Information loss in an optimal maximum likelihood decoding

TL;DR

This paper quantifies the information loss in neural decoding when using maximum likelihood methods, showing that small distortions cause quadratic loss in mutual information.

Contribution

It introduces a framework to measure information loss due to decoding distortions and characterizes its quadratic dependence on small probability distortions.

Findings

Information loss is quadratic for slight probability distortions.

The decoding process can be viewed as an artificial distortion of joint probabilities.

Quantitative measures of information loss are provided.

Abstract

The mutual information between a set of stimuli and the elicited neural responses is compared to the corresponding decoded information. The decoding procedure is presented as an artificial distortion of the joint probabilities between stimuli and responses. The information loss is quantified. Whenever the probabilities are only slightly distorted, the information loss is shown to be quadratic in the distortion