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DecodingAlgorithms.m
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DecodingAlgorithms.m
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classdef DecodingAlgorithms
% DECODINGALGORITHMS A class that contains static functions for
% decoding the hidden states of linear discrete stochastic systems or
% hybrid linear discrete stochastic systems subject to gaussian noise.
% The observations can come from either a gaussian observation model
% or via a point process observation model.
%
% <a href="matlab: methods('DecodingAlgorithms')">methods</a>
% Reference page in Help browser
% <a href="matlab: doc('DecodingAlgorithms')">doc DecodingAlgorithms</a>
%
% nSTAT v1 Copyright (C) 2012 Masschusetts Institute of Technology
% Cajigas, I, Malik, WQ, Brown, EN
% This program is free software; you can redistribute it and/or
% modify it under the terms of the GNU General Public License as published
% by the Free Software Foundation; either version 2 of the License, or
% (at your option) any later version.
%
% This program is distributed in the hope that it will be useful,
% but WITHOUT ANY WARRANTY; without even the implied warranty of
% MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE.
% See the GNU General Public License for more details.
%
% You should have received a copy of the GNU General Public License
% along with this program; if not, write to the Free Software Foundation,
% Inc., 59 Temple Place, Suite 330, Boston, MA 02111-1307 USA
properties
end
methods (Static)
%% Point Process Adaptive Filter
%PPDecodeFilter takes an object of class CIF describing the
%conditional intensity function. This routine is more generic since
%all of the computations for the PPAF are done symbolically based
%on the CIF object. However, it also means that this version is
%must slower than the linear version below.
function [x_p, W_p, x_u, W_u, x_uT,W_uT,x_pT, W_pT, WConvIter] = PPDecodeFilter(A, Q, Px0, dN,lambdaCIFColl,binwidth,x0,Pi0, yT,PiT,estimateTarget,Wconv)
% A can be static or can be a different matrix for each time N
if(nargin<13||isempty(Wconv))
Wconv =[];
end
[C,N] = size(dN); % N time samples, C cells
ns=size(A,1); % number of states
if(nargin<12 || isempty(estimateTarget))
estimateTarget=0;
end
if(nargin<11 || isempty(PiT))
if(estimateTarget==1)
PiT = zeros(size(Q));
else
PiT = 0*diag(ones(ns,1))*1e-6;
end
end
if(nargin<9 || isempty(Pi0))
Pi0 = zeros(ns,ns);
end
if(nargin<10 || isempty(yT))
yT=[];
Amat = A;
Qmat = Q;
ft = zeros(size(Amat,2),N);
PiT = zeros(size(Q));
else
PitT= zeros(ns,ns,N); % Pi(t,T) in Srinivasan et al.
QT = zeros(ns,ns,N); % The noise covaraince given target observation (Q_t)
if(estimateTarget==1)
PitT(:,:,N)=Q; % Pi(T,T)=Pi_T + Q_T, setting PiT=0
else
PitT(:,:,N)=PiT+Q;
end
PhitT = zeros(ns,ns,N);% phi(t,T) - transition matrix from time T to t
% PhiTt = zeros(ns,ns,N);% phi(T,t) - transition matrix from time t to T
PhitT(:,:,N) = eye(ns,ns); % phi(T,T) = I
B = zeros(ns,ns,N); % See Equation 2.21 in Srinivasan et. al
for n=N:-1:2
invA=eye(size(A))/A;
% state transition matrix
PhitT(:,:,n-1)= invA*PhitT(:,:,n);
% PhiTt(:,:,n)= A^(N-n);
% Equation 2.16 in Srinivasan et al. Note there is a typo in the paper.
