Héctor Climente-González

Peter Naylor, Benjamin Poignard, Héctor Climente-González et al.

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.

Tobias Freidling, Benjamin Poignard, Héctor Climente-González et al.

Detecting influential features in non-linear and/or high-dimensional data is a challenging and increasingly important task in machine learning. Variable selection methods have thus been gaining much attention as well as post-selection inference. Indeed, the selected features can be significantly flawed when the selection procedure is not accounted for. We propose a selective inference procedure using the so-called model-free "HSIC-Lasso" based on the framework of truncated Gaussians combined with the polyhedral lemma. We then develop an algorithm, which allows for low computational costs and provides a selection of the regularisation parameter. The performance of our method is illustrated by both artificial and real-world data based experiments, which emphasise a tight control of the type-I error, even for small sample sizes.

Dinesh Singh, Héctor Climente-González, Mathis Petrovich et al.

Biological data including gene expression data are generally high-dimensional and require efficient, generalizable, and scalable machine-learning methods to discover their complex nonlinear patterns. The recent advances in machine learning can be attributed to deep neural networks (DNNs), which excel in various tasks in terms of computer vision and natural language processing. However, standard DNNs are not appropriate for high-dimensional datasets generated in biology because they have many parameters, which in turn require many samples. In this paper, we propose a DNN-based, nonlinear feature selection method, called the feature selection network (FsNet), for high-dimensional and small number of sample data. Specifically, FsNet comprises a selection layer that selects features and a reconstruction layer that stabilizes the training. Because a large number of parameters in the selection and reconstruction layers can easily result in overfitting under a limited number of samples, we use two tiny networks to predict the large, virtual weight matrices of the selection and reconstruction layers. Experimental results on several real-world, high-dimensional biological datasets demonstrate the efficacy of the proposed method.