# Estimation of mutual information for real-valued data with error bars and controlled bias

## TL;DR

This paper enhances mutual information estimation for real-valued data by expanding applicability, providing bias verification, variance estimation, and parameter selection, with demonstrations on synthetic and biological data.

## Contribution

It introduces improvements to the Kraskov estimator, including bias control, variance estimation, and applicability expansion, with validation on diverse datasets.

## Key findings

- Improved estimator with controlled bias and variance.
- Effective on synthetic, neurophysiological, and systems biology data.
- Provides a criterion for optimal parameter selection.

## Abstract

Estimation of mutual information between (multidimensional) real-valued variables is used in analysis of complex systems, biological systems, and recently also quantum systems. This estimation is a hard problem, and universally good estimators provably do not exist. Kraskov et al. (PRE, 2004) introduced a successful mutual information estimation approach based on the statistics of distances between neighboring data points, which empirically works for a wide class of underlying probability distributions. Here we improve this estimator by (i) expanding its range of applicability, and by providing (ii) a self-consistent way of verifying the absence of bias, (iii) a method for estimation of its variance, and (iv) a criterion for choosing the values of the free parameter of the estimator. We demonstrate the performance of our estimator on synthetic data sets, as well as on neurophysiological and systems biology data sets.