% This is the correct expression. The term Q_t-1 does not
% need to be mulitplied by phi(t-1,t)
PitT(:,:,n-1) = invA*PitT(:,:,n)*invA'+Q;
if(n<=N)
B(:,:,n) = A-(Q/PitT(:,:,n))*A; %Equation 2.21 in Srinivasan et. al
QT(:,:,n) = Q-(Q/PitT(:,:,n))*Q';
end
end
% PhiTt(:,:,1)= A^(N-1);
B(:,:,1) = A-(Q/PitT(:,:,1))*A;
QT(:,:,1) = Q-(Q/PitT(:,:,1))*Q';
% See Equations 2.23 through 2.26 in Srinivasan et. al
if(estimateTarget==1)
% beta = [beta ;zeros(ns,C)];
for n=1:N
psi = B(:,:,n);
if(n==N)
gammaMat = eye(ns,ns);
else
gammaMat = (Q/PitT(:,:,n))*PhitT(:,:,n);
end
Amat(:,:,n) = [psi,gammaMat;
zeros(ns,ns), eye(ns,ns)];
% if(n>1)
% tUnc(:,:,n) = tUnc(:,:,n-1)+PhiTt(:,:,n)*Q*PhiTt(:,:,n)';
% else
% tUnc(:,:,n) = PhiTt(:,:,n)*Q*PhiTt(:,:,n)';
% end
Qmat(:,:,n) = [QT(:,:,n), zeros(ns,ns);
zeros(ns,ns) zeros(ns,ns)];
end
else
Amat = B;
Qmat = QT;
for n=1:N
ft(:,n) = (Q/PitT(:,:,n))*PhitT(:,:,n)*yT;
end
end
end
if(nargin<8 || isempty(x0))
x0=zeros(size(A,2),1);
end
if(nargin<7)
binwidth = .001; % in seconds
end
%%
% Return values are
% x_p: state estimates given the past x_k|k-1
% W_p: error covariance estimates given the past
% x_u: state updates given the data - x_k|k
% W_u: error covariance updates given the data
[C,N] = size(dN); % N time samples, C cells
%% Initialize the PPAF
x_p = zeros( size(Amat,2), N+1 );
x_u = zeros( size(Amat,2), N );
W_p = zeros( size(Amat,2),size(Amat,2), N+1 );
W_u = zeros( size(Amat,2),size(Amat,2), N );
if(~isempty(yT))
if(det(Pi0)==0) % Assume x0 is known exactly
else %else
invPi0 = pinv(Pi0);
invPitT= pinv(PitT(:,:,1));
Pi0New = pinv(invPi0+invPitT);
Pi0New(isnan(Pi0New))=0;
x0New = Pi0New*(invPi0*x0+invPitT*PhitT(:,:,1)*yT);
x0=x0New; Pi0 = Pi0New;
end
end
if(~isempty(yT) && estimateTarget==1)
x0= [x0;yT]; %simultaneous estimation of target requires state augmentation
end
if((estimateTarget==1 && ~isempty(yT)) || isempty(yT))
x_p(:,1)= Amat(:,:,1)*x0;
else
invPitT = pinv(PitT(:,:,1));
% invPhitT = pinv(PhitT(:,:,1));
invA = pinv(A);
invPhi0T = pinv(invA*PhitT(:,:,1));
ut(:,1) = (Q*invPitT)*PhitT(:,:,1)*(yT-invPhi0T*x0);
[x_p(:,1), W_p(:,:,1)] = DecodingAlgorithms.PPDecode_predict(x0, Pi0, Amat(:,:,min(size(Amat,3),n)), Qmat(:,:,min(size(Qmat,3))));
x_p(:,1) = x_p(:,1)+ut(:,1);
W_p(:,:,1) = W_p(:,:,1) + (Q*invPitT)*A*Pi0*A'*(Q*invPitT)';
% x_p(:,1)= Amat(:,:,1)*x0 + ft(:,1);
end
if(estimateTarget==1 && ~isempty(yT))
Pi0New = [Pi0, zeros(ns,ns);
zeros(ns,ns) , zeros(ns,ns)];
W_p(:,:,1) = Amat(:,:,1)*Pi0New*Amat(:,:,1)'+Qmat(:,:,1);
elseif(estimateTarget==0 && isempty(yT))
W_p(:,:,1) = Amat(:,:,1)*Pi0*Amat(:,:,1)'+Qmat(:,:,1);
end %Otherwise we computed it above.
for n=1:N
[x_u(:,n), W_u(:,:,n)] = DecodingAlgorithms.PPDecode_update( x_p(:,n), W_p(:,:,n), dN(:,1:n),lambdaCIFColl, binwidth,n);
% [x_p(:,n+1), W_p(:,:,n+1)] = DecodingAlgorithms.PPDecode_predict(x_u(:,n), W_u(:,:,n), Amat(:,:,min(size(A,3),n)), Qmat(:,:,min(size(Qmat,3))));
if((estimateTarget==1 && ~isempty(yT)) || isempty(yT))
[x_p(:,n+1), W_p(:,:,n+1)] = DecodingAlgorithms.PPDecode_predict(x_u(:,n), W_u(:,:,n), Amat(:,:,min(size(A,3),n)), Qmat(:,:,min(size(Qmat,3))));
else
%ut= Q_{t}\Pi(t,T)^{-1}\phi(t,T)(y_{T}-phi(T,t-1)x_{t-1}
if(n<N)
ut(:,n+1) = (Q*pinv(PitT(:,:,n+1)))*PhitT(:,:,n+1)*(yT-pinv(PhitT(:,:,n))*x_u(:,n));
% ut(:,n+1) = ut(:,n+1)*delta;
[x_p(:,n+1), W_p(:,:,n+1)] = DecodingAlgorithms.PPDecode_predict(x_u(:,n), W_u(:,:,n), Amat(:,:,min(size(A,3),n)), Qmat(:,:,min(size(Qmat,3))));
x_p(:,n+1) = x_p(:,n+1)+ut(:,n+1);
W_p(:,:,n+1) = W_p(:,:,n+1) + (Q*pinv(PitT(:,:,n+1)))*A*W_u(:,:,n)*A'*(Q*pinv(PitT(:,:,n+1)))';
end
end
if(n>1 && isempty(Wconv))
diffWun = abs(trace(W_u(:,:,n))-W_u(:,:,n-1));
mAbsdiffWun = max(max(diffWun));
if(mAbsdiffWun<1e-6)
Wconv=W_u(:,:,n);
WConvIter = n;
else
WConvIter=[];
end
end
end
if(~isempty(yT) && estimateTarget==1)
%decompose the augmented state space into estimates of the state
%vector and the target position
x_uT = x_u(ns+1:2*ns,:);
W_uT = W_u(ns+1:2*ns,ns+1:2*ns,:);
x_pT = x_p(ns+1:2*ns,:);
W_pT = W_p(ns+1:2*ns,ns+1:2*ns,:);
x_u = x_u(1:ns,:);
W_u = W_u(1:ns,1:ns,:);
x_p = x_p(1:ns,:);
W_p = W_p(1:ns,1:ns,:);
else
x_uT = [];
W_uT = [];
x_pT = [];
W_pT = [];
end
end
%PPDecodeFilterLinear takes in a linear representation of the
%conditional intensity terms. These are the terms that are inside
%the exponential in a Poisson or Binomial description of the CIF.
