Online and Offline Robust Multivariate Linear Regression

• URL: http://arxiv.org/abs/2404.19496v1
• Date: Tue, 30 Apr 2024 12:30:48 GMT
• Title: Online and Offline Robust Multivariate Linear Regression
• Authors: Antoine Godichon-Baggioni, Stephane S. Robin, Laure Sansonnet,
• Abstract summary: We introduce two methods each considered contrast: (i) online gradient descent algorithms and their averaged versions and (ii) offline fix-point algorithms. Because the variance matrix of the noise is usually unknown, we propose to plug a robust estimate of it in the Mahalanobis-based gradient descent algorithms.
• Score: 0.3277163122167433
• License: http://arxiv.org/licenses/nonexclusive-distrib/1.0/
• Abstract: We consider the robust estimation of the parameters of multivariate Gaussian linear regression models. To this aim we consider robust version of the usual (Mahalanobis) least-square criterion, with or without Ridge regularization. We introduce two methods each considered contrast: (i) online stochastic gradient descent algorithms and their averaged versions and (ii) offline fix-point algorithms. Under weak assumptions, we prove the asymptotic normality of the resulting estimates. Because the variance matrix of the noise is usually unknown, we propose to plug a robust estimate of it in the Mahalanobis-based stochastic gradient descent algorithms. We show, on synthetic data, the dramatic gain in terms of robustness of the proposed estimates as compared to the classical least-square ones. Well also show the computational efficiency of the online versions of the proposed algorithms. All the proposed algorithms are implemented in the R package RobRegression available on CRAN.

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