Model-Augmented Estimation of Conditional Mutual Information for Feature Selection

TL;DR

This paper introduces a two-step neural network-based method for efficient Markov blanket feature selection by improving conditional independence testing in high-dimensional data.

Contribution

It proposes a novel approach combining neural network mappings with $k$-NN CI testing to enhance feature selection in high-dimensional settings.

Findings

Improved CI testing performance on synthetic data.

Effective feature selection demonstrated on real datasets.

Abstract

Markov blanket feature selection, while theoretically optimal, is generally challenging to implement. This is due to the shortcomings of existing approaches to conditional independence (CI) testing, which tend to struggle either with the curse of dimensionality or computational complexity. We propose a novel two-step approach which facilitates Markov blanket feature selection in high dimensions. First, neural networks are used to map features to low-dimensional representations. In the second step, CI testing is performed by applying the $k$-NN conditional mutual information estimator to the learned feature maps. The mappings are designed to ensure that mapped samples both preserve information and share similar information about the target variable if and only if they are close in Euclidean distance. We show that these properties boost the performance of the $k$-NN estimator in the second step. The performance of the proposed method is evaluated on both synthetic and real data.