arXiv subjects

Mélina Gallopin

Publications and source records attributed to Mélina Gallopin.

4 recordsLinked to original sources

arXiv2026

A comprehensive guideline for regularization-path variable selection in high-dimensional Gaussian linear regression

This paper provides a comprehensive comparison of complete regularization-path-based variable selection procedures in high-dimensional Gaussian linear regression. Our simulation study stands out from previous ones for several reasons. First, it offers comprehensive guidelines for complete variable selection, from regularization path construction to final variable subset selection. In particular, we compare jointly two convex regularization functions (Lasso and Elastic-Net) with two optimization algorithms (LARS and cyclic coordinate descent) and a range of model selection and variable identification techniques. Second, we also incorporate methods with non-asymptotic theoretical guarantees, which are typically not included in existing reviews. It is unrealistic to expect a single method that works best. Still, we provide detailed guidance on which methods perform best under different evaluation criteria, including pROC-AUC, MSE, recall, specificity, and FDP, and that are robust to data scenarios, including varying variable dependency structures. Overall, Elastic-Net combined with the LARS algorithm provides the most reliable regularization path, while the preferred final selection procedure depends on whether prediction performances, support recovery or false discovery control is prioritized. We show that some methods are empirically better for a given criterion than others, even though the latter were designed to control for it theoretically. Regarding new developments in a non-asymptotic setting, we highlight the quality of LinSelect and the need, as future work, to fine-tune the unknown constants of data-dependent penalties in high-dimensional Gaussian linear regression models.

stat.AP↗

arXiv2024

Stable network inference in high-dimensional graphical model using single-linkage

Stability, akin to reproducibility, is crucial in statistical analysis. This paper examines the stability of sparse network inference in high-dimensional graphical models, where selected edges should remain consistent across different samples. Our study focuses on the Graphical Lasso and its decomposition into two steps, with the first step involving hierarchical clustering using single linkage.We provide theoretical proof that single linkage is stable, evidenced by controlled distances between two dendrograms inferred from two samples. Practical experiments further illustrate the stability of the Graphical Lasso's various steps, including dendrograms, variable clusters, and final networks. Our results, validated through both theoretical analysis and practical experiments using simulated and real datasets, demonstrate that single linkage is more stable than other methods when a modular structure is present.

math.ST↗

arXiv2017

Nonlinear network-based quantitative trait prediction from transcriptomic data

Quantitatively predicting phenotype variables by the expression changes in a set of candidate genes is of great interest in molecular biology but it is also a challenging task for several reasons. First, the collected biological observations might be heterogeneous and correspond to different biological mechanisms. Secondly, the gene expression variables used to predict the phenotype are potentially highly correlated since genes interact though unknown regulatory networks. In this paper, we present a novel approach designed to predict quantitative trait from transcriptomic data, taking into account the heterogeneity in biological samples and the hidden gene regulatory networks underlying different biological mechanisms. The proposed model performs well on prediction but it is also fully parametric, which facilitates the downstream biological interpretation. The model provides clusters of individuals based on the relation between gene expression data and the phenotype, and also leads to infer a gene regulatory network specific for each cluster of individuals. We perform numerical simulations to demonstrate that our model is competitive with other prediction models, and we demonstrate the predictive performance and the interpretability of our model to predict alcohol sensitivity from transcriptomic data on real data from Drosophila Melanogaster Genetic Reference Panel (DGRP).

stat.AP↗

arXiv2016

Block-diagonal covariance selection for high-dimensional Gaussian graphical models

Gaussian graphical models are widely utilized to infer and visualize networks of dependencies between continuous variables. However, inferring the graph is difficult when the sample size is small compared to the number of variables. To reduce the number of parameters to estimate in the model, we propose a non-asymptotic model selection procedure supported by strong theoretical guarantees based on an oracle inequality and a minimax lower bound. The covariance matrix of the model is approximated by a block-diagonal matrix. The structure of this matrix is detected by thresholding the sample covariance matrix, where the threshold is selected using the slope heuristic. Based on the block-diagonal structure of the covariance matrix, the estimation problem is divided into several independent problems: subsequently, the network of dependencies between variables is inferred using the graphical lasso algorithm in each block. The performance of the procedure is illustrated on simulated data. An application to a real gene expression dataset with a limited sample size is also presented: the dimension reduction allows attention to be objectively focused on interactions among smaller subsets of genes, leading to a more parsimonious and interpretable modular network.

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