eprintid: 10080256 rev_number: 25 eprint_status: archive userid: 608 dir: disk0/10/08/02/56 datestamp: 2019-11-14 15:32:01 lastmod: 2021-12-06 00:17:52 status_changed: 2019-11-14 15:32:01 type: article metadata_visibility: show creators_name: Williamson, RS creators_name: Sahani, M creators_name: Pillow, JW title: The Equivalence of Information-Theoretic and Likelihood-Based Methods for Neural Dimensionality Reduction ispublished: pub divisions: UCL divisions: B02 divisions: C08 divisions: D76 keywords: Neurons, Statistical models, Covariance, Entropy, Linear filters, Probability distribution, Macaque, Optimization note: 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 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. date: 2015-04-01 date_type: published publisher: PUBLIC LIBRARY SCIENCE official_url: https://doi.org/10.1371/journal.pcbi.1004141 oa_status: green full_text_type: pub language: eng primo: open primo_central: open_green verified: verified_manual elements_id: 895404 doi: 10.1371/journal.pcbi.1004141 lyricists_name: Sahani, Maneesh lyricists_id: MSAHA91 actors_name: Flynn, Bernadette actors_id: BFFLY94 actors_role: owner full_text_status: public publication: PLOS Computational Biology volume: 11 number: 4 article_number: e1004141 pages: 31 citation: Williamson, RS; Sahani, M; Pillow, JW; (2015) The Equivalence of Information-Theoretic and Likelihood-Based Methods for Neural Dimensionality Reduction. PLOS Computational Biology , 11 (4) , Article e1004141. 10.1371/journal.pcbi.1004141 <https://doi.org/10.1371/journal.pcbi.1004141>. Green open access document_url: https://discovery.ucl.ac.uk/id/eprint/10080256/1/journal.pcbi.1007139.s001.PDF