The equivalence of information-theoretic and likelihood-based methods for neural dimensionality reduction

TL;DR

This paper demonstrates that the maximally informative dimensions (MID) method in neuroscience is equivalent to maximum likelihood estimation in a linear-nonlinear-Poisson model, and extends it to non-Poisson spiking models for better stimulus feature identification.

Contribution

It establishes the equivalence between information-theoretic and likelihood-based methods for neural dimensionality reduction and introduces new model-based approaches for non-Poisson spiking statistics.

Findings

MID is a maximum-likelihood estimator for LNP models.

Empirical single-spike information aligns with Poisson log-likelihood.

New methods improve stimulus feature detection for non-Poisson neurons.

Abstract

Stimulus dimensionality-reduction methods in neuroscience seek to identify a low-dimensional space of stimulus features that affect a neuron's probability of spiking. One popular method, known as maximally informative dimensions (MID), uses an information-theoretic quantity known as "single-spike information" to identify this space. Here we examine MID from a model-based perspective. We show that MID is a maximum-likelihood estimator for the parameters of a linear-nonlinear-Poisson (LNP) model, and that the empirical single-spike information corresponds to the normalized log-likelihood under a Poisson model. This equivalence implies that MID does not necessarily find maximally informative stimulus dimensions when spiking is not well described as Poisson. We provide several examples to illustrate this shortcoming, and derive a lower bound on the information lost when spiking is Bernoulli in discrete time bins. To overcome this limitation, we introduce model-based dimensionality reduction methods for neurons with non-Poisson firing statistics, and show that they can be framed equivalently in likelihood-based or information-theoretic terms. Finally, we show how to overcome practical limitations on the number of stimulus dimensions that MID can estimate by constraining the form of the non-parametric nonlinearity in an LNP model. We illustrate these methods with simulations and data from primate visual cortex.