/dev/assets/themes/documenter-dark.css index c94a294d..ec054ecc 100644 --- a/dev/assets/themes/documenter-dark.css +++ b/dev/assets/themes/documenter-dark.css @@ -1,7 +1,7 @@ -@keyframes spinAround{from{transform:rotate(0deg)}to{transform:rotate(359deg)}}html.theme--documenter-dark .tabs,html.theme--documenter-dark .pagination-previous,html.theme--documenter-dark .pagination-next,html.theme--documenter-dark .pagination-link,html.theme--documenter-dark .pagination-ellipsis,html.theme--documenter-dark .breadcrumb,html.theme--documenter-dark .file,html.theme--documenter-dark .button,.is-unselectable,html.theme--documenter-dark .modal-close,html.theme--documenter-dark .delete{-webkit-touch-callout:none;-webkit-user-select:none;-moz-user-select:none;-ms-user-select:none;user-select:none}html.theme--documenter-dark .navbar-link:not(.is-arrowless)::after,html.theme--documenter-dark .select:not(.is-multiple):not(.is-loading)::after{border:3px solid rgba(0,0,0,0);border-radius:2px;border-right:0;border-top:0;content:" 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kbd.button.is-outlined.is-loading.is-hovered::after,html.theme--documenter-dark .button.is-dark.is-outlined.is-loading:focus::after,html.theme--documenter-dark .content kbd.button.is-outlined.is-loading:focus::after,html.theme--documenter-dark .button.is-dark.is-outlined.is-loading.is-focused::after,html.theme--documenter-dark .content kbd.button.is-outlined.is-loading.is-focused::after{border-color:transparent transparent #ecf0f1 #ecf0f1 !important}html.theme--documenter-dark .button.is-dark.is-outlined[disabled],html.theme--documenter-dark .content kbd.button.is-outlined[disabled],fieldset[disabled] html.theme--documenter-dark .button.is-dark.is-outlined,fieldset[disabled] html.theme--documenter-dark .content kbd.button.is-outlined{background-color:transparent;border-color:#282f2f;box-shadow:none;color:#282f2f}html.theme--documenter-dark .button.is-dark.is-inverted.is-outlined,html.theme--documenter-dark .content 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figure:not(:first-child){margin-top:2em}html.theme--documenter-dark .content figure:not(:last-child){margin-bottom:2em}html.theme--documenter-dark .content figure img{display:inline-block}html.theme--documenter-dark .content figure figcaption{font-style:italic}html.theme--documenter-dark .content pre{-webkit-overflow-scrolling:touch;overflow-x:auto;padding:0;white-space:pre;word-wrap:normal}html.theme--documenter-dark .content sup,html.theme--documenter-dark .content sub{font-size:75%}html.theme--documenter-dark .content table{width:100%}html.theme--documenter-dark .content table td,html.theme--documenter-dark .content table th{border:1px solid #5e6d6f;border-width:0 0 1px;padding:0.5em 0.75em;vertical-align:top}html.theme--documenter-dark .content table th{color:#f2f2f2}html.theme--documenter-dark .content table th:not([align]){text-align:left}html.theme--documenter-dark .content table thead td,html.theme--documenter-dark .content table thead th{border-width:0 0 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.button.is-light.is-inverted.is-outlined.is-loading:focus::after,html.theme--documenter-dark .button.is-light.is-inverted.is-outlined.is-loading.is-focused::after{border-color:transparent transparent #ecf0f1 #ecf0f1 !important}html.theme--documenter-dark .button.is-light.is-inverted.is-outlined[disabled],fieldset[disabled] html.theme--documenter-dark .button.is-light.is-inverted.is-outlined{background-color:transparent;border-color:rgba(0,0,0,0.7);box-shadow:none;color:rgba(0,0,0,0.7)}html.theme--documenter-dark .button.is-dark,html.theme--documenter-dark .content kbd.button{background-color:#282f2f;border-color:transparent;color:#fff}html.theme--documenter-dark .button.is-dark:hover,html.theme--documenter-dark .content kbd.button:hover,html.theme--documenter-dark .button.is-dark.is-hovered,html.theme--documenter-dark .content kbd.button.is-hovered{background-color:#232829;border-color:transparent;color:#fff}html.theme--documenter-dark .button.is-dark:focus,html.theme--documenter-dark 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kbd.button.is-loading::after{border-color:transparent transparent #fff #fff !important}html.theme--documenter-dark .button.is-dark.is-outlined,html.theme--documenter-dark .content kbd.button.is-outlined{background-color:transparent;border-color:#282f2f;color:#282f2f}html.theme--documenter-dark .button.is-dark.is-outlined:hover,html.theme--documenter-dark .content kbd.button.is-outlined:hover,html.theme--documenter-dark .button.is-dark.is-outlined.is-hovered,html.theme--documenter-dark .content kbd.button.is-outlined.is-hovered,html.theme--documenter-dark .button.is-dark.is-outlined:focus,html.theme--documenter-dark .content kbd.button.is-outlined:focus,html.theme--documenter-dark .button.is-dark.is-outlined.is-focused,html.theme--documenter-dark .content kbd.button.is-outlined.is-focused{background-color:#282f2f;border-color:#282f2f;color:#fff}html.theme--documenter-dark .button.is-dark.is-outlined.is-loading::after,html.theme--documenter-dark .content 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html.theme--documenter-dark .button.is-dark.is-outlined,fieldset[disabled] html.theme--documenter-dark .content kbd.button.is-outlined{background-color:transparent;border-color:#282f2f;box-shadow:none;color:#282f2f}html.theme--documenter-dark .button.is-dark.is-inverted.is-outlined,html.theme--documenter-dark .content kbd.button.is-inverted.is-outlined{background-color:transparent;border-color:#fff;color:#fff}html.theme--documenter-dark .button.is-dark.is-inverted.is-outlined:hover,html.theme--documenter-dark .content kbd.button.is-inverted.is-outlined:hover,html.theme--documenter-dark .button.is-dark.is-inverted.is-outlined.is-hovered,html.theme--documenter-dark .content kbd.button.is-inverted.is-outlined.is-hovered,html.theme--documenter-dark .button.is-dark.is-inverted.is-outlined:focus,html.theme--documenter-dark .content kbd.button.is-inverted.is-outlined:focus,html.theme--documenter-dark .button.is-dark.is-inverted.is-outlined.is-focused,html.theme--documenter-dark .content kbd.button.is-inverted.is-outlined.is-focused{background-color:#fff;color:#282f2f}html.theme--documenter-dark .button.is-dark.is-inverted.is-outlined.is-loading:hover::after,html.theme--documenter-dark .content kbd.button.is-inverted.is-outlined.is-loading:hover::after,html.theme--documenter-dark .button.is-dark.is-inverted.is-outlined.is-loading.is-hovered::after,html.theme--documenter-dark .content kbd.button.is-inverted.is-outlined.is-loading.is-hovered::after,html.theme--documenter-dark .button.is-dark.is-inverted.is-outlined.is-loading:focus::after,html.theme--documenter-dark .content kbd.button.is-inverted.is-outlined.is-loading:focus::after,html.theme--documenter-dark .button.is-dark.is-inverted.is-outlined.is-loading.is-focused::after,html.theme--documenter-dark .content kbd.button.is-inverted.is-outlined.is-loading.is-focused::after{border-color:transparent transparent #282f2f #282f2f !important}html.theme--documenter-dark 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.docstring>section>a.button.is-outlined.is-hovered.docs-sourcelink,html.theme--documenter-dark .button.is-primary.is-outlined:focus,html.theme--documenter-dark .docstring>section>a.button.is-outlined.docs-sourcelink:focus,html.theme--documenter-dark .button.is-primary.is-outlined.is-focused,html.theme--documenter-dark .docstring>section>a.button.is-outlined.is-focused.docs-sourcelink{background-color:#375a7f;border-color:#375a7f;color:#fff}html.theme--documenter-dark .button.is-primary.is-outlined.is-loading::after,html.theme--documenter-dark .docstring>section>a.button.is-outlined.is-loading.docs-sourcelink::after{border-color:transparent transparent #375a7f #375a7f !important}html.theme--documenter-dark .button.is-primary.is-outlined.is-loading:hover::after,html.theme--documenter-dark .docstring>section>a.button.is-outlined.is-loading.docs-sourcelink:hover::after,html.theme--documenter-dark .button.is-primary.is-outlined.is-loading.is-hovered::after,html.theme--documenter-dark 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.button.is-warning.is-active{background-color:#946e00;border-color:transparent;color:#fff}html.theme--documenter-dark .button.is-warning[disabled],fieldset[disabled] html.theme--documenter-dark .button.is-warning{background-color:#ad8100;border-color:#ad8100;box-shadow:none}html.theme--documenter-dark .button.is-warning.is-inverted{background-color:#fff;color:#ad8100}html.theme--documenter-dark .button.is-warning.is-inverted:hover,html.theme--documenter-dark .button.is-warning.is-inverted.is-hovered{background-color:#f2f2f2}html.theme--documenter-dark .button.is-warning.is-inverted[disabled],fieldset[disabled] html.theme--documenter-dark .button.is-warning.is-inverted{background-color:#fff;border-color:transparent;box-shadow:none;color:#ad8100}html.theme--documenter-dark .button.is-warning.is-loading::after{border-color:transparent transparent #fff #fff !important}html.theme--documenter-dark 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.button.is-danger.is-light{background-color:#fdeeec;color:#ec311d}html.theme--documenter-dark .button.is-danger.is-light:hover,html.theme--documenter-dark .button.is-danger.is-light.is-hovered{background-color:#fce3e0;border-color:transparent;color:#ec311d}html.theme--documenter-dark .button.is-danger.is-light:active,html.theme--documenter-dark .button.is-danger.is-light.is-active{background-color:#fcd8d5;border-color:transparent;color:#ec311d}html.theme--documenter-dark .button.is-small,html.theme--documenter-dark #documenter .docs-sidebar form.docs-search>input.button{font-size:.75rem}html.theme--documenter-dark .button.is-small:not(.is-rounded),html.theme--documenter-dark #documenter .docs-sidebar form.docs-search>input.button:not(.is-rounded){border-radius:3px}html.theme--documenter-dark .button.is-normal{font-size:1rem}html.theme--documenter-dark .button.is-medium{font-size:1.25rem}html.theme--documenter-dark .button.is-large{font-size:1.5rem}html.theme--documenter-dark .button[disabled],fieldset[disabled] html.theme--documenter-dark .button{background-color:#8c9b9d;border-color:#5e6d6f;box-shadow:none;opacity:.5}html.theme--documenter-dark .button.is-fullwidth{display:flex;width:100%}html.theme--documenter-dark .button.is-loading{color:transparent !important;pointer-events:none}html.theme--documenter-dark .button.is-loading::after{position:absolute;left:calc(50% - (1em * 0.5));top:calc(50% - (1em * 0.5));position:absolute !important}html.theme--documenter-dark .button.is-static{background-color:#282f2f;border-color:#5e6d6f;color:#dbdee0;box-shadow:none;pointer-events:none}html.theme--documenter-dark .button.is-rounded,html.theme--documenter-dark #documenter .docs-sidebar form.docs-search>input.button{border-radius:9999px;padding-left:calc(1em + 0.25em);padding-right:calc(1em + 0.25em)}html.theme--documenter-dark .buttons{align-items:center;display:flex;flex-wrap:wrap;justify-content:flex-start}html.theme--documenter-dark .buttons .button{margin-bottom:0.5rem}html.theme--documenter-dark .buttons .button:not(:last-child):not(.is-fullwidth){margin-right:.5rem}html.theme--documenter-dark .buttons:last-child{margin-bottom:-0.5rem}html.theme--documenter-dark .buttons:not(:last-child){margin-bottom:1rem}html.theme--documenter-dark .buttons.are-small .button:not(.is-normal):not(.is-medium):not(.is-large){font-size:.75rem}html.theme--documenter-dark .buttons.are-small .button:not(.is-normal):not(.is-medium):not(.is-large):not(.is-rounded){border-radius:3px}html.theme--documenter-dark .buttons.are-medium .button:not(.is-small):not(.is-normal):not(.is-large){font-size:1.25rem}html.theme--documenter-dark .buttons.are-large .button:not(.is-small):not(.is-normal):not(.is-medium){font-size:1.5rem}html.theme--documenter-dark .buttons.has-addons .button:not(:first-child){border-bottom-left-radius:0;border-top-left-radius:0}html.theme--documenter-dark .buttons.has-addons 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#documenter .docs-sidebar ul.docs-menu ul.internal{margin:0 0.5rem 0.5rem;border-top:1px solid #5e6d6f}html.theme--documenter-dark #documenter .docs-sidebar ul.docs-menu ul.internal li{font-size:.85rem;border-left:none;margin-left:0;margin-top:0.5rem}html.theme--documenter-dark #documenter .docs-sidebar ul.docs-menu ul.internal .tocitem{width:100%;padding:0}html.theme--documenter-dark #documenter .docs-sidebar ul.docs-menu ul.internal .tocitem::before{content:"⚬";margin-right:0.4em}html.theme--documenter-dark #documenter .docs-sidebar form.docs-search{margin:auto;margin-top:0.5rem;margin-bottom:0.5rem}html.theme--documenter-dark #documenter .docs-sidebar form.docs-search>input{width:14.4rem}html.theme--documenter-dark #documenter .docs-sidebar #documenter-search-query{color:#868c98;width:14.4rem;box-shadow:inset 0 1px 2px rgba(10,10,10,0.1)}@media screen and (min-width: 1056px){html.theme--documenter-dark #documenter .docs-sidebar 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Theme: Default Description: Original highlight.js style Author: (c) Ivan Sagalaev @@ -6,4 +6,4 @@ Website: https://highlightjs.org/ License: see project LICENSE Touched: 2021 -*/pre code.hljs{display:block;overflow-x:auto}code.hljs{padding:3px 5px}.hljs{background:#F0F0F0;color:#444}.hljs-comment{color:#888888}.hljs-tag,.hljs-punctuation{color:#444a}.hljs-tag .hljs-name,.hljs-tag .hljs-attr{color:#444}.hljs-keyword,.hljs-attribute,.hljs-selector-tag,.hljs-meta .hljs-keyword,.hljs-doctag,.hljs-name{font-weight:bold}.hljs-type,.hljs-string,.hljs-number,.hljs-selector-id,.hljs-selector-class,.hljs-quote,.hljs-template-tag,.hljs-deletion{color:#880000}.hljs-title,.hljs-section{color:#880000;font-weight:bold}.hljs-regexp,.hljs-symbol,.hljs-variable,.hljs-template-variable,.hljs-link,.hljs-selector-attr,.hljs-operator,.hljs-selector-pseudo{color:#BC6060}.hljs-literal{color:#78A960}.hljs-built_in,.hljs-bullet,.hljs-code,.hljs-addition{color:#397300}.hljs-meta{color:#1f7199}.hljs-meta .hljs-string{color:#4d99bf}.hljs-emphasis{font-style:italic}.hljs-strong{font-weight:bold} +*/pre code.hljs{display:block;overflow-x:auto;padding:1em}code.hljs{padding:3px 5px}.hljs{background:#F3F3F3;color:#444}.hljs-comment{color:#697070}.hljs-tag,.hljs-punctuation{color:#444a}.hljs-tag .hljs-name,.hljs-tag .hljs-attr{color:#444}.hljs-keyword,.hljs-attribute,.hljs-selector-tag,.hljs-meta .hljs-keyword,.hljs-doctag,.hljs-name{font-weight:bold}.hljs-type,.hljs-string,.hljs-number,.hljs-selector-id,.hljs-selector-class,.hljs-quote,.hljs-template-tag,.hljs-deletion{color:#880000}.hljs-title,.hljs-section{color:#880000;font-weight:bold}.hljs-regexp,.hljs-symbol,.hljs-variable,.hljs-template-variable,.hljs-link,.hljs-selector-attr,.hljs-operator,.hljs-selector-pseudo{color:#ab5656}.hljs-literal{color:#695}.hljs-built_in,.hljs-bullet,.hljs-code,.hljs-addition{color:#397300}.hljs-meta{color:#1f7199}.hljs-meta .hljs-string{color:#38a}.hljs-emphasis{font-style:italic}.hljs-strong{font-weight:bold}.gap-4{gap:1rem} diff --git a/dev/assets/themeswap.js b/dev/assets/themeswap.js index c58e993e..9f5eebe6 100644 --- a/dev/assets/themeswap.js +++ b/dev/assets/themeswap.js @@ -1,20 +1,17 @@ // Small function to quickly swap out themes. Gets put into the tag.. function set_theme_from_local_storage() { - // Intialize the theme to null, which means default + // Initialize the theme to null, which means default var theme = null; // If the browser supports the localstorage and is not disabled then try to get the // documenter theme - if(window.localStorage != null) { + if (window.localStorage != null) { // Get the user-picked theme from localStorage. May be `null`, which means the default // theme. - theme = window.localStorage.getItem("documenter-theme"); + theme = window.localStorage.getItem("documenter-theme"); } - // Check if the browser supports user color preference - var darkPreference = false; // Check if the users preference is for dark color scheme - if(window.matchMedia('(prefers-color-scheme: dark)').matches === true) { - darkPreference = true; - } + var darkPreference = + window.matchMedia("(prefers-color-scheme: dark)").matches === true; // Initialize a few variables for the loop: // // - active: will contain the index of the theme that should be active. Note that there @@ -24,43 +21,64 @@ function set_theme_from_local_storage() { // // - disabled: style sheets that should be disabled (i.e. all the theme style sheets // that are not the currently active theme) - var active = null; var disabled = []; var darkTheme = null; + var active = null; + var disabled = []; + var primaryLightTheme = null; + var primaryDarkTheme = null; for (var i = 0; i < document.styleSheets.length; i++) { var ss = document.styleSheets[i]; // The tag of each style sheet is expected to have a data-theme-name attribute // which must contain the name of the theme. The names in localStorage much match this. var themename = ss.ownerNode.getAttribute("data-theme-name"); // attribute not set => non-theme stylesheet => ignore - if(themename === null) continue; + if (themename === null) continue; // To distinguish the default (primary) theme, it needs to have the data-theme-primary // attribute set. - var isprimary = (ss.ownerNode.getAttribute("data-theme-primary") !