Optimal Encoding and Decoding for Point Process Observations: an Approximate Closed-Form Filter

TL;DR

This paper introduces an analytically tractable Bayesian approximation for optimal filtering with point process observations, providing insights into encoding strategies relevant to computational neuroscience.

Contribution

It develops a novel closed-form filter that simplifies analysis of optimal encoding and decoding, surpassing traditional numerical methods in interpretability.

Findings

Approximate filter closely matches particle filtering results

Framework offers new insights into sensory cell tuning

Supports biological observations of sensory encoding

Abstract

The process of dynamic state estimation (filtering) based on point process observations is in general intractable. Numerical sampling techniques are often practically useful, but lead to limited conceptual insight about optimal encoding/decoding strategies, which are of significant relevance to Computational Neuroscience. We develop an analytically tractable Bayesian approximation to optimal filtering based on point process observations, which allows us to introduce distributional assumptions about sensor properties, that greatly facilitate the analysis of optimal encoding in situations deviating from common assumptions of uniform coding. Numerical comparison with particle filtering demonstrate the quality of the approximation. The analytic framework leads to insights which are difficult to obtain from numerical algorithms, and is consistent with biological observations about the distribution of sensory cells' tuning curve centers.