Estimating linear-nonlinear models using Renyi divergences

Authors: Kouh, Minjoon; Sharpee, Tatyana

Source: Network: Computation in Neural Systems, Volume 20, Number 2, June 2009 , pp. 49-68(20)

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Abstract:

This article compares a family of methods for characterizing neural feature selectivity using natural stimuli in the framework of the linear-nonlinear model. In this model, the spike probability depends in a nonlinear way on a small number of stimulus dimensions. The relevant stimulus dimensions can be found by optimizing a Renyi divergence that quantifies a change in the stimulus distribution associated with the arrival of single spikes. Generally, good reconstructions can be obtained based on optimization of Renyi divergence of any order, even in the limit of small numbers of spikes. However, the smallest error is obtained when the Renyi divergence of order 1 is optimized. This type of optimization is equivalent to information maximization, and is shown to saturate the Cramer-Rao bound describing the smallest error allowed for any unbiased method. We also discuss conditions under which information maximization provides a convenient way to perform maximum likelihood estimation of linear-nonlinear models from neural data.

Keywords: information theory; natural scenes; single neuron computation; visual system

Document Type: Research article

DOI: http://dx.doi.org/10.1080/09548980902950891

Affiliations: 1: The Computational Neurobiology Laboratory, The Salk Institute for Biological Studies, La Jolla, CA,The Center for Theoretical Biological Physics, University of California, San Diego, La Jolla, CA, USA

Publication date: 2009-06-01

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