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Time-rescaling methods for the estimation and assessment of non-Poisson neural encoding models
Jonathan W Pillow

Wed Dec 09 07:00 PM -- 11:59 PM (PST) @ None #None
Recent work on the statistical modeling of neural responses has focused on modulated renewal processes in which the spike rate is a function of the stimulus and recent spiking history. Typically, these models incorporate spike-history dependencies via either: (A) a conditionally-Poisson process with rate dependent on a linear projection of the spike train history (e.g., generalized linear model); or (B) a modulated non-Poisson renewal process (e.g., inhomogeneous gamma process). Here we show that the two approaches can be combined, resulting in a {\it conditional renewal} (CR) model for neural spike trains. This model captures both real and rescaled-time effects, and can be fit by maximum likelihood using a simple application of the time-rescaling theorem [1]. We show that for any modulated renewal process model, the log-likelihood is concave in the linear filter parameters only under certain restrictive conditions on the renewal density (ruling out many popular choices, e.g. gamma with $\kappa \neq1$), suggesting that real-time history effects are easier to estimate than non-Poisson renewal properties. Moreover, we show that goodness-of-fit tests based on the time-rescaling theorem [1] quantify relative-time effects, but do not reliably assess accuracy in spike prediction or stimulus-response modeling. We illustrate the CR model with applications to both real and simulated neural data.

Author Information

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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