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The Equivalence of Information-Theoretic and Likelihood-Based Methods for Neural Dimensionality Reduction

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 in...

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Autores principales: Williamson, Ross S., Sahani, Maneesh, Pillow, Jonathan W.
Formato: Online Artículo Texto
Lenguaje:English
Publicado: Public Library of Science 2015
Materias:
Acceso en línea:https://www.ncbi.nlm.nih.gov/pmc/articles/PMC4382343/
https://www.ncbi.nlm.nih.gov/pubmed/25831448
http://dx.doi.org/10.1371/journal.pcbi.1004141
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author Williamson, Ross S.
Sahani, Maneesh
Pillow, Jonathan W.
author_facet Williamson, Ross S.
Sahani, Maneesh
Pillow, Jonathan W.
author_sort Williamson, Ross S.
collection PubMed
description 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.
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spelling pubmed-43823432015-04-09 The Equivalence of Information-Theoretic and Likelihood-Based Methods for Neural Dimensionality Reduction Williamson, Ross S. Sahani, Maneesh Pillow, Jonathan W. PLoS Comput Biol Research Article 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. Public Library of Science 2015-04-01 /pmc/articles/PMC4382343/ /pubmed/25831448 http://dx.doi.org/10.1371/journal.pcbi.1004141 Text en © 2015 Williamson et al http://creativecommons.org/licenses/by/4.0/ This is an open-access article distributed under the terms of the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original author and source are properly credited.
spellingShingle Research Article
Williamson, Ross S.
Sahani, Maneesh
Pillow, Jonathan W.
The Equivalence of Information-Theoretic and Likelihood-Based Methods for Neural Dimensionality Reduction
title The Equivalence of Information-Theoretic and Likelihood-Based Methods for Neural Dimensionality Reduction
title_full The Equivalence of Information-Theoretic and Likelihood-Based Methods for Neural Dimensionality Reduction
title_fullStr The Equivalence of Information-Theoretic and Likelihood-Based Methods for Neural Dimensionality Reduction
title_full_unstemmed The Equivalence of Information-Theoretic and Likelihood-Based Methods for Neural Dimensionality Reduction
title_short The Equivalence of Information-Theoretic and Likelihood-Based Methods for Neural Dimensionality Reduction
title_sort equivalence of information-theoretic and likelihood-based methods for neural dimensionality reduction
topic Research Article
url https://www.ncbi.nlm.nih.gov/pmc/articles/PMC4382343/
https://www.ncbi.nlm.nih.gov/pubmed/25831448
http://dx.doi.org/10.1371/journal.pcbi.1004141
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