%If such a representation is available, use of this routine is
%recommended because it is much faster.
function [x_p, W_p, x_u, W_u, x_uT,W_uT,x_pT, W_pT] = PPDecodeFilterLinear(A, Q, dN,mu,beta,fitType,delta,gamma,windowTimes,x0, Pi0, yT,PiT,estimateTarget,Wconv)
% [x_p, W_p, x_u, W_u] = PPDecodeFilterLinear(CIFType,A, Q, dN,beta,gamma,x0, xT)
% Point process adaptive filter with the assumption of linear
% expresion for the conditional intensity functions (see below). If
% the terms in the conditional intensity function include
% polynomial powers of a variable for example, these expressions do
% not hold. Use the PPDecodeFilter instead since it will compute
% these expressions symbolically. However, because of the matlab
% symbolic toolbox, it runs much slower than this version.
%
% If a final value for xT is given then the approach of Srinivasan
% et. al (2006) is used for concurrent estimate of the state and
% the target. This involves state augmentation of the original
% state space model. If a final value is not specified then the
% standard Point Process Adaptive Filter of Eden et al (2004) is
% used instead.
%
% Assumes in both cases that
% x_t = A*x_{t-1} + w_{t} w_{t} ~ Normal with zero me and
% covariance Q
%
%
% Paramerters:
%
% A: The state transition matrix from the x_{t-1} to x_{t}
%
% Q: The covariance of the process noise w_t
%
% dN: A C x N matrix of ones and zeros corresponding to the
% observed spike trains. N is the number of time steps in
% my code. C is the number of cells
%
% mu: Cx1 vector of baseline firing rates for each cell. In
% the CIF expression in 'fitType' description
% mu_c=mu(c);
%
% beta: nsxC matrix of coefficients for the conditional
% intensity function. ns is the number of states in x_t
% In the conditional intesity function description below
% beta_c = beta(:,c)';
%
% fitType: 'poisson' or 'binomial'. Determines how the beta and
% gamma coefficients are used to compute the conditional
% intensity function.
% For the cth cell:
% If poisson: lambda*delta = exp(mu_c+beta_c*x + gamma_c*hist_c)
% If binomial: logit(lambda*delta) = mu_c+beta_c*x + gamma_c*hist_c
%
% delta: The number of seconds per time step. This is used to compute
% th history effect for each spike train using the input
% windowTimes and gamma
%
% gamma: length(windowTimes)-1 x C matrix of the history
% coefficients for each window in windowTimes. In the 'fitType'
% expression above:
% gamma_c = gamma(:,c)';
% If gamma is a length(windowTimes)-1x1 vector, then the
% same history coefficients are used for each cell.
%
% windowTimes: Defines the distinct windows of time (in seconds)
% that will be computed for each spike train.
%
% xT: Target Position
%
% PiT: Target Uncertainty
%
% estimateTarget: By default (==0), it is assumed that that the
% initial target information is fixed. Set to 1 in order to
% simultaneously estimate the target location via
% state augmentation
%
%
%
% Code for reaching to final target adapted from:
% L. Srinivasan, U. T. Eden, A. S. Willsky, and E. N. Brown,
% "A state-space analysis for reconstruction of goal-directed
% movements using neural signals.,"
% Neural computation, vol. 18, no. 10, pp. 2465?2494, Oct. 2006.
%
% Point Process Adaptive Filter from
% U. T. Eden, L. M. Frank, R. Barbieri, V. Solo, and E. N. Brown,
% "Dynamic analysis of neural encoding by point process adaptive
% filtering.,"
% Neural computation, vol. 16, no. 5, pp. 971?998, May. 2004.
if(nargin<15||isempty(Wconv))
Wconv =[];
end
[C,N] = size(dN); % N time samples, C cells
ns=size(A,1); % number of states
if(nargin<14 || isempty(estimateTarget))
estimateTarget=0;
end
if(nargin<10 || isempty(x0))
x0=zeros(ns,1);
end
if(nargin<9 || isempty(windowTimes))
windowTimes=[];
end
if(nargin<8 || isempty(gamma))
gamma=0;
end
if(nargin<7 || isempty(delta))
delta = .001;
end
if(nargin<13 || isempty(PiT))
if(estimateTarget==1)
PiT = zeros(size(Q));
else
PiT = 0*diag(ones(ns,1))*1e-6;
end
end
if(nargin<11 || isempty(Pi0))
Pi0 = zeros(ns,ns);
end
if(nargin<12 || isempty(yT))
yT=[];
Amat = A;
Qmat = Q;
ft = zeros(size(Amat,2),N);
PiT = zeros(size(Q));
else
PitT= zeros(ns,ns,N); % Pi(t,T) in Srinivasan et al.
