# Efficient Approximate Solutions to Mutual Information Based Global Feature Selection

## TL;DR

This paper introduces two novel global approximation algorithms, TPower and LowRank, for efficiently solving the NP-hard problem of mutual information-based feature selection under conditional independence assumptions, demonstrating superior performance.

## Contribution

The paper presents two new algorithms, TPower and LowRank, that provide effective approximations for the intractable CMI-based feature selection problem, improving over existing methods.

## Key findings

- TPower and LowRank algorithms achieve high-quality feature selection.
- Experimental results show superior performance over existing methods.
- Algorithms are effective across multiple datasets.

## Abstract

Mutual Information (MI) is often used for feature selection when developing classifier models. Estimating the MI for a subset of features is often intractable. We demonstrate, that under the assumptions of conditional independence, MI between a subset of features can be expressed as the Conditional Mutual Information (CMI) between pairs of features. But selecting features with the highest CMI turns out to be a hard combinatorial problem. In this work, we have applied two unique global methods, Truncated Power Method (TPower) and Low Rank Bilinear Approximation (LowRank), to solve the feature selection problem. These algorithms provide very good approximations to the NP-hard CMI based feature selection problem. We experimentally demonstrate the effectiveness of these procedures across multiple datasets and compare them with existing MI based global and iterative feature selection procedures.