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An analytical study of population coding of dynamic stimuli
Citation key Susemihl2011a
Author Susemihl, A.K., and Opper, M.
Year 2011
ISSN 1662-5188
DOI 10.3389/conf.fncom.2011.53.00157
Journal Front. Comput. Neurosci. Conference Abstract: BC11 : Computational Neuroscience & Neurotechnology Bernstein Conference & Neurex Annual Meeting 2011
Number 00157
Month October
Abstract Many aspects of human perception can be understood as arising from probabilistic inference. Particularly when integrating cues from different sources with different reliability humans have been observed to integrate these cues optimally in a Bayesian sense [1, 2]. Claims of optimality of the observed behavior abound, although little theoretical work has been done to establish this. Here we propose an analytical model of stimulus reconstruction from noisy spike trains, in which we are able to solve for the mean squared error of an ideal Bayesian observer. Furthermore, this is done in a time-dependent fashion which allows us to study the evolution of the error. We present analytical results for a simplified labeled-line population coding model of Poisson spiking neurons with Gaussian-shaped tuning functions. By drawing the stimuli from a Gaussian process distribution and under the assumption of strongly overlapping tuning functions, we are able to derive a time-dependent filtering scheme for the reconstruction of the stimulus. From that we find a differential equation for the mean squared error of an ideal Bayesian observer. This has been studied via direct simulation of the spike trains and a mean-field approximation. We observe the existence of a finite optimal tuning width for both cases. This has been reported before for the case of static stimuli [3]. Our findings are also consistent with findings of tuning function adaptation in primates [4]. The present work seeks to provide a comprehensive and solid approach to- wards neural coding in a dynamic framework. We believe a thorough analysis of neural coding could shed light on phenomena as tuning function adaptation and shapes of tuning functions in the context of Bayes optimality. The approach is also very flexible so that a number of systems could be investigated with it. There are some natural extensions to the present work, namely the inclusion of more complex spike generation mechanisms and the analysis of high-dimensional cases. This work provides a first step towards a mathematical and ecological theory of sensory processing.
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