QT = zeros(ns,ns,N); % The noise covaraince given target observation (Q_t)
QN =Q(:,:,min(size(Q,3),N));
if(estimateTarget==1)
PitT(:,:,N)=QN; % Pi(T,T)=Pi_T + Q_T, setting PiT=0
else
PitT(:,:,N)=PiT+QN;
end
PhitT = zeros(ns,ns,N);% phi(t,T) - transition matrix from time T to t
% PhiTt = zeros(ns,ns,N);% phi(T,t) - transition matrix from time t to T
PhitT(:,:,N) = eye(ns,ns); % phi(T,T) = I
B = zeros(ns,ns,N); % See Equation 2.21 in Srinivasan et. al
for n=N:-1:2
An =A(:,:,min(size(A,3),n));
Qn =Q(:,:,min(size(Q,3),n));
invA=pinv(An);
% state transition matrix
PhitT(:,:,n-1)= invA*PhitT(:,:,n);
% PhiTt(:,:,n)= A^(N-n);
% Equation 2.16 in Srinivasan et al. Note there is a typo in the paper.
% This is the correct expression. The term Q_t-1 does not
% need to be mulitplied by phi(t-1,t)
PitT(:,:,n-1) = invA*PitT(:,:,n)*invA'+Qn;
if(n<=N)
B(:,:,n) = An-(Qn*pinv(PitT(:,:,n)))*An; %Equation 2.21 in Srinivasan et. al
QT(:,:,n) = Qn-(Qn*pinv(PitT(:,:,n)))*Qn';
end
end
A1=A(:,:,min(size(A,3),1));
Q1=Q(:,:,min(size(Q,3),1));
B(:,:,1) = A1-(Q1*pinv(PitT(:,:,1)))*A1;
QT(:,:,1) = Q1-(Q1*pinv(PitT(:,:,1)))*Q1';
% See Equations 2.23 through 2.26 in Srinivasan et. al
if(estimateTarget==1)
beta = [beta ;zeros(ns,C)];
for n=1:N
An =A(:,:,min(size(A,3),n));
Qn =Q(:,:,min(size(Q,3),n));
psi = B(:,:,n);
if(n==N)
gammaMat = eye(ns,ns);
else
gammaMat = (Qn*pinv(PitT(:,:,n)))*PhitT(:,:,n);
end
Amat(:,:,n) = [psi,gammaMat;
zeros(ns,ns), eye(ns,ns)];
Qmat(:,:,n) = [QT(:,:,n), zeros(ns,ns);
zeros(ns,ns) zeros(ns,ns)];
end
else
Amat = B;
Qmat = QT;
for n=1:N
An =A(:,:,min(size(A,3),n));
Qn =Q(:,:,min(size(Q,3),n));
ft(:,n) = (Qn*pinv(PitT(:,:,n)))*PhitT(:,:,n)*yT;
end
end
end
minTime=0;
maxTime=(size(dN,2)-1)*delta;
C=size(dN,1);
if(~isempty(windowTimes))
histObj = History(windowTimes,minTime,maxTime);
HkAll = zeros(size(dN,2),length(windowTimes)-1,C);
for c=1:C
nst{c} = nspikeTrain( (find(dN(c,:)==1)-1)*delta);
nst{c}.setMinTime(minTime);
nst{c}.setMaxTime(maxTime);
nst{c}=nst{c}.resample(1/delta);
HkAll(:,:,c) = histObj.computeHistory(nst{c}).dataToMatrix;
% HkAll{c} = histObj.computeHistory(nst{c}).dataToMatrix;
end
if(size(gamma,2)==1 && C>1) % if more than 1 cell but only 1 gamma
gammaNew(:,c) = gamma;
else
gammaNew=gamma;
end
gamma = gammaNew;
else
for c=1:C
% HkAll{c} = zeros(N,1);
HkAll(:,:,c) = zeros(N,1);
gammaNew(c)=0;
end
gamma=gammaNew;
end
if(size(gamma,2)~=C)
gamma=gamma';
end
% Initialize the PPAF
x_p = zeros( size(Amat,2), N+1 );
x_u = zeros( size(Amat,2), N );
W_p = zeros( size(Amat,2),size(Amat,2), N+1 );
W_u = zeros( size(Amat,2),size(Amat,2), N );
if(~isempty(yT))
if(det(Pi0)==0) % Assume x0 is known exactly
else %else
invPi0 = pinv(Pi0);
invPitT= pinv(PitT(:,:,1));
Pi0New = pinv(invPi0+invPitT);
Pi0New(isnan(Pi0New))=0;
x0New = Pi0New*(invPi0*x0+invPitT*PhitT(:,:,1)*yT);
x0=x0New; Pi0 = Pi0New;
end
end
if(~isempty(yT) && estimateTarget==1)
x0= [x0;yT]; %simultaneous estimation of target requires state augmentation
end
if((estimateTarget==1 && ~isempty(yT)) || isempty(yT))
x_p(:,1)= Amat(:,:,1)*x0;
else
invPitT = pinv(PitT(:,:,1));
% invPhitT = pinv(PhitT(:,:,1));
A1 = A(:,:,min(size(A,3),1));
