TY  - JOUR
EP  - 31
AV  - public
VL  - 11
Y1  - 2015/04/01/
TI  - The Equivalence of Information-Theoretic and Likelihood-Based Methods for Neural Dimensionality Reduction
N1  - Copyright © 2015 Williamson et al. This is an open access article distributed under the terms of the Creative Commons Attribution License (http://creativecommons.org/licenses/by/4.0/), which permits unrestricted use, distribution, and reproduction in any medium, provided the original author and source are credited
IS  - 4
PB  - PUBLIC LIBRARY SCIENCE
UR  - https://doi.org/10.1371/journal.pcbi.1004141
ID  - discovery10080256
N2  - 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.
KW  - Neurons
KW  -  Statistical models
KW  -  Covariance
KW  -  Entropy
KW  -  Linear filters
KW  -  Probability distribution
KW  -  Macaque
KW  -  Optimization
A1  - Williamson, RS
A1  - Sahani, M
A1  - Pillow, JW
JF  - PLOS Computational Biology
ER  -