Laboratoire de Mathématiques Raphaël Salem

UMR 6085 CNRS - Université de Rouen Normandie

Networks are tools used to represent species relationships in microbiology and ecology. Gaussian Graphical Models provide with a mathematical framework for the inference of networks representing conditional dependence relationships, allowing for a clear separation of direct and indirect effects. However observed data are often discrete counts and the inference cannot be directly performed within this framework.
This talk presents a methodology for network inference from species observed abundances based on the Matrix Tree Theorem to perform an efficient and complete exploration of the spanning tree space. The inference, which takes place in a latent space of the observed counts, is performed with an Expectation-Maximization algorithm. The procedure uses a gradient ascent strategy, with adaptative bounds to ensure numerical stability.
We will then see the method’s behaviour on large networks, and present an idea for the edge selection based on stability. Finally, as a perspective to the task of network inference we show how to obtain partial correlation estimates using Lauritzen’s maximum likelihood formula.

Cet exposé rentre dans le cadre de l'ANR SMILES ANR-18-CE40-0014.