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 "singl...
| Main Authors: | , , |
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| Format: | Article |
| Language: | English |
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Public Library of Science (PLoS)
2015-04-01
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| Series: | PLoS Computational Biology |
| Online Access: | http://europepmc.org/articles/PMC4382343?pdf=render |
| _version_ | 1811268563732791296 |
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| author | Ross S Williamson Maneesh Sahani Jonathan W Pillow |
| author_facet | Ross S Williamson Maneesh Sahani Jonathan W Pillow |
| author_sort | Ross S Williamson |
| collection | DOAJ |
| 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. |
| first_indexed | 2024-04-12T21:24:30Z |
| format | Article |
| id | doaj.art-31110d924d0d4f8485c969f8a65d025b |
| institution | Directory Open Access Journal |
| issn | 1553-734X 1553-7358 |
| language | English |
| last_indexed | 2024-04-12T21:24:30Z |
| publishDate | 2015-04-01 |
| publisher | Public Library of Science (PLoS) |
| record_format | Article |
| series | PLoS Computational Biology |
| spelling | doaj.art-31110d924d0d4f8485c969f8a65d025b2022-12-22T03:16:12ZengPublic Library of Science (PLoS)PLoS Computational Biology1553-734X1553-73582015-04-01114e100414110.1371/journal.pcbi.1004141The equivalence of information-theoretic and likelihood-based methods for neural dimensionality reduction.Ross S WilliamsonManeesh SahaniJonathan W PillowStimulus 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.http://europepmc.org/articles/PMC4382343?pdf=render |
| spellingShingle | Ross S Williamson Maneesh Sahani Jonathan W Pillow The equivalence of information-theoretic and likelihood-based methods for neural dimensionality reduction. PLoS Computational Biology |
| 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 |
| url | http://europepmc.org/articles/PMC4382343?pdf=render |
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