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Characterizing neural dependencies with Poisson copula models
Pietro Berkes · Frank Wood · Jonathan W Pillow

Wed Dec 10 09:50 AM -- 09:51 AM (PST) @
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The coding of information by neural populations depends critically on the statistical dependencies between neuronal responses. However, there is no simple model that combines the observations that (1) marginal distributions over single-neuron spike counts are often approximately Poisson; and (2) joint distributions over the responses of multiple neurons are often strongly dependent. Here, we show that both marginal and joint properties of neural responses can be captured using Poisson copula models. Copulas are joint distributions that allow random variables with arbitrary marginals to be combined while incorporating arbitrary dependencies between them. Different copulas capture different kinds of dependencies, allowing for a richer and more detailed description of dependencies than traditional summary statistics, such as correlation coefficients. We explore a variety of Poisson copula models for joint neural response distributions, and derive an efficient maximum likelihood procedure for estimating them. We apply these models to neuronal data collected in and macaque motor cortex, and quantify the improvement in coding accuracy afforded by incorporating the dependency structure between pairs of neurons.

Author Information

Pietro Berkes (Brandeis University)
Frank Wood (University of British Columbia)

Dr. Wood is an associate professor in the Department of Engineering Science at the University of Oxford. Before that he was an assistant professor of Statistics at Columbia University and a research scientist at the Columbia Center for Computational Learning Systems. He formerly was a postdoctoral fellow of the Gatsby Computational Neuroscience Unit of the University College London. He holds a PhD from Brown University (’07) and BS from Cornell University (’96), both in computer science. Dr. Wood is the original architect of both the Anglican and Probabilistic-C probabilistic programming systems. He conducts AI-driven research at the boundary of probabilistic programming, Bayesian modeling, and Monte Carlo methods. Dr. Wood holds 6 patents, has authored over 50 papers, received the AISTATS best paper award in 2009, and has been awarded faculty research awards from Xerox, Google and Amazon. Prior to his academic career he was a successful entrepreneur having run and sold the content-based image retrieval company ToFish! to AOL/Time Warner and served as CEO of Interfolio.

Jonathan W Pillow (UT Austin)

Jonathan Pillow is an assistant professor in Psychology and Neurobiology at the University of Texas at Austin. He graduated from the University of Arizona in 1997 with a degree in mathematics and philosophy, and was a U.S. Fulbright fellow in Morocco in 1998. He received his Ph.D. in neuroscience from NYU in 2005, and was a Royal Society postdoctoral reserach fellow at the Gatsby Computational Neuroscience Unit, UCL from 2005 to 2008. His recent work involves statistical methods for understanding the neural code in single neurons and neural populations, and his lab conducts psychophysical experiments designed to test Bayesian models of human sensory perception.

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