Q1 = Q(:,:,min(size(Q,3),1));
invA = pinv(A1);
invPhi0T = pinv(invA*PhitT(:,:,1));
ut(:,1) = (Q1*invPitT)*PhitT(:,:,1)*(yT-invPhi0T*x0);
[x_p(:,1), W_p(:,:,1)] = DecodingAlgorithms.PPDecode_predict(x0, Pi0, Amat(:,:,min(size(Amat,3),n)), Qmat(:,:,min(size(Qmat,3))));
x_p(:,1) = x_p(:,1)+ut(:,1);
W_p(:,:,1) = W_p(:,:,1) + (Q1*invPitT)*A1*Pi0*A1'*(Q1*invPitT)';
% x_p(:,1)= Amat(:,:,1)*x0 + ft(:,1);
end
if(estimateTarget==1 && ~isempty(yT))
Pi0New = [Pi0, zeros(ns,ns);
zeros(ns,ns) , zeros(ns,ns)];
W_p(:,:,1) = Amat(:,:,1)*Pi0New*Amat(:,:,1)'+Qmat(:,:,1);
elseif(estimateTarget==0 && isempty(yT))
W_p(:,:,1) = Amat(:,:,1)*Pi0*Amat(:,:,1)'+Qmat(:,:,1);
end %Otherwise we computed it above.
HkPerm = permute(HkAll,[2 3 1]);
clear t;
for n=1:N
[x_u(:,n), W_u(:,:,n)] = DecodingAlgorithms.PPDecode_updateLinear(x_p(:,n), W_p(:,:,n), dN,mu,beta,fitType,gamma,HkPerm,n,Wconv);
% The prediction step is identical to the symbolic implementation since
% it is independent of the CIF
if((estimateTarget==1 && ~isempty(yT)) || isempty(yT))
[x_p(:,n+1), W_p(:,:,n+1)] = DecodingAlgorithms.PPDecode_predict(x_u(:,n), W_u(:,:,n), Amat(:,:,min(size(Amat,3),n)), Qmat(:,:,min(size(Qmat,3))),Wconv);
else
%ut= Q_{t}\Pi(t,T)^{-1}\phi(t,T)(y_{T}-phi(T,t-1)x_{t-1}
if(n<N)
An = A(:,:,min(size(A,3),n));
Qn = Q(:,:,min(size(Q,3),n));
invPitT = pinv(PitT(:,:,n+1));
invPhitm1T = pinv(PhitT(:,:,n));
ut(:,n+1) = (Qn*invPitT)*PhitT(:,:,n+1)*(yT-invPhitm1T*x_u(:,n));
% ut(:,n+1) = ut(:,n+1)*delta;
[x_p(:,n+1), W_p(:,:,n+1)] = DecodingAlgorithms.PPDecode_predict(x_u(:,n), W_u(:,:,n), Amat(:,:,min(size(A,3),n)), Qmat(:,:,min(size(Qmat,3))));
x_p(:,n+1) = x_p(:,n+1)+ut(:,n+1);
W_p(:,:,n+1) = W_p(:,:,n+1) + (Qn*invPitT)*An*W_u(:,:,n)*An'*(Qn*invPitT)';
end
end
end
if(~isempty(yT) && estimateTarget==1)
%decompose the augmented state space into estimates of the state
%vector and the target position
x_uT = x_u(ns+1:2*ns,:);
W_uT = W_u(ns+1:2*ns,ns+1:2*ns,:);
x_pT = x_p(ns+1:2*ns,:);
W_pT = W_p(ns+1:2*ns,ns+1:2*ns,:);
x_u = x_u(1:ns,:);
W_u = W_u(1:ns,1:ns,:);
x_p = x_p(1:ns,:);
W_p = W_p(1:ns,1:ns,:);
else
x_uT = [];
W_uT = [];
x_pT = [];
W_pT = [];
end
end
%% Point Process Fixed-Interval Smoother
function [x_pLag, W_pLag, x_uLag, W_uLag] = PP_fixedIntervalSmoother(A, Q, dN, lags, mu,beta,fitType,delta,gamma,windowTimes,x0, Pi0)
[~,N] = size(dN); % N time samples, C cells
ns=size(A,1); % number of states
if(nargin<11 || isempty(x0))
x0=zeros(ns,1);
end
if(nargin<10 || isempty(windowTimes))
windowTimes=[];
end
if(nargin<9 || isempty(gamma))
gamma=0;
end
if(nargin<8 || isempty(delta))
delta = .001;
end
if(nargin<12 || isempty(Pi0))
Pi0 = zeros(ns,ns);
end
minTime=0;
maxTime=(size(dN,2)-1)*delta;
C=size(dN,1);
if(~isempty(windowTimes))
histObj = History(windowTimes,minTime,maxTime);
HkAll = zeros(size(dN,2),length(windowTimes)-1,C);
for c=1:C
nst{c} = nspikeTrain( (find(dN(c,:)==1)-1)*delta);
nst{c}.setMinTime(minTime);
nst{c}.setMaxTime(maxTime);
nst{c}=nst{c}.resample(1/delta);
HkAll(:,:,c) = histObj.computeHistory(nst{c}).dataToMatrix;
% HkAll{c} = histObj.computeHistory(nst{c}).dataToMatrix;
end
