VLR - variational inference for low-rank STRFs

This repository contains a Matlab toolbox for inferring approximate posterior estimates of the temporal and spatial components of a spatio-temporal receptive field (STRF) with low-rank structure. To cite this code, please refer to our paper

@article{duncker2023scalable,
  title={Scalable Variational Inference for Low-Rank Spatiotemporal Receptive Fields},
  author={Duncker, Lea and Ruda, Kiersten M and Field, Greg D and Pillow, Jonathan W},
  journal={Neural Computation},
  volume={35},
  number={6},
  pages={995--1027},
  year={2023},
  publisher={MIT Press}
}

Code Usage

Data Format

The toolbox expects data input in the form of a response vector Y and a stimulus X. For N samples, Y is an N x 1 vector and X is an N x D matrix, where D is the total number of stimulus coeffients. The spatial receptive field dimensions will need to match those of the stimulus. For example, for an image with D=800 total coefficients and dimensions nkx1 = 20 and nkx2 = 40, the spatial receptive field would have dimensions RFdims = [nkx1 nkx2].

The code also requires specifying the length of a single time bin (dtbin), the total extent of the temporal receptive field both in terms of the number of coefficients (nkt) and in units of time (tmax), and a minimum temporal lengthscale (minlen_t in units of time).

Specifiying Priors

Since the code implements maximum aposterior estimation for receptive fields with low-rank structure, the first step is to define a covariance function and specify which prior to use for the temporal and spatial components of the STRF. The toolbox contains a number of commonly used priors for hierarchical receptive field estimation, which can be combined in a flexible way. The available covariance functions, their names in the toolbox, and implied prior assumptions are summarized below

prior covariance	name	receptive field component	assumptions about receptive field	Reference
Automatic Smoothness Determination	ASD	spatial, temporal	receptive field varies smoothly over its coefficients	[2]
Autmatic Locality Determination	ALD	spatial	receptive field varies smoothly and its non-zero coefficeints are localized	[3]
Temporal Recency Determination	TRD	temporal	receptive field smoothness increases with extent in time (non-stationary smoothness)	[1]
Ridge Regression	RR	spatial, temporal	uncorrelated RF coefficients

To build an ALD prior for the spatial component of the receptive field, and a TRD prior for the temporal component, you can call the following code

% build prior for spatial receptive field
RFdims = [nkx1 nkx2];
spatPrior = build_vlrPrior('ALD',RFdims);

% build prior for temporal receptive field
minlen_t = 5*dtbin;  % minimum temporal lengthscale (in s)
tempPrior = build_vlrPrior('TRD',nkt,minlen_t,tmax);

To initialise the hyperparameters of the priors based on an estimate of the spike-triggered-average kSTA of dimensions nkt x D , call

[tempPrior, spatPrior] = initialiseHprs_vlrPriors(kSTA,tempPrior,spatPrior);

Building the model

After having specified the priors for each receptive field component, a model for a spatio-temporal receptive field with rank rnk can be built by calling

opts = []; % use default options
rnk = 2; % specify rank of STRF
% build model structure
mdl = build_vlrModel(Y,X,rnk,spatPrior,tempPrior,opts);

This also computes the sufficient statistics of the input data, so it might take longer for large sample sizes.

Optimizing the model

The model structure mdl contains initial estimates for the hyperparameters and receptive field components. In order to find the maximum aposteriori estimate, run variational Expectation Maximisation (vEM) by calling

mdl = fit_vlrModel(mdl);

Final STRF estimate

Finally, one can obtain a full-sized STRF estimate kMAP from the optimized model structure by calling

[mutHat,muxHat]  = getSTRF_vlrModel(mdl);
kMAP = mutHat*muxHat';

mutHat and muxHat are the orthogonalised temporal and spatial receptive field components, respectively.

Further examples on how to use the code are provided in the demos folder.

References:

[1] L Duncker, JW Pillow. Scalable variational inference for low-rank spatio-temporal receptive fields. Neural Computation. 2023.

[2] M Sahani, and J F Linden. Evidence optimization techniques for estimating stimulus-response functions. Advances in neural information processing systems. 2003.

[3] M Park and J W Pillow, Receptive field inference with localized priors. PLoS computational biology, 7(10), 2011, p.e1002219.