Séance du 17 octobre 2022

Séance organisée par Marc Hoffmann et Judith Rousseau.

Lieu : IHP, salle 314

14.00 : Nathan HARA (Université de Genève)

Titre : Statistical methods for exoplanet detection

Résumé : One of the biggest challenges of the next 50 years will be to search for life in planets outside the Solar System. A prerequisite is to be able to detect an Earth clones around nearby stars, but this is currently infeasible. Instrument systematics and signals originating from the star are still routinely an order of magnitude greater than the planetary signals. Overcoming this limitation is primarily a data analysis problem. We will first cast exoplanet detection as a multivariate, non uniformly sampled time series analysis problem. We will then focus on detection criteria, and present an exoplanet detection criterion that has maximum utility, which can be seen as an extension of Bayesian multiple hypothesis testing when the hypotheses are indexed by continuous variables.

15.00 : Cristina BUTUCEA (ENSAE)

Titre : Off-the-grid learning of mixture models.

Résumé : We consider a general non-linear model where the signal is a finite mixture of an unknown, possibly increasing, number of features issued from a continuous dictionary parameterized by a real non-linear parameter. The signal is observed with Gaussian (possibly correlated) noise in either a continuous or a discrete setup. We propose an off-the-grid optimization method to estimate both the non-linear parameters of the features and the linear parameters of the mixture. We bound the prediction risk with high probability, the rates are up to log-factors similar to the rates attained by the Lasso predictor in the linear regression model. We also establish convergence rates that quantify with high probability the quality of estimation for both the linear and the non-linear parameters. (This is joint work with J.F. Delmas, A. Dutfoy and C. Hardy.)

16.00 : Julien STOEHR (Paris-Dauphine PSL)

Titre : Monte Carlo EM for Poisson Log-Normal model

Résumé : 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 confidence region. (Joint work with Stéphane Robin, Sorbonne Université, LPSM.) Key words : Poisson Log-Normal model, M-estimator, importance sampling.