if(size(gamma,2)==1 && C>1) % if more than 1 cell but only 1 gamma
gammaNew(:,c) = gamma;
else
gammaNew=gamma;
end
gamma = gammaNew;
else
for c=1:C
% HkAll{c} = zeros(N,1);
HkAll(:,:,c) = zeros(N,1);
gammaNew(c)=0;
end
gamma=gammaNew;
end
if(size(gamma,2)~=C)
gamma=gamma';
end
%% Initialize the PPAF
x_p = zeros( size(A,2), N+1 );
x_u = zeros( size(A,2), N );
W_p = zeros( size(A,2),size(A,2), N+1 );
W_u = zeros( size(A,2),size(A,2), N );
% Assumes that the dynamics only start at time 1 so that A(:,:,0)=I
x_p(:,1) = x0;
W_p(:,:,1) = Pi0;
HkPerm = permute(HkAll,[2 3 1]);
x_uLag = zeros(size(x_u));
W_uLag = zeros(size(W_u));
x_pLag = zeros(size(x_p));
W_pLag = zeros(size(W_p));
for n=1:N
[x_u(:,n), W_u(:,:,n)] = DecodingAlgorithms.PPDecode_updateLinear(x_p(:,n), W_p(:,:,n), dN,mu,beta,fitType,gamma,HkPerm,n);
[x_p(:,n+1), W_p(:,:,n+1)] = DecodingAlgorithms.PPDecode_predict(x_u(:,n), W_u(:,:,n), A(:,:,min(size(A,3),n)), Q(:,:,min(size(Q,3),n)));
x_K=zeros(ns, lags);
W_K=zeros(ns,ns,lags);
LnMinusk=zeros(ns, ns, lags);
if(n>(lags))
for k=1:lags
LnMinusk(:,:,k)=W_u(:,:,n-k)*A(:,:,min(size(A,3),n-k))'/W_p(:,:,n+1-k);
if(k==1)
x_K(:,k) = x_u(:,n-k)+LnMinusk(:,:,k)*(x_u(:,n+1-k)-x_p(:,n+1-k));
W_K(:,:,k)=W_u(:,:,n-k)+LnMinusk(:,:,k)*(W_u(:,:,n+1-k)-W_p(:,:,n+1-k))*LnMinusk(:,:,k)';
else
x_K(:,k) = x_u(:,n-k)+LnMinusk(:,:,k)*(x_K(:,k-1)-x_p(:,n+1-k));
W_K(:,:,k)=W_u(:,:,n-k)+LnMinusk(:,:,k)*(W_K(:,:,k-1)-W_p(:,:,n+1-k))*LnMinusk(:,:,k)';
end
W_K(:,:,k) = 0.5*(W_K(:,:,k)+W_K(:,:,k)');
end
end
x_uLag(:,n)=x_K(:,lags);
W_uLag(:,:,n)=W_K(:,:,lags);
if(lags>1)
x_pLag(:,n+1)=x_K(:,lags-1);
W_pLag(:,:,n+1)=W_K(:,:,lags);
else
x_pLag(:,n+1)=x_u(:,n);
W_pLag(:,:,n+1)=W_u(:,:,n);
end
end
end
% PPAF Prediction Step
function [x_p, W_p] = PPDecode_predict(x_u, W_u, A, Q,Wconv)
if((nargin<5)||isempty(Wconv))
Wconv=[];
end
% The PPDecode prediction step
x_p = A * x_u;
if(isempty(Wconv))
W_p = A * W_u * A' + Q;
condNum=rcond(W_p);
if(condNum<eps || isa(condNum,'nan'));
W_p=W_u;
end
else
W_p = Wconv;
end
W_p = 0.5*(W_p+W_p');
end
% PPAF Update Step
%PPDecode_update takes in an object of class CIF
function [x_u, W_u,lambdaDeltaMat] = PPDecode_update(x_p, W_p, dN,lambdaIn,binwidth,time_index,WuConv)
% The PPDecode update step that finds the state estimate based on new
% data
%Original Code
if(nargin<7||isempty(WuConv))
WuConv=[];
end
clear lambda;
if(isa(lambdaIn,'cell'))
lambda = lambdaIn;
elseif(isa(lambdaIn,'CIF'))
lambda{1} = lambdaIn;
else
error('Lambda must be a cell of CIFs or a CIF');
end
clear gradientMat lambdaDeltaMat;
sumValVec=zeros(size(W_p,1),1);
sumValMat=zeros(size(W_p,2),size(W_p,2));
lambdaDeltaMat = zeros(length(lambda),1);
for C=1:length(lambda)
if(isempty(lambda{C}.historyMat))
spikeTimes =(find(dN(C,:)==1)-1)*binwidth;
nst = nspikeTrain(spikeTimes);
nst.resample(1/binwidth);
lambdaDeltaMat(C,1) = lambda{C}.evalLambdaDelta(x_p,time_index,nst);
sumValVec = sumValVec+dN(C,end)*lambda{C}.evalGradientLog(x_p,time_index,nst)'-lambda{C}.evalGradient(x_p,time_index,nst)';
sumValMat = sumValMat-dN(C,end)*lambda{C}.evalJacobianLog(x_p,time_index,nst)'+lambda{C}.evalJacobian(x_p,time_index,nst)';
