Chenghui Zheng

Chenghui Zheng, Garvesh Raskutti

Feature selection is a classical problem in statistics and machine learning, and it continues to remain an extremely challenging problem especially in the context of unknown non-linear relationships with dependent features. On the other hand, Shapley values are a classic solution concept from cooperative game theory that is widely used for feature attribution in general non-linear models with highly-dependent features. However, Shapley values are not naturally suited for feature selection since they tend to capture both direct effects from each feature to the response and indirect effects through other features. In this paper, we combine the advantages of Shapley values and adapt them to feature selection by proposing \emph{MinShap}, a modification of the Shapley value framework along with a suite of other related algorithms. In particular for MinShap, instead of taking the average marginal contributions over permutations of features, considers the minimum marginal contribution across permutations. We provide a theoretical foundation motivated by the faithfulness assumption in DAG (directed acyclic graphical models), a guarantee for the Type I error of MinShap, and show through numerical simulations and real data experiments that MinShap tends to outperform state-of-the-art feature selection algorithms such as LOCO, GCM and Lasso in terms of both accuracy and stability. We also introduce a suite of algorithms related to MinShap by using the multiple testing/p-value perspective that improves performance in lower-sample settings and provide supporting theoretical guarantees.

Chenghui Zheng, Garvesh Raskutti

Feature selection and importance estimation in a model-agnostic setting is an ongoing challenge of significant interest. Wrapper methods are commonly used because they are typically model-agnostic, even though they are computationally intensive. In this paper, we focus on feature selection methods related to the Generalized Covariance Measure (GCM) and Leave-One-Covariate-Out (LOCO) estimation, and provide a comparison based on relative efficiency. In particular, we present a theoretical comparison under three model settings: linear models, non-linear additive models, and single index models that mimic a single-layer neural network. We complement this with extensive simulations and real data examples. Our theoretical results, along with empirical findings, demonstrate that GCM-related methods generally outperform LOCO under suitable regularity conditions. Furthermore, we quantify the asymptotic relative efficiency of these approaches. Our simulations and real data analysis include widely used machine learning methods such as neural networks and gradient boosting trees.