Stephane S. Robin | Searcharxiv

arXiv2024

Online and Offline Robust Multivariate Linear Regression

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.

math.ST↗

arXiv2024

Composite likelihood inference for the Poisson log-normal model

The Poisson log-normal model is a latent variable model that provides a generic framework for the analysis of multivariate count data. Inferring its parameters can be a daunting task since the conditional distribution of the latent variables given the observed ones is intractable. For this model, variational approaches are the golden standard solution as they prove to be computationally efficient but lack theoretical guarantees on the estimates. Sampling-based solutions are quite the opposite. We first define a Monte Carlo EM algorithm that can achieve maximum likelihood estimators, but that is computationally efficient only for low-dimensional latent spaces. We then propose a novel inference procedure combining the EM framework with composite likelihood and importance sampling estimates. The algorithm preserves the desirable asymptotic properties of maximum likelihood estimators while circumventing the high-dimensional integration bottleneck, thus maintaining computational feasibility for moderately large datasets. This approach enables grounded parameter estimation, confidence intervals, and hypothesis testing. Application to the Barents Sea fish dataset demonstrates the algorithm capacity to identify significant environmental effects and residual interspecies correlations.

stat.CO↗