== null); - // Check if the theme is primary dark theme - var isDarkTheme = (ss.ownerNode.getAttribute("data-theme-primary-dark") !== null); - // If ss is for dark theme then set the value of darkTheme to the name of the theme - if(isDarkTheme) darkTheme = themename; + if (ss.ownerNode.getAttribute("data-theme-primary") !== null) { + primaryLightTheme = themename; + } + // Check if the theme is primary dark theme so that we could store its name in darkTheme + if (ss.ownerNode.getAttribute("data-theme-primary-dark") !== null) { + primaryDarkTheme = themename; + } // If we find a matching theme (and it's not the default), we'll set active to non-null - if(themename === theme) active = i; + if (themename === theme) active = i; // Store the style sheets of inactive themes so that we could disable them - if(themename !== theme) disabled.push(ss); + if (themename !== theme) disabled.push(ss); } - if(active !== null) { + var activeTheme = null; + if (active !== null) { // If we did find an active theme, we'll (1) add the theme--$(theme) class to - document.getElementsByTagName('html')[0].className = "theme--" + theme; - // and (2) disable all the other theme stylesheets - disabled.forEach(function(ss){ - ss.disabled = true; - }); + document.getElementsByTagName("html")[0].className = "theme--" + theme; + activeTheme = theme; + } else { + // If we did _not_ find an active theme, then we need to fall back to the primary theme + // which can either be dark or light, depending on the user's OS preference. + var activeTheme = darkPreference ? primaryDarkTheme : primaryLightTheme; + // In case it somehow happens that the relevant primary theme was not found in the + // preceding loop, we abort without doing anything. + if (activeTheme === null) { + console.error("Unable to determine primary theme."); + return; + } + // When switching to the primary light theme, then we must not have a class name + // for the tag. That's only for non-primary or the primary dark theme. + if (darkPreference) { + document.getElementsByTagName("html")[0].className = + "theme--" + activeTheme; + } else { + document.getElementsByTagName("html")[0].className = ""; + } } - else if(darkTheme !== null && darkPreference === true) { - // If we did find an active theme, we'll (1) add the theme--$(theme) class to - document.getElementsByTagName('html')[0].className = "theme--" + darkTheme; - // and (2) disable all the other theme stylesheets - disabled.forEach(function(ss){ - if (ss.ownerNode.getAttribute("data-theme-name") !== darkTheme) { - ss.disabled = true; - } - }); + for (var i = 0; i < document.styleSheets.length; i++) { + var ss = document.styleSheets[i]; + // The tag of each style sheet is expected to have a data-theme-name attribute + // which must contain the name of the theme. The names in localStorage much match this. + var themename = ss.ownerNode.getAttribute("data-theme-name"); + // attribute not set => non-theme stylesheet => ignore + if (themename === null) continue; + // we'll disable all the stylesheets, except for the active one + ss.disabled = !(themename == activeTheme); } } set_theme_from_local_storage(); diff --git a/dev/assets/warner.js b/dev/assets/warner.js index 5531c885..3f6f5d00 100644 --- a/dev/assets/warner.js +++ b/dev/assets/warner.js @@ -1,49 +1,52 @@ -function maybeAddWarning () { - // DOCUMENTER_NEWEST is defined in versions.js, DOCUMENTER_CURRENT_VERSION and DOCUMENTER_STABLE - // in siteinfo.js. - // If either of these are undefined something went horribly wrong, so we abort. - if ( - window.DOCUMENTER_NEWEST === undefined || - window.DOCUMENTER_CURRENT_VERSION === undefined || - window.DOCUMENTER_STABLE === undefined - ) { - return - }; +function maybeAddWarning() { + // DOCUMENTER_NEWEST is defined in versions.js, DOCUMENTER_CURRENT_VERSION and DOCUMENTER_STABLE + // in siteinfo.js. + // If either of these are undefined something went horribly wrong, so we abort. + if ( + window.DOCUMENTER_NEWEST === undefined || + window.DOCUMENTER_CURRENT_VERSION === undefined || + window.DOCUMENTER_STABLE === undefined + ) { + return; + } - // Current version is not a version number, so we can't tell if it's the newest version. Abort. - if (!/v(\d+\.)*\d+/.test(window.DOCUMENTER_CURRENT_VERSION)) { - return - }; + // Current version is not a version number, so we can't tell if it's the newest version. Abort. + if (!/v(\d+\.)*\d+/.test(window.DOCUMENTER_CURRENT_VERSION)) { + return; + } - // Current version is newest version, so no need to add a warning. - if (window.DOCUMENTER_NEWEST === window.DOCUMENTER_CURRENT_VERSION) { - return - }; + // Current version is newest version, so no need to add a warning. + if (window.DOCUMENTER_NEWEST === window.DOCUMENTER_CURRENT_VERSION) { + return; + } - // Add a noindex meta tag (unless one exists) so that search engines don't index this version of the docs. - if (document.body.querySelector('meta[name="robots"]') === null) { - const meta = document.createElement('meta'); - meta.name = 'robots'; - meta.content = 'noindex'; + // Add a noindex meta tag (unless one exists) so that search engines don't index this version of the docs. + if (document.body.querySelector('meta[name="robots"]') === null) { + const meta = document.createElement("meta"); + meta.name = "robots"; + meta.content = "noindex"; - document.getElementsByTagName('head')[0].appendChild(meta); - }; + document.getElementsByTagName("head")[0].appendChild(meta); + } - const div = document.createElement('div'); - div.classList.add('outdated-warning-overlay'); - const closer = document.createElement('button'); - closer.classList.add('outdated-warning-closer', 'delete'); - closer.addEventListener('click', function () { - document.body.removeChild(div); - }); - const href = window.documenterBaseURL + '/../' + window.DOCUMENTER_STABLE; - div.innerHTML = 'This documentation is not for the latest stable release, but for either the development version or an older release.
    Click here to go to the documentation for the latest stable release.'; - div.appendChild(closer); - document.body.appendChild(div); -}; + const div = document.createElement("div"); + div.classList.add("outdated-warning-overlay"); + const closer = document.createElement("button"); + closer.classList.add("outdated-warning-closer", "delete"); + closer.addEventListener("click", function () { + document.body.removeChild(div); + }); + const href = window.documenterBaseURL + "/../" + window.DOCUMENTER_STABLE; + div.innerHTML = + 'This documentation is not for the latest stable release, but for either the development version or an older release.
    Click here to go to the documentation for the latest stable release.'; + div.appendChild(closer); + document.body.appendChild(div); +} -if (document.readyState === 'loading') { - document.addEventListener('DOMContentLoaded', maybeAddWarning); +if (document.readyState === "loading") { + document.addEventListener("DOMContentLoaded", maybeAddWarning); } else { - maybeAddWarning(); -}; + maybeAddWarning(); +} diff --git a/dev/bigdata/0414cb23.svg b/dev/bigdata/0414cb23.svg new file mode 100644 index 00000000..45372c87 --- /dev/null +++ b/dev/bigdata/0414cb23.svg @@ -0,0 +1,188 @@ + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + diff --git a/dev/bigdata/index.html b/dev/bigdata/index.html index ec452329..717d23fe 100644 --- a/dev/bigdata/index.html +++ b/dev/bigdata/index.html @@ -1,9 +1,9 @@ -Big Data · OnlineStats Documentation
    Edit on GitHub

