Finding Optimal Diverse Feature Sets with Alternative Feature Selection

TL;DR

This paper introduces a formal framework for finding multiple diverse feature sets with similar predictive performance, addressing the limitation of traditional methods that produce only one feature set.

Contribution

It formalizes alternative feature selection as an optimization problem, proposes solver-based methods, analyzes complexity, and evaluates the approach on multiple datasets.

Findings

Alternative feature sets can achieve high prediction quality.

The optimization problem is NP-hard but admits constant-factor approximations.

Heuristic search methods effectively find diverse feature sets.

Abstract

Feature selection is popular for obtaining small, interpretable, yet highly accurate prediction models. Conventional feature-selection methods typically yield one feature set only, which might not suffice in some scenarios. For example, users might be interested in finding alternative feature sets with similar prediction quality, offering different explanations of the data. In this article, we introduce alternative feature selection and formalize it as an optimization problem. In particular, we define alternatives via constraints and enable users to control the number and dissimilarity of alternatives. We consider sequential as well as simultaneous search for alternatives. Next, we discuss how to integrate conventional feature-selection methods as objectives. In particular, we describe solver-based search methods to tackle the optimization problem. Further, we analyze the complexity of this optimization problem and prove NP-hardness. Additionally, we show that a constant-factor approximation exists under certain conditions and propose corresponding heuristic search methods. Finally, we evaluate alternative feature selection in comprehensive experiments with 30 binary-classification datasets. We observe that alternative feature sets may indeed have high prediction quality, and we analyze factors influencing this outcome.