Apparaît dans la collection : Nexus Trimester - 2016 - Inference Problems Theme
Sampling from various kinds of distributions is an issue of paramount importance in statistics since it is often the key ingredient for constructing estimators, test procedures or confidence intervals. In many situations, the exact sampling from a given distribution is impossible or computationally expensive and, therefore, one needs to resort to approximate sampling strategies. However, there is no well-developed theory providing meaningful nonasymptotic guarantees for the approximate sampling procedures, especially in the high-dimensional problems. In this talk, we present some recent advances in this direction by focusing on the problem of sampling from a multivariate distribution having a smooth and log-concave density. We establish nonasymptotic bounds for the error of approximating the true distribution by the one obtained by the Langevin Monte Carlo method and its variants. The computational complexity of the resulting sampling method will be discussed along with the main steps of the proof of the central result.