else % we already have computed the history effect and can just use it - much faster
lambdaDeltaMat(C,1) = lambda{C}.evalLambdaDelta(x_p,time_index);
sumValVec = sumValVec+dN(C,end)*lambda{C}.evalGradientLog(x_p,time_index)'-lambda{C}.evalGradient(x_p,time_index)';
sumValMat = sumValMat-dN(C,end)*lambda{C}.evalJacobianLog(x_p,time_index)'+lambda{C}.evalJacobian(x_p,time_index)';
end
end
% Use pinv so that we do a SVD and ignore the zero singular values
% Sometimes because of the state space model definition and how information
% is integrated from distinct CIFs the sumValMat is very sparse. This
% allows us to prevent inverting singular matrices
if(isempty(WuConv))
% invWp = pinv(W_p);
% invWu = invWp + sumValMat;
% invWu = 0.5*(invWu+invWu');
% Wu = pinv(invWu);
I=eye(size(W_p));
Wu=W_p*(I-(I+sumValMat*W_p)\(sumValMat*W_p));
% Make sure that the update covariate is positive definite.
% W_u=nearestSPD(Wu);
W_u=Wu;
W_u=0.5*(W_u+W_u');
else
W_u=0.5*(WuConv+WuConv');
end
x_u = x_p + W_u*(sumValVec);
end
%PPDecode_updateLinear takes in a linear representation of the CIF
%(much faster)
function [x_u, W_u,lambdaDeltaMat] = PPDecode_updateLinear(x_p, W_p, dN,mu,beta,fitType,gamma,HkAll,time_index,WuConv)
C = size(dN,1); % N time samples, C cells
if(nargin<10|| isempty(WuConv))
WuConv=[];
end
if(nargin<9 || isempty(time_index))
time_index=1;
end
if(nargin<8 || isempty(HkAll))
[C,N]=size(dN);
numWindows = size(HkAll,2);
HkAll = zeros(N,numWindows,C);
% HkAll=cell(C,1);
% for c=1:C
% HkAll{c}=0;
% end
end
if(nargin<7 || isempty(gamma))
gamma=zeros(1,C);
end
if(nargin<6 || isempty(fitType))
fitType = 'poisson';
end
sumValVec=zeros(size(W_p,1),1);
sumValMat=zeros(size(W_p,2),size(W_p,2));
lambdaDeltaMat = zeros(C,1);
if(numel(gamma)==1 && gamma==0)
gamma = zeros(size(mu))';
end
if(strcmp(fitType,'binomial'))
% Histtermperm = permute(HkAll,[2 3 1]); need to send it a
% permuted version of HkAll
Histterm = HkAll(:,:,time_index);
if(size(Histterm,2)~=size(mu,1))
Histterm=Histterm';
end
linTerm = mu+beta'*x_p + diag(gamma'*Histterm);
lambdaDeltaMat = exp(linTerm)./(1+exp(linTerm));
if(any(isnan(lambdaDeltaMat))||any(isinf(lambdaDeltaMat)))
indNan = isnan(lambdaDeltaMat);
indInf = isinf(lambdaDeltaMat);
lambdaDeltaMat(indNan)=1;
lambdaDeltaMat(indInf)=1;
end
sumValVec=sum(repmat(((dN(:,time_index)-lambdaDeltaMat(:,1)).*(1-lambdaDeltaMat(:,1)))',size(beta,1),1).*beta,2);
tempVec = ((dN(:,time_index)+(1-2*(lambdaDeltaMat(:,1)))).*(1-(lambdaDeltaMat(:,1))).*(lambdaDeltaMat(:,1)))';
% tempVec((tempVec<0))=0;
% tempVec((tempVec>1))=1;
sumValMat = (repmat(tempVec,size(beta,1),1).*beta)*beta';
elseif(strcmp(fitType,'poisson'))
Histterm = HkAll(:,:,time_index);
if(~any(gamma~=0))
Histterm = Histterm';
end
if(size(Histterm,2)~=size(mu,1))
Histterm=Histterm';
end
linTerm = mu+beta'*x_p + diag(gamma'*Histterm);
lambdaDeltaMat = exp(linTerm);
if(any(isnan(lambdaDeltaMat))||any(isinf(lambdaDeltaMat)))
indNan = isnan(lambdaDeltaMat);
indInf = isinf(lambdaDeltaMat);
lambdaDeltaMat(indNan)=1;
lambdaDeltaMat(indInf)=1;
end
sumValVec=sum(repmat(((dN(:,time_index)-lambdaDeltaMat(:,1)))',size(beta,1),1).*beta,2);
