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Second Order Dimensionality Reduction Using Minimum and Maximum Mutual Information Models

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  • Jeffrey D Fitzgerald
  • Ryan J Rowekamp
  • Lawrence C Sincich
  • Tatyana O Sharpee

Abstract

Conventional methods used to characterize multidimensional neural feature selectivity, such as spike-triggered covariance (STC) or maximally informative dimensions (MID), are limited to Gaussian stimuli or are only able to identify a small number of features due to the curse of dimensionality. To overcome these issues, we propose two new dimensionality reduction methods that use minimum and maximum information models. These methods are information theoretic extensions of STC that can be used with non-Gaussian stimulus distributions to find relevant linear subspaces of arbitrary dimensionality. We compare these new methods to the conventional methods in two ways: with biologically-inspired simulated neurons responding to natural images and with recordings from macaque retinal and thalamic cells responding to naturalistic time-varying stimuli. With non-Gaussian stimuli, the minimum and maximum information methods significantly outperform STC in all cases, whereas MID performs best in the regime of low dimensional feature spaces. Author Summary: Neurons are capable of simultaneously encoding information about multiple features of sensory stimuli in their spikes. The dimensionality reduction methods that currently exist to extract those relevant features are either biased for non-Gaussian stimuli or fall victim to the curse of dimensionality. In this paper we introduce two information theoretic extensions of the spike-triggered covariance method. These new methods use the concepts of minimum and maximum mutual information to identify the stimulus features encoded in the spikes of a neuron. Using simulated and experimental neural data, these methods are shown to perform well both in situations where conventional approaches are appropriate and where they fail. These new techniques should improve the characterization of neural feature selectivity in areas of the brain where the application of currently available approaches is restricted.

Suggested Citation

  • Jeffrey D Fitzgerald & Ryan J Rowekamp & Lawrence C Sincich & Tatyana O Sharpee, 2011. "Second Order Dimensionality Reduction Using Minimum and Maximum Mutual Information Models," PLOS Computational Biology, Public Library of Science, vol. 7(10), pages 1-9, October.
    • Handle: RePEc:plo:pcbi00:1002249
    DOI: 10.1371/journal.pcbi.1002249
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    References listed on IDEAS

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    1. Yan Karklin & Michael S. Lewicki, 2009. "Emergence of complex cell properties by learning to generalize in natural scenes," Nature, Nature, vol. 457(7225), pages 83-86, January.
    2. Miguel Maravall & Rasmus S Petersen & Adrienne L Fairhall & Ehsan Arabzadeh & Mathew E Diamond, 2007. "Shifts in Coding Properties and Maintenance of Information Transmission during Adaptation in Barrel Cortex," PLOS Biology, Public Library of Science, vol. 5(2), pages 1-12, January.
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    Cited by:

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    3. Lucas Theis & Andrè Maia Chagas & Daniel Arnstein & Cornelius Schwarz & Matthias Bethge, 2013. "Beyond GLMs: A Generative Mixture Modeling Approach to Neural System Identification," PLOS Computational Biology, Public Library of Science, vol. 9(11), pages 1-9, November.
    4. Ross S Williamson & Maneesh Sahani & Jonathan W Pillow, 2015. "The Equivalence of Information-Theoretic and Likelihood-Based Methods for Neural Dimensionality Reduction," PLOS Computational Biology, Public Library of Science, vol. 11(4), pages 1-31, April.
    5. Jian K Liu & Tim Gollisch, 2015. "Spike-Triggered Covariance Analysis Reveals Phenomenological Diversity of Contrast Adaptation in the Retina," PLOS Computational Biology, Public Library of Science, vol. 11(7), pages 1-30, July.
    6. Johnatan Aljadeff & Ronen Segev & Michael J Berry II & Tatyana O Sharpee, 2013. "Spike Triggered Covariance in Strongly Correlated Gaussian Stimuli," PLOS Computational Biology, Public Library of Science, vol. 9(9), pages 1-12, September.
    7. James M McFarland & Yuwei Cui & Daniel A Butts, 2013. "Inferring Nonlinear Neuronal Computation Based on Physiologically Plausible Inputs," PLOS Computational Biology, Public Library of Science, vol. 9(7), pages 1-18, July.

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