    Big Data

    OnlineStats + CSV

    The CSV package offers a very memory-efficient way of iterating through the rows of a (possibly larger-than-memory) CSV file.

    Example

    Here is a toy example (Iris dataset) of how to iterate through the rows of a CSV file one-by-one and calculate histograms grouped by another variable.

    using OnlineStats, CSV, Plots
+
    Big Data
    OnlineStats + CSV
    The CSV package offers a very memory-efficient way of iterating through the rows of a (possibly larger-than-memory) CSV file.
    Example
    Here is a toy example (Iris dataset) of how to iterate through the rows of a CSV file one-by-one and calculate histograms grouped by another variable.
    using OnlineStats, CSV, Plots
 
 url = "https://gist.githubusercontent.com/joshday/df7bdaa1d58b398592e7656395de6335/raw/5a1c83f498f8ca7e25ff2372340e44b3389be9b1/iris.csv"
 
@@ -15,195 +15,7 @@
 
 fit!(o, itr)
 
-plot(o, layout=(3,1))
    
-
-
-  
-    
-  
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    Threaded Parallelism
    The ThreadsX package offers multithreaded implementations of many functions in Base and supports OnlineStats via ThreadsX.reduce(::OnlineStat, data).
    Distributed Parallelism
    OnlineStats can be merged together to facilitate Embarassingly parallel computations.
    Note
    In general, fit! is a cheaper operation than merge!.
    Warn
    Not every OnlineStat can be merged.  In these cases, OnlineStats either uses an approximation or provides a warning that no merging occurred.
    Examples
    Simplified (Not Actually in Parallel)
    y1 = randn(10_000)
+plot(o, layout=(3,1))
    Example block output
    Threaded Parallelism
    The ThreadsX package offers multithreaded implementations of many functions in Base and supports OnlineStats via ThreadsX.reduce(::OnlineStat, data).
    Distributed Parallelism
    OnlineStats can be merged together to facilitate Embarassingly parallel computations.
    Note
    In general, fit! is a cheaper operation than merge!.
    Warn
    Not every OnlineStat can be merged.  In these cases, OnlineStats either uses an approximation or provides a warning that no merging occurred.
    Examples
    Simplified (Not Actually in Parallel)
    y1 = randn(10_000)
 y2 = randn(10_000)
 y3 = randn(10_000)
 
@@ -223,4 +35,4 @@ 
    
+end
    diff --git a/dev/collections/index.html b/dev/collections/index.html index c78ac086..48e668de 100644 --- a/dev/collections/index.html +++ b/dev/collections/index.html @@ -1,20 +1,20 @@ -Collections of Stats · OnlineStats Documentation
    Edit on GitHub

    Collections of Stats

    There are a few special OnlineStats that group together other OnlineStats: Series and Group.

    Series

    A Series tracks stats that should be applied to the same data stream.

    y = rand(1000)
+
    Collections of Stats
    There are a few special OnlineStats that group together other OnlineStats: Series and Group.
    Series
    A Series tracks stats that should be applied to the same data stream.
    y = rand(1000)
 
 s = Series(Mean(), Variance())
 
 fit!(s, y)
    Series
-├─ Mean: n=1_000 | value=0.508948
-└─ Variance: n=1_000 | value=0.0805292
+├─ Mean: n=1_000 | value=0.504287
+└─ Variance: n=1_000 | value=0.0782128
 
    Group
    A Group tracks stats that should be applied to different data streams.
    g = Group(Mean(), CountMap(Bool))
 
 itr = zip(randn(100), rand(Bool, 100))
 
 fit!(g, itr)
    Group
-├─ Mean: n=100 | value=-0.0299302
-└─ CountMap: n=100 | value=OrderedDict{Bool, Int64}(1=>47, 0=>53)
-
    
+├─ Mean: n=100 | value=-0.0123374
+└─ CountMap: n=100 | value=OrderedDict{Bool, Int64}(0=>51, 1=>49)
+
    diff --git a/dev/dataviz/1318d8d0.svg b/dev/dataviz/1318d8d0.svg new file mode 100644 index 00000000..074ac12c --- /dev/null +++ b/dev/dataviz/1318d8d0.svg @@ -0,0 +1,1872 @@ + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + 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-1,16318 +1,73 @@ -Data Visualization · OnlineStats Documentation
    Edit on GitHub

    Data Visualization

    Note

    Each of the following examples plots one million data points, but can scale to infinitely many observations, since only a summary (OnlineStat) of the data is plotted.

    Partitions

    The Partition type summarizes sections of a data stream using any OnlineStat, and is therefore extremely useful in visualizing huge datasets, as summaries are plotted rather than every single observation.

    Continuous Data

    y = cumsum(randn(10^6)) + 100randn(10^6)
+
    Data Visualization
    Note
    Each of the following examples plots one million data points, but can scale to infinitely many observations, since only a summary (OnlineStat) of the data is plotted.
    Partitions
    The Partition type summarizes sections of a data stream using any OnlineStat, and is therefore extremely useful in visualizing huge datasets, as summaries are plotted rather than every single observation.
    Continuous Data
    y = cumsum(randn(10^6)) + 100randn(10^6)
 
 o = Partition(KHist(10))
 
 fit!(o, y)
 
-plot(o)
    
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    o = Partition(Series(Mean(), Extrema()))
+plot(o)
    Example block output
    o = Partition(Series(Mean(), Extrema()))
 
 fit!(o, y)
 
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    Categorical Data
    y = rand(["a", "a", "b", "c"], 10^6)
+plot(o)
    Example block output
    Categorical Data
    y = rand(["a", "a", "b", "c"], 10^6)
 
 o = Partition(CountMap(String), 75)
 
 fit!(o, y)
 
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    Indexed Partitions
    The Partition type can only track the number of observations in the x-axis.  If you wish to plot one variable against another, you can use an IndexedPartition.
    x = randn(10^6)
+plot(o)
    Example block output
    Indexed Partitions
    The Partition type can only track the number of observations in the x-axis.  If you wish to plot one variable against another, you can use an IndexedPartition.
    x = randn(10^6)
 y = x + randn(10^6)
 
 o = fit!(IndexedPartition(Float64, KHist(40), 40), zip(x, y))
 
