An information-theoretic generalization of spike-triggered average and covariance analysis

J W Pillow and E P Simoncelli

Published in Computational and Systems Neuroscience (CoSyNe), (II-153), Mar 2006.
One of the central problems in sensory neuroscience is that of characterizing the neural code: the mapping from sensory stimuli to spike responses. Recent work has sought to address this problem with the use of statistical tools for dimensionality reduction. A simple intuition underlies these methods: although the space of all stimuli (e.g. the space of all images) is enormous, most attributes of these stimuli do not have any effect on the neuron's response. We can therefore attempt to model the neural code by finding a low-dimensional feature space within which the neuron computes its response [Bialek & de Ruyter van Steveninck 05].

Two basic methods have been developed to estimate the features that define the subspace underlying a neuron's response. The first looks for changes in the mean and/or variance of the spike-triggered stimulus ensemble (i.e., the set of stimuli that elicited a spike from the neuron), relative to those of the raw stimulus ensemble, which correspond to the spike-triggered average (STA) and the eigenvectors of the spike-triggered covariance (STC) matrix [de Ruyter van Steveninck & Bialek 88, Bialek et al 91, Simoncelli et al 04, Bialek & de Ruyter van Steveninck 05]. A second method searches directly for the feature space that preserves maximal information about the response [Paninski 03, Sharpee et al, 04].

Here, we describe a framework for dimensionality reduction in neural models that occupies a middle ground between STA/STC analysis and full information maximization. We assume that the spike-triggered ensemble is completely characterized by its mean (STA) and covariance (STC), and can thus be approximated as Gaussian. We then use an information-theoretic criterion to find the relevant feature subspace. The resulting solution has several useful properties: (1) it provides a common framework for spike-triggered average and covariance analysis, incorporating the joint effects of the mean and covariance on neural response, and allowing subspace dimensions to be ranked in order of their informativeness; (2) the Gaussian assumption leads to computationally efficient and robust information maximization, and the data requirements for recovery of a linear stage of high dimensionality are relatively modest; (3) it provides an explicit "default" model of the nonlinear stage that maps the filter responses to spike rate, even in high-dimensional feature spaces; (4) it is equivalent to maximizing the likelihood of the spike train given the stimuli under the assumed model; and (5) it can be applied to novel problems, such as the estimation of a model with space-time separable filters. We demonstrate the effectiveness of the method by applying it to the recorded extracelluar responses of macaque retinal ganglion cells and V1 cells.

  • Listing of all publications