2015/06/19 by Guillaume Bouchard, Balaji Lakshminarayanan, Bouchard, Guillaume +1
Computer Science · Mathematics · #Bayesian Methods and Mixture Models #FOS: Computer and information sciences #FOS: Mathematics #Functional Analysis (math.FA) #Gaussian Processes and Bayesian Inference #Machine Learning (cs.LG) #Machine Learning (stat.ML) #Statistical Methods and Bayesian Inference
paper · pdf · doi:10.48550/arxiv.1506.06100
openalex publication_date 2015/06/19 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
We introduce the Variational Holder (VH) bound as an alternative to Variational Bayes (VB) for approximate Bayesian inference. Unlike VB which typically involves maximization of a non-convex lower bound with respect to the variational parameters, the VH bound involves minimization of a convex upper bound to the intractable integral with respect to the variational parameters. Minimization of the VH bound is a convex optimization problem; hence the VH method can be applied using off-the-shelf convex optimization algorithms and the approximation error of the VH bound can also be analyzed using tools from convex optimization literature. We present experiments on the task of integrating a truncated multivariate Gaussian distribution and compare our method to VB, EP and a state-of-the-art numerical integration method for this problem.