Monte-Carlo EM for Poisson Log-Normal model

Jeudi 23 mars 2023, 10:15 à 11:15

Salle des séminaires, M.0.1

Julien Stoehr

CEREMADE, Univ. Paris Dauphine

Poisson Log-Normal model [Aitchison and Ho, 1989] is an incomplete data model for which the maximum likelihood estimator is not available via EM algorithm since the conditional distribution of the latent variable given the observed one is intractable. Efficient variational schemes have been proposed in the past few years. Even though they are computationally fast, they lack theoretical garanties and do not provide any confidence region. In this talk, I will present an ongoing work on how to design a Monte Carlo EM algorithm, that satisfactorily scales up with the size of the data, in order to get maximum likelihood estimator or maximum composite likelihood estimator and its related information matrix.

Keywords : Poisson Log-Normal model, M-estimator, importance sampling.

Joint work with Stéphane Robin (Sorbonne Université, LPSM).