Fixed-Form Variational Posterior Approximation through Stochastic Linear Regression

Variational Bayesian Inference with Stochastic Search

Mean-field variational inference is a method for approximate Bayesian posterior inference. It approximates a full posterior distribution with a factorized set of distributions by maximizing a lower bound on the marginal likelihood. This requires the ability to integrate a sum of terms in the log joint likelihood using this factorized distribution. Often not all integrals are in closed form, whi...

Markov Chain Monte Carlo and Variational Inference: Bridging the Gap

Recent advances in stochastic gradient variational inference have made it possible to perform variational Bayesian inference with posterior approximations containing auxiliary random variables. This enables us to explore a new synthesis of variational inference and Monte Carlo methods where we incorporate one or more steps of MCMC into our variational approximation. We describe the theoretical ...

Bayesian parameter estimation via variational methods

We consider a logistic regression model with a Gaussian prior distribution over the parameters. We show that an accurate variational transformation can be used to obtain a closed form approximation to the posterior distribution of the parameters thereby yielding an approximate posterior predictive model. This approach is readily extended to binary graphical model with complete observations. For...

A Relaxed Extra Gradient Approximation Method of Two Inverse-Strongly Monotone Mappings for a General System of Variational Inequalities, Fixed Point and Equilibrium Problems

An Alternative View of Variational Bayes and Minimum Variational Stochastic Complexity

Bayesian learning is widely used in many applied datamodelling problems and is often accompanied with approximation schemes since it requires intractable computation of the posterior distributions. In this study, we focus on the two approximation methods, the variational Bayes and the local variational approximation. We show that the variational Bayes approach for statistical models with latent...