Sparse inference in Poisson log-normal model by approximating the L0-norm

Togo Jean Yves Kioye, Clermont Auvergne University

Co-authors: Paul-Marie Grollemund, Clermont Auvergne University; Jocelyn Chauvet, ICES Research Center; Christophe Chassard, French National Research Institute for Agriculture, Food and the Environment

Abstract: Variable selection methods are essential in statistical modelling to improve interpretability by identifying the most relevant predictors. This article focuses on the Poisson Log Normal (PLN) model, widely used for analysing multivariate count data in fields like ecology and agronomy. Recent advancements, such as those by Chiquet et al. (2021), highlight sparse network inference using the evidence lower bound of the likelihood combined with an L1-penalty on the precision matrix. This paper introduces an alternative approach based on the Smooth Information Criterion (SIC, O’Neill and Burke (2023)), which smoothly approximates the L0-penalty, removing the need for cross-validation to tune regularisation parameters. The study targets the coefficient matrix of the PLN model, proposing an inference procedure for effective variable selection. The method integrates the SIC penalisation algorithm with the PLN model fitting algorithm, a variational EM algorithm. To support our proposal, we provide theoretical results and insights about the penalisation method, we perform simulation studies to assess the method, which is also applied on real datasets from a study of microbial communities in milk production.