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Beyond GLMs: A Generative Mixture Modeling Approach to Neural System Identification

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  • Lucas Theis
  • Andrè Maia Chagas
  • Daniel Arnstein
  • Cornelius Schwarz
  • Matthias Bethge

Abstract

Generalized linear models (GLMs) represent a popular choice for the probabilistic characterization of neural spike responses. While GLMs are attractive for their computational tractability, they also impose strong assumptions and thus only allow for a limited range of stimulus-response relationships to be discovered. Alternative approaches exist that make only very weak assumptions but scale poorly to high-dimensional stimulus spaces. Here we seek an approach which can gracefully interpolate between the two extremes. We extend two frequently used special cases of the GLM—a linear and a quadratic model—by assuming that the spike-triggered and non-spike-triggered distributions can be adequately represented using Gaussian mixtures. Because we derive the model from a generative perspective, its components are easy to interpret as they correspond to, for example, the spike-triggered distribution and the interspike interval distribution. The model is able to capture complex dependencies on high-dimensional stimuli with far fewer parameters than other approaches such as histogram-based methods. The added flexibility comes at the cost of a non-concave log-likelihood. We show that in practice this does not have to be an issue and the mixture-based model is able to outperform generalized linear and quadratic models.Author Summary: An essential goal of sensory systems neuroscience is to characterize the functional relationship between neural responses and external stimuli. Of particular interest are the nonlinear response properties of single cells. Inherently linear approaches such as generalized linear modeling can nevertheless be used to fit nonlinear behavior by choosing an appropriate feature space for the stimulus. This requires, however, that one has already obtained a good understanding of a cells nonlinear properties, whereas more flexible approaches are necessary for the characterization of unexpected nonlinear behavior. In this work, we present a generalization of some frequently used generalized linear models which enables us to automatically extract complex stimulus-response relationships from recorded data. We show that our model can lead to substantial quantitative and qualitative improvements over generalized linear and quadratic models, which we illustrate on the example of primary afferents of the rat whisker system.

Suggested Citation

  • 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.
  • Handle: RePEc:plo:pcbi00:1003356
    DOI: 10.1371/journal.pcbi.1003356
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    References listed on IDEAS

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    1. 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.
    2. 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.
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    Cited by:

    1. Sepp Kollmorgen & Richard H R Hahnloser, 2014. "Dynamic Alignment Models for Neural Coding," PLOS Computational Biology, Public Library of Science, vol. 10(3), pages 1-19, March.
    2. Ivar L Thorson & Jean Liénard & Stephen V David, 2015. "The Essential Complexity of Auditory Receptive Fields," PLOS Computational Biology, Public Library of Science, vol. 11(12), pages 1-33, December.
    3. 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.

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