Date: Wednesday, 20 March 2024, at 12:30pm (Paris) and 7:30pm (Singapore)

Dual format: ESSEC Paris La Défense (CNIT), Room 237
and via Zoom, please click here

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.

Kind regards,
Jeremy Heng, Olga Klopp, Roberto Reno, and Marie Kratz
https://crear.essec.edu/crear-events/working-group-on-risk
and Riada Djebbar (Singapore Actuarial Society - ERM)