Optimal Encoding and Decoding for Point Process Observations: an Approximate Closed-Form Filter
This work addresses a fundamental challenge in Computational Neuroscience by offering a closed-form filter for optimal encoding and decoding, though it is incremental as it builds on existing Bayesian methods with specific distributional assumptions.
The authors tackled the intractable problem of dynamic state estimation from point process observations by developing an analytically tractable Bayesian approximation, which demonstrated quality comparable to particle filtering in numerical comparisons and provided insights consistent with biological sensory cell distributions.
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.