A Kernel-Based Calculation of Information on a Metric Space

TL;DR

This paper introduces a kernel-based method for estimating mutual information in metric spaces, motivated by neuroscience applications, and demonstrates its effectiveness on simulated electrophysiological data.

Contribution

It presents a novel kernel density estimation technique for mutual information calculation on metric spaces, linking it to k-nearest-neighbor methods.

Findings

Kernel density estimation on metric spaces resembles k-nearest-neighbor methods.

The approach successfully applied to simulated electrophysiological data.

Provides a new tool for neuroscience data analysis.

Abstract

Kernel density estimation is a technique for approximating probability distributions. Here, it is applied to the calculation of mutual information on a metric space. This is motivated by the problem in neuroscience of calculating the mutual information between stimuli and spiking responses; the space of these responses is a metric space. It is shown that kernel density estimation on a metric space resembles the k-nearest-neighbor approach. This approach is applied to a toy dataset designed to mimic electrophysiological data.