Sparse minimum Redundancy Maximum Relevance for feature selection

We propose a feature screening method that integrates both feature-feature and feature-target relationships. Inactive features are identified via a penalized minimum Redundancy Maximum Relevance (mRMR) procedure, which is the continuous version of the classic mRMR penalized by a non-convex regularizer, and where the parameters estimated as zero coefficients represent the set of inactive features. We establish the conditions under which zero coefficients are correctly identified to guarantee accurate recovery of inactive features. We introduce a multi-stage procedure based on the knockoff filter enabling the penalized mRMR to discard inactive features while controlling the false discovery rate (FDR). Our method performs comparably to HSIC-LASSO but is more conservative in the number of selected features. It only requires setting an FDR threshold, rather than specifying the number of features to retain. The effectiveness of the method is illustrated through simulations and real-world datasets. The code to reproduce this work is available on the following GitHub: https://github.com/PeterJackNaylor/SmRMR.

Post-selection inference with HSIC-Lasso

Detecting influential features in complex (non-linear and/or high-dimensional) datasets is key for extracting the relevant information. Most of the popular selection procedures, however, require assumptions on the underlying data - such as distributional ones -, which barely agree with empirical observations. Therefore, feature selection based on nonlinear methods, such as the model-free HSIC-Lasso, is a more relevant approach. In order to ensure valid inference among the chosen features, the selection procedure must be accounted for. In this paper, we propose selective inference with HSIC-Lasso using the framework of truncated Gaussians together with the polyhedral lemma. Based on these theoretical foundations, we develop an algorithm allowing for low computational costs and the treatment of the hyper-parameter selection issue. The relevance of our method is illustrated using artificial and real-world datasets. In particular, our empirical findings emphasise that type-I error control at the considered level can be achieved.