-plot(o)
    
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    x = rand(10^6)
+plot(o)
    Example block output
    x = rand(10^6)
 y = rand(1:5, 10^6)
 
 o = fit!(IndexedPartition(Float64, CountMap(Int)), zip(x,y))
 
-plot(o, xlab = "X", ylab = "Y")
    
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    Due to a limitation with Plots.jl, Date and DateTime will sometimes be converted to their Dates.value when plotted.  To get human-readable tick labels, you can use the xformatter keyword argument to plot.
    using Dates
+plot(o, xlab = "X", ylab = "Y")
    Example block output
    Due to a limitation with Plots.jl, Date and DateTime will sometimes be converted to their Dates.value when plotted.  To get human-readable tick labels, you can use the xformatter keyword argument to plot.
    using Dates
 
 x = rand(Date(2019):Day(1):Date(2020), 10^6)
 y = Dates.value.(x) .+ 30randn(10^6)
 
 o = fit!(IndexedPartition(Date, KHist(20)), zip(x,y))
 
-plot(o, xformatter = x -> string(Date(Dates.UTInstant(Day(x)))))
    
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    K-Indexed Partitions
    A KIndexedPartition is simlar to an IndexedPartition, but uses a different method of binning the x variable (centroids vs. intervals), similar to that of KHist.
    For the sake of performance, you must provide a function that creates the OnlineStat you wish to calculate for the y variable.
    x = randn(10^6)
+plot(o, xformatter = x -> string(Date(Dates.UTInstant(Day(x)))))
    Example block output
    K-Indexed Partitions
    A KIndexedPartition is simlar to an IndexedPartition, but uses a different method of binning the x variable (centroids vs. intervals), similar to that of KHist.
    For the sake of performance, you must provide a function that creates the OnlineStat you wish to calculate for the y variable.
    x = randn(10^6)
 y = x + randn(10^6)
 
 o = fit!(KIndexedPartition(Float64, () -> KHist(20)), zip(x, y))
 
-plot(o)
    
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    s = fit!(Series(KHist(25), Hist(-5:.2:5), ExpandingHist(100)), randn(10^6))
-plot(s, link = :x, label = ["KHist" "Hist" "ExpandingHist"])
    
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    Average Shifted Histograms (ASH)
    • ASH is a semi-parametric density estimation method that is similar to Kernel Density Estimation, but uses a fine partition histogram instead of individual observations to perform the smoothing.
    o = fit!(Ash(ExpandingHist(1000), 5), randn(10^6))
-plot(o)
    
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    Approximate CDF
    o = fit!(OrderStats(1000), randn(10^6))
+plot(o)
    Example block output
    Histograms
    s = fit!(Series(KHist(25), Hist(-5:.2:5), ExpandingHist(100)), randn(10^6))
+plot(s, link = :x, label = ["KHist" "Hist" "ExpandingHist"])
    Example block output
    Average Shifted Histograms (ASH)
    • ASH is a semi-parametric density estimation method that is similar to Kernel Density Estimation, but uses a fine partition histogram instead of individual observations to perform the smoothing.
    o = fit!(Ash(ExpandingHist(1000), 5), randn(10^6))
+plot(o)
    Example block output
    Approximate CDF
    o = fit!(OrderStats(1000), randn(10^6))
 
-plot(o)
    
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    Mosaic Plots
    The Mosaic type allows you to plot the relationship between two categorical variables. It is typically more useful than a bar plot, as class probabilities are given by the horizontal widths.
    using RDatasets
+plot(o)
    Example block output
    Mosaic Plots
    The Mosaic type allows you to plot the relationship between two categorical variables. It is typically more useful than a bar plot, as class probabilities are given by the horizontal widths.
    using RDatasets
 t = dataset("ggplot2", "diamonds")
 
 o = Mosaic(eltype(t.Cut), eltype(t.Color))
 
 fit!(o, zip(t.Cut, t.Color))
 
-plot(o, legendtitle="Color", xlabel="Cut")
    
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    HeatMap
    o = HeatMap(-5:.1:5, -0:.1:10)
+plot(o, legendtitle="Color", xlabel="Cut")
    Example block output
    HeatMap
    o = HeatMap(-5:.1:5, -0:.1:10)
 
 x, y = randn(10^6), 5 .+ randn(10^6)
 
 fit!(o, zip(x, y))
 
-plot(o)
    
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    plot(o, marginals=false, legend=true)
    
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    Traces
    A Trace will take snapshots of an OnlineStat as it is fitted, allowing you view how the value changed as observations were added.  This can be useful for identifying concept drift or finding optimal hyperparameters for stochastic approximation methods like StatLearn.
    y = range(1, 20, length=10^6) .* randn(10^6)
+plot(o)
    Example block output
    plot(o, marginals=false, legend=true)
    Example block output
    Traces
    A Trace will take snapshots of an OnlineStat as it is fitted, allowing you view how the value changed as observations were added.  This can be useful for identifying concept drift or finding optimal hyperparameters for stochastic approximation methods like StatLearn.
    y = range(1, 20, length=10^6) .* randn(10^6)
 
 o = Trace(Extrema())
 
 fit!(o, y)
 
-plot(o)
    
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    Naive Bayes Classifier
    The NBClassifier type stores conditional histograms of the predictor variables, allowing you to plot approximate "group by" distributions:
    # make data
+plot(o)
    Example block output
    Naive Bayes Classifier
    The NBClassifier type stores conditional histograms of the predictor variables, allowing you to plot approximate "group by" distributions:
    # make data
 x = randn(10^6, 5)
 y = x * [1,3,5,7,9] .> 0
 
 o = NBClassifier(5, Bool)  # 5 predictors with Boolean categories
 fit!(o, zip(eachrow(x), y))
-plot(o)
    
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+plot(o)
    Example block output
    diff --git a/dev/demos/index.html b/dev/demos/index.html index aac8cc58..2f9d167c 100644 --- a/dev/demos/index.html +++ b/dev/demos/index.html @@ -1,6 +1,6 @@ -Demos · OnlineStats Documentation
    Edit on GitHub
    +
    diff --git a/dev/howfitworks/index.html b/dev/howfitworks/index.html index 7553cbc7..ff3c5090 100644 --- a/dev/howfitworks/index.html +++ b/dev/howfitworks/index.html @@ -1,14 +1,14 @@ -Details of Updating (fit!) · OnlineStats Documentation
    Edit on GitHub

    Details of Updating (fit!)

    Core Principles

    • Stats are subtypes of OnlineStat{T} where T is the type of a single observation.
      • E.g. Mean <: OnlineStat{Number}
    • fit!(o::OnlineStat{T}, data::T)
      • Update o with the single observation data.
    • fit!(o::OnlineStat{T}, data::S)
      • Iterate through data and fit! each item.

    Why is Fitting Based on Iteration?

    Reason 1: OnlineStats doesn't make assumptions on the shape of your data

    Consider CovMatrix, for which a single observation is an AbstractVector, Tuple, or NamedTuple. If I try to fit! it with a Matrix, it's ambiguous whether I want rows or columns of the matrix to be treated as individual observations.

