Information-theoretic Feature Selection via Tensor Decomposition and Submodularity

TL;DR

This paper introduces a novel feature selection method that leverages tensor decomposition and submodularity to efficiently maximize high-order mutual information, improving prediction performance while reducing computational complexity.

Contribution

It proposes a low-rank tensor model of the joint probability distribution and formulates feature selection as a submodular maximization problem with theoretical guarantees.

Findings

Outperforms state-of-the-art methods on standard datasets

Reduces complexity of high-order mutual information estimation

Provides a greedy algorithm with performance guarantees

Abstract

Feature selection by maximizing high-order mutual information between the selected feature vector and a target variable is the gold standard in terms of selecting the best subset of relevant features that maximizes the performance of prediction models. However, such an approach typically requires knowledge of the multivariate probability distribution of all features and the target, and involves a challenging combinatorial optimization problem. Recent work has shown that any joint Probability Mass Function (PMF) can be represented as a naive Bayes model, via Canonical Polyadic (tensor rank) Decomposition. In this paper, we introduce a low-rank tensor model of the joint PMF of all variables and indirect targeting as a way of mitigating complexity and maximizing the classification performance for a given number of features. Through low-rank modeling of the joint PMF, it is possible to circumvent the curse of dimensionality by learning principal components of the joint distribution. By indirectly aiming to predict the latent variable of the naive Bayes model instead of the original target variable, it is possible to formulate the feature selection problem as maximization of a monotone submodular function subject to a cardinality constraint - which can be tackled using a greedy algorithm that comes with performance guarantees. Numerical experiments with several standard datasets suggest that the proposed approach compares favorably to the state-of-art for this important problem.