Variational Inference via Rényi Bound Optimization and Multiple-Source Adaptation

Variational inference provides a way to approximate probability densities through optimization. It does so by optimizing an upper or a lower bound of the likelihood of the observed data (the evidence). The classic variational inference approach suggests maximizing the Evidence Lower Bound (ELBO). Recent studies proposed to optimize the variational Rényi bound (VR) and the χ upper bound. However, these estimates, which are based on the Monte Carlo (MC) approximation, either underestimate the bound or exhibit a high variance. In this work, we introduce a new upper bound, termed the Variational Rényi Log Upper bound (VRLU), which is based on the existing VR bound. In contrast to the existing VR bound, the MC approximation of the VRLU bound maintains the upper bound property. Furthermore, we devise a (sandwiched) upper-lower bound variational inference method, termed the Variational Rényi Sandwich (VRS), to jointly optimize the upper and lower bounds. We present a set of experiments, designed to evaluate the new VRLU bound and to compare the VRS method with the classic Variational Autoencoder (VAE) and the VR methods. Next, we apply the VRS approximation to the Multiple-Source Adaptation problem (MSA). MSA is a real-world scenario where data are collected from multiple sources that differ from one another by their probability distribution over the input space. The main aim is to combine fairly accurate predictive models from these sources and create an accurate model for new, mixed target domains. However, many domain adaptation methods assume prior knowledge of the data distribution in the source domains. In this work, we apply the suggested VRS density estimate to the Multiple-Source Adaptation problem (MSA) and show, both theoretically and empirically, that it provides tighter error bounds and improved performance, compared to leading MSA methods.