    Note

    See eachrow and eachcol (after typing using LinearAlgebra).

    x = randn(1000, 2)
+
    Details of Updating (fit!)
    Core Principles
    • Stats are subtypes of OnlineStat{T} where T is the type of a single observation.
      • E.g. Mean <: OnlineStat{Number}
    • fit!(o::OnlineStat{T}, data::T)
      • Update o with the single observation data.
    • fit!(o::OnlineStat{T}, data::S)
      • Iterate through data and fit! each item.
    Why is Fitting Based on Iteration?
    Reason 1: OnlineStats doesn't make assumptions on the shape of your data
    Consider CovMatrix, for which a single observation is an AbstractVector, Tuple, or NamedTuple. If I try to fit! it with a Matrix, it's ambiguous whether I want rows or columns of the matrix to be treated as individual observations.
    Note
    See eachrow and eachcol (after typing using LinearAlgebra).
    x = randn(1000, 2)
 
 fit!(CovMatrix(), eachrow(x))
 
-fit!(CovMatrix(), eachcol(x'))
    CovMatrix: n=1_000 | value=[0.989115 -0.0513987; -0.0513987 1.08399]
    Reason 2: OnlineStats works out-of-the-box with many data structures
    Tabular data structures such as those in JuliaDB iterate over named tuples of rows, so things like this just work:
    using JuliaDB
+fit!(CovMatrix(), eachcol(x'))
    CovMatrix: n=1_000 | value=[0.989115 -0.0513987; -0.0513987 1.08399]
    Reason 2: OnlineStats works out-of-the-box with many data structures
    Tabular data structures such as those in JuliaDB iterate over named tuples of rows, so things like this just work:
    using JuliaDB
 
 t = table(randn(100), randn(100))
 
-fit!(2Mean(), t)
    A Common Error
    Consider the following example:
    julia> fit!(Mean(), "asdf")ERROR: The input for Mean is Number.  Found Char.
    This causes an error because:
    1. "asdf" is not a Number, so OnlineStats attempts to iterate through it
    2. Iterating through "asdf" begins with the character 'a'
    
+fit!(2Mean(), t)

    A Common Error

    Consider the following example:

    julia> fit!(Mean(), "asdf")ERROR: The input for Mean is Number.  Found Char.

    This causes an error because:

    1. "asdf" is not a Number, so OnlineStats attempts to iterate through it
    2. Iterating through "asdf" begins with the character 'a'
    diff --git a/dev/index.html b/dev/index.html index c3923f25..401f5cf2 100644 --- a/dev/index.html +++ b/dev/index.html @@ -1,12 +1,12 @@ -Welcome! · OnlineStats Documentation
    Edit on GitHub

    Star us on GitHub!

    Star -

    Welcome!

    OnlineStats does statistics and data visualization for big/streaming data via online algorithms. Each algorithm:

    1. processes data one observation at a time.
    2. uses O(1) memory.

    Basics

    1) Creating

    • Stats are subtypes of OnlineStat{T} where T is the type of a single observation.
    julia> using OnlineStats
    julia> m = Mean()Mean: n=0 | value=0.0
    julia> supertype(Mean)OnlineStat{Number}

    2) Updating

    • Stats can be updated with single or multiple observations e.g. fit!(m, 1) and fit!(m, [1,2,3]).
    julia> y = randn(100);
    julia> fit!(m, y)Mean: n=100 | value=0.0802305
    julia> value(m)0.08023048634351752

    3) Merging

    • Stats can be merged.
    julia> y2 = randn(100);
    julia> m2 = fit!(Mean(), y2)Mean: n=100 | value=-0.0581861
    julia> merge!(m, m2)Mean: n=200 | value=0.0110222
    Warn

    Some OnlineStats are not analytically mergeable. In these cases, you will see a warning that either no merging occurred or that the merge is approximate.

    +

    Welcome!

    OnlineStats does statistics and data visualization for big/streaming data via online algorithms. Each algorithm:

    1. processes data one observation at a time.
    2. uses O(1) memory.

    Basics

    1) Creating

    • Stats are subtypes of OnlineStat{T} where T is the type of a single observation.
    julia> using OnlineStats
    julia> m = Mean()Mean: n=0 | value=0.0
    julia> supertype(Mean)OnlineStat{Number}

    2) Updating

    • Stats can be updated with single or multiple observations e.g. fit!(m, 1) and fit!(m, [1,2,3]).
    julia> y = randn(100);
    julia> fit!(m, y)Mean: n=100 | value=0.0802305
    julia> value(m)0.08023048634351752

    3) Merging

    • Stats can be merged.
    julia> y2 = randn(100);
    julia> m2 = fit!(Mean(), y2)Mean: n=100 | value=-0.0581861
    julia> merge!(m, m2)Mean: n=200 | value=0.0110222
    Warn

    Some OnlineStats are not analytically mergeable. In these cases, you will see a warning that either no merging occurred or that the merge is approximate.

    diff --git a/dev/ml/ef74e602.svg b/dev/ml/ef74e602.svg new file mode 100644 index 00000000..9eeabbf6 --- /dev/null +++ b/dev/ml/ef74e602.svg @@ -0,0 +1,98 @@ + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + diff --git a/dev/ml/index.html b/dev/ml/index.html index 69a375cb..4e9907c7 100644 --- a/dev/ml/index.html +++ b/dev/ml/index.html @@ -1,9 +1,9 @@ -Statistical Learning · OnlineStats Documentation
    Edit on GitHub

    Statistical Learning

    The StatLearn (short for statistical learning) OnlineStat uses stochastic approximation methods to estimate models that take the form:

    $\hat\beta = \argmin_\beta \frac{1}{n} \sum_i f(y_i, x_i'\beta) + \sum_j \lambda_j g(\beta_j),$

    where

    • $f$ is a loss function of a response variable and linear preditor.
    • $\lambda_j$'s are nonnegative regularization parameters.
    • $g$ is a penalty function.

    For example, LASSO Regression fits this form with:

    • $f(y_i, x_i'\beta) = \frac{1}{2}(y_i - x_i'\beta) ^ 2$
    • $g(\beta_j) = |\beta_j|$

    OnlineStats implements interchangeable loss and penalty functions to use for both regression and classification problems. See the StatLearn docstring for details.

    Stochastic Approximation

    An important note is that StatLearn is unable to estimate coefficients exactly (For precision in regression problems, see LinReg). The upside is that it makes estimating certain models possible in an online fashion.

    For example, it is not possible to get the same coefficients for logistic regression from an O(1)-memory online algorithm as you would get from its offline counterpart. This is because the logistic regression likelihood's sufficient statistics scale with the number of observations.

    All this to say: StatLearn lets you do things that would otherwise not be possible at the cost of returning noisy estimates.

    Algorithms

    Besides the loss and penalty functions, you can also plug in a variety of fitting algorithms to StatLearn. Some of these methods are based on the stochastic gradient (gradient of loss evaluated on a single observation). Other methods are based on the majorization-minimization (MM) principle[1], which offers some guarantees on numerical stability (sometimes at the cost of slower learning).

    It is a good idea to test out different algorithms on a sample of your dataset. Plotting the coefficients over time can give you an idea of the stability of the estimates. Use Trace, a wrapper around an OnlineStat, to automatically take equally-spaced snapshots of an OnlineStat's state. Keep in mind the early observations will cause bigger jumps in the cofficients than later observations (based on the learning rate; see Weights. To add further complexity, learning rates (supplied by the rate keyword argument) do not affect each algorithm's learning uniformly. You may need to test different combinations of algorithm/learning rate to find an "optimal" pairing.

    using OnlineStats, Plots
+
    Statistical Learning
    The StatLearn (short for statistical learning) OnlineStat uses stochastic approximation methods to estimate models that take the form:
    $\hat\beta = \argmin_\beta \frac{1}{n} \sum_i f(y_i, x_i'\beta) + \sum_j \lambda_j g(\beta_j),$
    where
    • $f$ is a loss function of a response variable and linear preditor.
    • $\lambda_j$'s are nonnegative regularization parameters.
    • $g$ is a penalty function.
    For example, LASSO Regression fits this form with:
    • $f(y_i, x_i'\beta) = \frac{1}{2}(y_i - x_i'\beta) ^ 2$
    • $g(\beta_j) = |\beta_j|$
    OnlineStats implements interchangeable loss and penalty functions to use for both regression and classification problems.  See the StatLearn docstring for details.
    Stochastic Approximation
    An important note is that StatLearn is unable to estimate coefficients exactly (For precision in regression problems, see LinReg).  The upside is that it makes estimating certain models possible in an online fashion.
    For example, it is not possible to get the same coefficients for logistic regression from an O(1)-memory online algorithm as you would get from its offline counterpart.  This is because the logistic regression likelihood's sufficient statistics scale with the number of observations.
    All this to say: StatLearn lets you do things that would otherwise not be possible at the cost of returning noisy estimates.
    Algorithms
    Besides the loss and penalty functions, you can also plug in a variety of fitting algorithms to StatLearn.  Some of these methods are based on the stochastic gradient (gradient of loss evaluated on a single observation).  Other methods are based on the majorization-minimization (MM) principle[1], which offers some guarantees on numerical stability (sometimes at the cost of slower learning).
    It is a good idea to test out different algorithms on a sample of your dataset.  Plotting the coefficients over time can give you an idea of the stability of the estimates.  Use Trace, a wrapper around an OnlineStat, to automatically take equally-spaced snapshots of an OnlineStat's state.  Keep in mind the early observations will cause bigger jumps in the cofficients than later observations (based on the learning rate; see Weights.  To add further complexity, learning rates (supplied by the rate keyword argument) do not affect each algorithm's learning uniformly.  You may need to test different combinations of algorithm/learning rate to find an "optimal" pairing.
    using OnlineStats, Plots
 
