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

Ross S Williamson; Maneesh Sahani; Jonathan W Pillow

doi:10.1371/journal.pcbi.1004141

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

PLoS Comput Biol. 2015 Apr 1;11(4):e1004141. doi: 10.1371/journal.pcbi.1004141. eCollection 2015 Apr.

Authors

Ross S Williamson¹, Maneesh Sahani², Jonathan W Pillow³

Affiliations

¹ Gatsby Computational Neuroscience Unit, University College London, London, UK; Centre for Mathematics and Physics in the Life Sciences and Experimental Biology, University College London, London, UK.
² Gatsby Computational Neuroscience Unit, University College London, London, UK.
³ Princeton Neuroscience Institute, Department of Psychology, Princeton University, Princeton, New Jersey, USA.

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.

Publication types

Comparative Study
Research Support, Non-U.S. Gov't
Research Support, U.S. Gov't, Non-P.H.S.

MeSH terms

Action Potentials / physiology*
Animals
Computer Simulation
Humans
Information Theory
Likelihood Functions*
Models, Neurological*
Models, Statistical*
Neurons / physiology*
Synaptic Transmission / physiology*

Grants and funding

This work was supported by the Engineering and Physical Sciences Research Council (support for RSW through the CoMPLEX Doctoral Training Program), the Gatsby Charitable Foundation (Gatsby Computational Neuroscience Unit support to RSW and MS) and Sloan Fellowship, McKnight Scholar’s award, and NSF CAREER award IIS-1150186 (support to JWP). The funders had no role in study design, data collection and analysis, decision to publish, or preparation of the manuscript.