Talk by Badr-Eddine Chérief-Abdellatif (CREST - ENSAE - Institut Polytechnique de Paris)

Title: "Theoretical study of variational inference"

Abstract: Bayesian inference provides an attractive learning framework to analyze and to sequentially update knowledge on streaming data, but is rarely computationally feasible in practice. In the recent years, variational inference (VI) has become more and more popular for approximating intractable posterior distributions in Bayesian statistics and machine learning. Nevertheless, despite promising results in real-life applications, only little attention has been put in the literature towards the theoretical properties of VI. In this talk, we aim to present some recent advances in theory of VI. First, we show that variational inference is consistent under mild conditions and retains the same properties than exact Bayesian inference in the batch setting. Then, we study several online VI algorithms that are inspired from sequential optimization in order to compute the variational approximations in an online fashion. We provide theoretical guarantees by deriving generalization bounds and we present empirical evidence in support of this.