 # fake data
 x = rand(Bool, 1000, 10)
@@ -23,102 +23,4 @@
     plot(o, xlab="Nobs", title="SGD Coefficients", lab=nothing),
     plot(o2, xlab="Nobs", title="MSPI Coefficients", lab=nothing),
     link=:y
-)
    
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    • 1At the moment, the only place to read about the stochastic MM algorithms in detail is Josh Day's dissertation.  Josh is working on an easier-to-digest introduction to these methods and is also happy to discuss them through GitHub issue/email.
    
+)
    Example block output
    • 1At the moment, the only place to read about the stochastic MM algorithms in detail is Josh Day's dissertation. Josh is working on an easier-to-digest introduction to these methods and is also happy to discuss them through GitHub issue/email.
    diff --git a/dev/search/index.html b/dev/search/index.html deleted file mode 100644 index 98fd296a..00000000 --- a/dev/search/index.html +++ /dev/null @@ -1,6 +0,0 @@ - -Search · OnlineStats Documentation

    Loading search...

      diff --git a/dev/stats_and_models/index.html b/dev/stats_and_models/index.html index 46e6f1b5..507d1de7 100644 --- a/dev/stats_and_models/index.html +++ b/dev/stats_and_models/index.html @@ -1,6 +1,6 @@ -Statistics and Models · OnlineStats Documentation
      Edit on GitHub

      Statistics and Models

      Univariate Statistics

      StatisticOnlineStat
      MeanMean
      VarianceVariance
      QuantilesQuantile, OrderStats, and P2Quantile
      Maximum/MinimumExtrema
      Skewness and kurtosisMoments
      SumSum
      Geometric MeanGeometricMean

      Plotting (See Data Visualization)

      Info

      Many OnlineStats have Plot recipes beyond what is listed here.

      PlotOnlineStat
      Big Data VizPartition, IndexedPartition, KIndexedPartition
      Mosaic PlotMosaic
      HeatMapHeatMap

      Time Series

      StatisticOnlineStat
      DifferenceDiff
      LagLag
      Autocorrelation/autocovarianceAutoCov
      Tracked historyTrace, StatLag

      Multivariate Analysis

      Statistic/ModelOnlineStat
      Covariance/correlation matrixCovMatrix
      Principal components analysisCovMatrix, CCIPCA
      K-means clusteringKMeans
      Multiple univariate statisticsGroup

      Nonparametric Density Estimation

      Statistic/ModelOnlineStat
      Histograms/continuous densityHist, KHist, and ExpandingHist
      ASH density (semiparametric, similar to KDE)Ash
      Approximate order statisticsOrderStats
      Count for each unique valueCountMap
      Approximate CDFOrderStats

      Parametric Density Estimation

      DistributionOnlineStat
      BetaFitBeta
      CauchyFitCauchy
      GammaFitGamma
      LogNormalFitLogNormal
      NormalFitNormal
      MultinomialFitMultinomial
      MvNormalFitMvNormal

      Machine/Statistical Learning

      ModelOnlineStat
      Linear (also ridge) regressionLinReg, LinRegBuilder
      Decision TreesFastTree
      Random ForestFastForest
      Naive Bayes ClassifierNBClassifier
      ML via Stochastic ApproximationStatLearn

      Other

      Statistic/ModelOnlineStat
      Handling Missing DataFilterTransform, CountMissing, SkipMissing
      Statistical BootstrapBootstrap
      Approx. count of distinct elementsHyperLogLog
      Approx. count of occurrencesCountMinSketch
      Random sampleReservoirSample
      Moving WindowMovingWindow, MovingTimeWindow

      Collection of Stats

      Statistic/ModelOnlineStat
      Univariate data streamSeries
      Multivariate data streamsGroup
      Group by categorical variableGroupBy

      Stochastic Approximation with StatLearn

      Regression and Classification Losses

      LossFunction
      $L_{2}$ Loss (squared error)OnlineStats.l2regloss
      $L_{1}$ Loss (absolute error)OnlineStats.l1regloss
      Logistic LossOnlineStats.logisticloss
      $L_{1}$ Hinge LossOnlineStats.l1hingeloss
      Generalized distance weighted discriminationOnlineStats.DWDLoss

      Penalty/regularization functions

      PenaltyFunction
      Nonezero
      LASSO ($L_{1}$ penalty)abs
      Ridge ($L_{2}$ penalty)abs2
      Elastic NetOnlineStats.ElasticNet

      Optimization Algorithms

      AlgorithmConstructor
      Stochastic Gradient DescentSGD
      RMSPropRMSPROP
      AdaGradADAGRAD
      AdaDeltaADADELTA
      ADAMADAM
      ADAMaxADAMAX
      MSPI (Majorized Stochastic Proximal Iteration)MSPI
      Online Majorization-Minimization (MM) - averaged surrogateOMAS
      Online MM - Averaged ParameterOMAP
      +

      Statistics and Models

      Univariate Statistics

      StatisticOnlineStat
      MeanMean
      VarianceVariance
      QuantilesQuantile, OrderStats, and P2Quantile
      Maximum/MinimumExtrema
      Skewness and kurtosisMoments
      SumSum
      Geometric MeanGeometricMean

      Plotting (See Data Visualization)

      Info

      Many OnlineStats have Plot recipes beyond what is listed here.

      PlotOnlineStat
      Big Data VizPartition, IndexedPartition, KIndexedPartition
      Mosaic PlotMosaic
      HeatMapHeatMap

      Time Series

      StatisticOnlineStat
      DifferenceDiff
      LagLag
      Autocorrelation/autocovarianceAutoCov
      Tracked historyTrace, StatLag

      Multivariate Analysis

      Statistic/ModelOnlineStat
      Covariance/correlation matrixCovMatrix
      Principal components analysisCovMatrix, CCIPCA
      K-means clusteringKMeans
      Multiple univariate statisticsGroup

      Nonparametric Density Estimation

      Statistic/ModelOnlineStat
      Histograms/continuous densityHist, KHist, and ExpandingHist
      ASH density (semiparametric, similar to KDE)Ash
      Approximate order statisticsOrderStats
      Count for each unique valueCountMap
      Approximate CDFOrderStats

      Parametric Density Estimation

      DistributionOnlineStat
      BetaFitBeta
      CauchyFitCauchy
      GammaFitGamma
      LogNormalFitLogNormal
      NormalFitNormal
      MultinomialFitMultinomial
      MvNormalFitMvNormal

      Machine/Statistical Learning

      ModelOnlineStat
      Linear (also ridge) regressionLinReg, LinRegBuilder
      Decision TreesFastTree
      Random ForestFastForest
      Naive Bayes ClassifierNBClassifier
      ML via Stochastic ApproximationStatLearn

      Other

      Statistic/ModelOnlineStat
      Handling Missing DataFilterTransform, CountMissing, SkipMissing
      Statistical BootstrapBootstrap
      Approx. count of distinct elementsHyperLogLog
      Approx. count of occurrencesCountMinSketch
      Random sampleReservoirSample
      Moving WindowMovingWindow, MovingTimeWindow