sumValMat = (repmat(lambdaDeltaMat(:,1)',size(beta,1),1).*beta)*beta';
end
if(isempty(WuConv))
usePInv=0;
if(usePInv==1)
% Use pinv so that we do a SVD and ignore the zero singular values
% Sometimes because of the state space model definition and how information
% is integrated from distinct CIFs the sumValMat is very sparse. This
% allows us to prevent inverting singular matrices
I=eye(size(W_p));
Wu=W_p*(I-(I+sumValMat*W_p)\(sumValMat*W_p));
condNum=rcond(Wu);
if(condNum<eps || isa(condNum,'nan'));
Wu=W_p;
end
else
I=eye(size(W_p));
Wu=W_p*(I-(I+sumValMat*W_p)\(sumValMat*W_p));
condNum=rcond(Wu);
if(condNum<eps || isa(condNum,'nan'));
Wu=W_p;
end
end
% Make sure that the update covariance is positive definite.
% W_u=nearestSPD(Wu);
W_u = Wu;
W_u=0.5*(W_u+W_u');
else
W_u = WuConv;
W_u=0.5*(W_u+W_u');
end
% figure(10); subplot(1,3,2);imagesc(W_u); pause(0.005);
x_u = x_p + W_u*(sumValVec);
end
%% Point Process Hybrid Filter
function [S_est, X, W, MU_u, X_s, W_s,pNGivenS]= PPHybridFilterLinear(A, Q, p_ij,Mu0, dN,mu,beta,fitType,binwidth,gamma,windowTimes,x0,Pi0, yT,PiT,estimateTarget,MinClassificationError)
% General-purpose filter design for neural prosthetic devices.
% Srinivasan L, Eden UT, Mitter SK, Brown EN.
% J Neurophysiol. 2007 Oct;98(4):2456-75. Epub 2007 May 23.
[C,N] = size(dN); % N time samples, C cells
nmodels = length(A);
for s=1:nmodels
ns(s)=size(A{s},1); % number of states
end
nsMax = max(ns);
if(nargin<17 || isempty(MinClassificationError))
MinClassificationError=0; %0: chooses the most probable discrete state estimate and take the
% probability weighted average
% of the continous states. This
% is the approximate MMSE
% filter.
%1: takes the most likely discrete state estimate and also the
% continuous states
% corresponding to the most
% likely discrete state model.
% This is approximately the
% Maximum Likelihood Filter
end
if(nargin<16 || isempty(estimateTarget))
estimateTarget=0;
end
if(nargin<15 || isempty(PiT))
for s=1:nmodels
if(estimateTarget==1)
PiT{s} = zeros(size(Q{s}));
else
PiT{s} = 0*diag(ones(ns(s),1))*1e-6;
end
end
end
if(nargin<13 || isempty(Pi0))
for s=1:nmodels
Pi0{s}(:,:) = zeros(ns(s),ns(s));
end
end
if(nargin<14 || isempty(yT))
for s=1:nmodels
yT{s}=[];
Amat{s} = A{s};
Qmat{s} = Q{s};
ft{s} = zeros(size(Amat{s},2),N);
PiT{s} = zeros(size(Q{s}));
betaNew{s} = beta;
end
beta = betaNew;
else
Pi0new=cell(1,nmodels);
for s=1:nmodels
PitT{s}= zeros(ns(s),ns(s),N); % Pi(t,T) in Srinivasan et al.
QT{s} = zeros(ns(s),ns(s),N); % The noise covaraince given target observation (Q_t)
if(estimateTarget==1)
PitT{s}(:,:,N)=Q{s}; % Pi(T,T)=Pi_T + Q_T, setting PiT=0
else
PitT{s}(:,:,N)=PiT{s}+Q{s};
end
PhitT{s} = zeros(ns(s),ns(s),N);% phi(t,T) - transition matrix from time T to t
% PhiTt = zeros(ns,ns,N);% phi(T,t) - transition matrix from time t to T
PhitT{s}(:,:,N) = eye(ns(s),ns(s)); % phi(T,T) = I
B{s} = zeros(ns(s),ns(s),N); % See Equation 2.21 in Srinivasan et. al
for n=N:-1:2
if(rcond(A{s})<1000*eps)
invA=pinv(A{s});
else
invA=eye(size(A{s}))/A{s};
end
% state transition matrix
PhitT{s}(:,:,n-1)= invA*PhitT{s}(:,:,n);
% PhiTt(:,:,n)= A^(N-n);