Méthodes Monte Carlo pour l'apprentissage automatique : contributions pratiques et théoriques pour l'échantillonnage préferentiel et les méthodes séquentielles
Janati, Yazid · HAL (Le Centre pour la Communication Scientifique Directe) · 2023
This thesis contributes to the vast domain of Monte Carlo methods with novel algorithms that aim at adressing high dimensional inference and uncertainty quantification. In a first part, we develop two novel methods for Importance Sampling. The first algorithm is a lightweight optimization based proposal for computing normalizing constants and which extends into a novel MCMC algorithm. The second one is a new scheme for learning sharp importance proposals. In a second part, we focus on Sequential Monte Carlo methods. We develop new estimators for the asymptotic variance of the particle filter and provide the first estimator of the asymptotic variance of a particle smoother. Next, we derive a procedure for parameter learning within hidden Markov models using a particle smoother with provably reduced bias. Finally, we devise a Sequential Monte Carlo algorithm for solving Bayesian linear inverse problems with generative model priors.