Variational Bayes on manifolds

Thomas Bayes ’ walk on manifolds

Convergence of the Bayes posterior measure is considered in canonical statistical settings where observations sit on a geometrical object such as a compact manifold, or more generally on a compact metric space verifying some conditions. A natural geometric prior based on randomly rescaled solutions of the heat equation is considered. Upper and lower bound posterior contraction rates are derived.

Auto-Encoding Variational Bayes

How can we perform efficient inference and learning in directed probabilistic models, in the presence of continuous latent variables with intractable posterior distributions, and large datasets? We introduce a stochastic variational inference and learning algorithm that scales to large datasets and, under some mild differentiability conditions, even works in the intractable case. Our contributi...

Streaming Variational Bayes

Overview • Large, streaming data sets are increasingly the norm • Inference for Big Data has generally been non-Bayesian • Advantages of Bayes: complex models, coherent treatment of uncertainty, etc. We deliver: • SDA-Bayes, a framework for Streaming, Distributed, Asynchronous Bayesian inference • Experiments demonstrating streaming topic discovery with comparable predictive performance to non-...

Chapter 24 : Variational Bayes

Tilted Variational Bayes

We present a novel method for approximate inference. Using some of the constructs from expectation propagation (EP), we derive a lower bound of the marginal likelihood in a similar fashion to variational Bayes (VB). The method combines some of the benefits of VB and EP: it can be used with light-tailed likelihoods (where traditional VB fails), and it provides a lower bound on the marginal likel...