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Spike train entropy-rate estimation using hierarchical Dirichlet process priors
Karin C Knudson · Jonathan W Pillow

Sat Dec 07 07:00 PM -- 11:59 PM (PST) @ Harrah's Special Events Center, 2nd Floor

Entropy rate quantifies the amount of disorder in a stochastic process. For spiking neurons, the entropy rate places an upper bound on the rate at which the spike train can convey stimulus information, and a large literature has focused on the problem of estimating entropy rate from spike train data. Here we present Bayes Least Squares and Empirical Bayesian entropy rate estimators for binary spike trains using Hierarchical Dirichlet Process (HDP) priors. Our estimator leverages the fact that the entropy rate of an ergodic Markov Chain with known transition probabilities can be calculated analytically, and many stochastic processes that are non-Markovian can still be well approximated by Markov processes of sufficient depth. Choosing an appropriate depth of Markov model presents challenges due to possibly long time dependencies and short data sequences: a deeper model can better account for long time-dependencies, but is more difficult to infer from limited data. Our approach mitigates this difficulty by using a hierarchical prior to share statistical power across Markov chains of different depths. We present both a fully Bayesian and empirical Bayes entropy rate estimator based on this model, and demonstrate their performance on simulated and real neural spike train data.

Author Information

Karin C Knudson (UT Austin)
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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