The Equivalence of Information-Theoretic and Likelihood-Based Methods for Neural Dimensionality Reduction - Williamson, Ross S.; Sahani, Maneesh; Pillow, Jonathan W. (PLOS Computational Biology, 2015)
Author Summary A popular approach to the neural coding problem is to identify a low-dimensional linear projection of the stimulus space that preserves the aspects of the stimulus that affect a neuron’s probability of spiking. Previous work has focused on both information-theoretic and likelihood-based estimators for finding such projections. Here, we show that these two approaches are in fact equivalent. We show that maximally informative dimensions (MID), a popular information-theoretic method for dimensionality reduction, is identical to the maximum-likelihood estimator for a particular linear-nonlinear encoding model with Poisson spiking. One implication of this equivalence is that MID may not find the information-theoretically optimal stimulus projection when spiking is non-Poisson, which we illustrate with a few simple examples. Using these insights, we propose novel dimensionality-reduction methods that incorporate non-Poisson spiking, and suggest new parametrizations that allow for tractable estimation of high-dimensional subspaces.