UCPH Statistics Seminar: Kamélia Daudel
Title: Alpha-divergence Variational Inference Meets Importance Weighted Auto-Encoders: Methodology and Asymptotics
Speaker: Kamélia Daudel from ESSEC Business School
Abstract: Variational Inference methods are optimization-based methods that have generated a lot of attention in Bayesian Statistics due to their applicability to high-dimensional machine learning problems. In particular, several algorithms involving the Variational Rényi (VR) bound have been proposed to optimize an alpha-divergence between a target posterior distribution and a variational distribution. Despite promising empirical results, those algorithms resort to biased stochastic gradient descent procedures and thus lack theoretical guarantees. In this paper, we formalize and study the VR-IWAE bound, a generalization of the Importance Weighted Auto-Encoder (IWAE) bound. We show that the VR-IWAE bound enjoys several desirable properties and notably leads to the same stochastic gradient descent procedure as the VR bound in the reparameterized case, but this time by relying on unbiased gradient estimators. We then provide two complementary theoretical analyses of the VR-IWAE bound and thus of the standard IWAE bound. Those analyses shed light on the benefits or lack thereof of these bounds. Lastly, we illustrate our theoretical claims over toy and real-data examples.
Daudel, J. Benton, Y. Shi and A. Doucet (2023). Alpha-divergence Variational Inference Meets Importance Weighted Auto-Encoders: Methodology and Asymptotics. Journal of Machine Learning Research, 24(243):1−83.