      Collection of Stats

      Statistic/ModelOnlineStat
      Univariate data streamSeries
      Multivariate data streamsGroup
      Group by categorical variableGroupBy

      Stochastic Approximation with StatLearn

      Regression and Classification Losses

      LossFunction
      $L_{2}$ Loss (squared error)OnlineStats.l2regloss
      $L_{1}$ Loss (absolute error)OnlineStats.l1regloss
      Logistic LossOnlineStats.logisticloss
      $L_{1}$ Hinge LossOnlineStats.l1hingeloss
      Generalized distance weighted discriminationOnlineStats.DWDLoss

      Penalty/regularization functions

      PenaltyFunction
      Nonezero
      LASSO ($L_{1}$ penalty)abs
      Ridge ($L_{2}$ penalty)abs2
      Elastic NetOnlineStats.ElasticNet

      Optimization Algorithms

      AlgorithmConstructor
      Stochastic Gradient DescentSGD
      RMSPropRMSPROP
      AdaGradADAGRAD
      AdaDeltaADADELTA
      ADAMADAM
      ADAMaxADAMAX
      MSPI (Majorized Stochastic Proximal Iteration)MSPI
      Online Majorization-Minimization (MM) - averaged surrogateOMAS
      Online MM - Averaged ParameterOMAP
      diff --git a/dev/weights/9cb01270.svg b/dev/weights/9cb01270.svg new file mode 100644 index 00000000..f3b92d3e --- /dev/null +++ b/dev/weights/9cb01270.svg @@ -0,0 +1,58 @@ + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + diff --git a/dev/weights/index.html b/dev/weights/index.html index edaffdaf..5b1d258b 100644 --- a/dev/weights/index.html +++ b/dev/weights/index.html @@ -1,72 +1,14 @@ -Weights · OnlineStats Documentation
      Edit on GitHub

      Weights

      Many OnlineStats are parameterized by a Weight that controls the influence of new observations. If the OnlineStat is capable of calculating the same result as a corresponding offline estimator, it will have a keyword argument weight. If the OnlineStat uses stochastic approximation, it will have a keyword argument rate (see this great resource on stochastic approximation algorithms).

      Consider how weights affect the influence of the next observation on an online mean $\theta^{(t)}$, as many OnlineStats use updates of this form. A larger weight $\gamma_t$ puts higher influence on the new observation $x_t$:

      \[\theta^{(t)} = (1-\gamma_t)\theta^{(t-1)} + \gamma_t x_t\]

      Note

      The values produced by a Weight must follow two rules:

      1. $\gamma_1 = 1$ (guarantees $\theta^{(1)} = x_1$)
      2. $\gamma_t \in (0, 1), \quad \forall t > 1$ (guarantees $\theta^{(t)}$ stays inside a convex space)
      - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -
      Info

      The notion of weighting in OnlineStats is fundamentally different than StatsBase.AbstractWeights.

      • In OnlineStats, a weight determines the influence of an observation compared to the current state of the statistic.
      • In StatsBase, a weight determines the influence of an observation in the overall calculation of the statistic.
      julia> using OnlineStats, StatsBaseERROR: ArgumentError: Package StatsBase not found in current path.
+
      Weights
      Many OnlineStats are parameterized by a Weight that controls the influence of new observations.  If the OnlineStat is capable of calculating the same result as a corresponding offline estimator, it will have a keyword argument weight.  If the OnlineStat uses stochastic approximation, it will have a keyword argument rate (see this great resource on stochastic approximation algorithms).
      Consider how weights affect the influence of the next observation on an online mean $\theta^{(t)}$, as many OnlineStats use updates of this form.  A larger weight  $\gamma_t$ puts higher influence on the new observation $x_t$:
      \[\theta^{(t)} = (1-\gamma_t)\theta^{(t-1)} + \gamma_t x_t\]
      Note
      The values produced by a Weight must follow two rules:
      1. $\gamma_1 = 1$ (guarantees $\theta^{(1)} = x_1$)
      2. $\gamma_t \in (0, 1), \quad \forall t > 1$ (guarantees $\theta^{(t)}$ stays inside a convex space)
      Example block output
      Info
      The notion of weighting in OnlineStats is fundamentally different than StatsBase.AbstractWeights.
      • In OnlineStats, a weight determines the influence of an observation compared to the current state of the statistic.
      • In StatsBase, a weight determines the influence of an observation in the overall calculation of the statistic.
      julia> using OnlineStats, StatsBaseERROR: ArgumentError: Package StatsBase not found in current path.
 - Run `import Pkg; Pkg.add("StatsBase")` to install the StatsBase package.
      julia> x = 1:99;
      julia> w = fill(0.1, 99);
      julia> # StatsBase: All weights == 0.1
        mean(x) ≈ mean(x, aweights(w)) ≈ mean(x, fweights(w)) ≈ mean(x, pweights(w))ERROR: UndefVarError: `aweights` not defined
      julia> # OnlineStats: All weights == 0.1
-       o = fit!(Mean(weight = n -> 0.1), x)Mean: n=99 | value=90.0003
      julia> mean(x)  # Every observation has equal influence over statistic.50.0
      julia> value(o)  # Recent observations have higher influence over statistic.90.00026561398887
      Weight Types
      OnlineStatsBase.ExponentialWeight — Type
      ExponentialWeight(λ::Float64)
+       o = fit!(Mean(weight = n -> 0.1), x)Mean: n=99 | value=90.0003
      julia> mean(x)  # Every observation has equal influence over statistic.50.0
      julia> value(o)  # Recent observations have higher influence over statistic.90.00026561398887
      Weight Types
      OnlineStatsBase.ExponentialWeight — Type
      ExponentialWeight(λ::Float64)
 ExponentialWeight(lookback::Int)
      Exponentially weighted observations.  Each weight is λ = 2 / (lookback + 1).  
      ExponentialWeight does not satisfy the usual assumption that γ(1) == 1.  Therefore, some statistics have an implicit starting value. 
      # E.g. Mean has an implicit starting value of 0.
 o = Mean(weight=ExponentialWeight(.1))
 fit!(o, 10)
-value(o) == 1
      $γ(t) = λ$
      OnlineStatsBase.LearningRate — Type
      LearningRate(r = .6)
      Slowly decreasing weight.  Satisfies the standard stochastic approximation assumption $∑ γ(t) = ∞, ∑ γ(t)^2 < ∞$ if $r ∈ (.5, 1]$.
      $γ(t) = inv(t ^ r)$
      Custom Weighting
      The Weight can be any callable object that receives the number of observations as its argument.  For example:
      • weight = inv will have the same result as weight = EqualWeight().
      • weight = x -> .01 will have the same result as weight = ExponentialWeight(.01)

      julia> y = randn(100);
      julia> fit!(Mean(weight = EqualWeight()), y)Mean: n=100 | value=0.000430232
      julia> fit!(Mean(weight = inv), y)Mean: n=100 | value=0.000430232
      Example of Weight Effects using Data with Concept Drift

      
-
      
+value(o) == 1

      $γ(t) = λ$

      source
      OnlineStatsBase.LearningRate — Type
      LearningRate(r = .6)

      Slowly decreasing weight. Satisfies the standard stochastic approximation assumption $∑ γ(t) = ∞, ∑ γ(t)^2 < ∞$ if $r ∈ (.5, 1]$.

      $γ(t) = inv(t ^ r)$

      source

      Custom Weighting

      The Weight can be any callable object that receives the number of observations as its argument. For example:

      • weight = inv will have the same result as weight = EqualWeight().
      • weight = x -> .01 will have the same result as weight = ExponentialWeight(.01)

      julia> y = randn(100);
      julia> fit!(Mean(weight = EqualWeight()), y)Mean: n=100 | value=0.000430232
      julia> fit!(Mean(weight = inv), y)Mean: n=100 | value=0.000430232

      Example of Weight Effects using Data with Concept Drift


      +