Alpha-divergence Variational Inference Meets Importance Weighted Auto-Encoders: Methodology and Asymptotics

Understand

Several algorithms involving the Variational R\'enyi (VR) bound have been proposed to minimize 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.