# Feature Selection via Mutual Information: New Theoretical Insights

## TL;DR

This paper introduces new theoretical insights into mutual information for feature selection, proposing a stopping criterion for greedy algorithms that guarantees bounded prediction error, supported by simulations.

## Contribution

It provides a novel theoretical framework linking mutual information to error bounds and introduces a stopping condition for greedy feature selection algorithms.

## Key findings

- Theoretical link between mutual information and regression/classification errors.
- A new stopping criterion guarantees bounded prediction error.
- Numerical simulations validate the theoretical results.

## Abstract

Mutual information has been successfully adopted in filter feature-selection methods to assess both the relevancy of a subset of features in predicting the target variable and the redundancy with respect to other variables. However, existing algorithms are mostly heuristic and do not offer any guarantee on the proposed solution. In this paper, we provide novel theoretical results showing that conditional mutual information naturally arises when bounding the ideal regression/classification errors achieved by different subsets of features. Leveraging on these insights, we propose a novel stopping condition for backward and forward greedy methods which ensures that the ideal prediction error using the selected feature subset remains bounded by a user-specified threshold. We provide numerical simulations to support our theoretical claims and compare to common heuristic methods.