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Published on: July 3, 2020
Estimating linear-nonlinear models using Renyi divergences
Minjoon Kouh1, Tatyana O Sharpee
1The Computational Neurobiology Laboratory, The Salk Institute for Biological Studies, La Jolla, CA 92037, USA.
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 Rényi 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 Rényi divergence of any order, even in the limit of small numbers of spikes. However, the smallest error is obtained when the Rényi 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.
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In contrast, nonlinear systems do not inherently possess these properties. However, for small deviations around an operating point, a nonlinear system can often be approximated as linear.
