The Variational Gaussian Approximation Revisited

Gaussian Variational Approximate Inference for Generalized Linear Mixed Models

Variational approximation methods have become a mainstay of contemporary Machine Learning methodology, but currently have little presence in Statistics. We devise an effective variational approximation strategy for fitting generalized linear mixed models (GLMM) appropriate for grouped data. It involves Gaussian approximation to the distributions of random effects vectors, conditional on the res...

Variational Inference for Sparse Spectrum Approximation in Gaussian Process Regression

Standard sparse pseudo-input approximations to the Gaussian process (GP) cannot handle complex functions well. Sparse spectrum alternatives attempt to answer this but are known to over-fit. We suggest the use of variational inference for the sparse spectrum approximation to avoid both issues. We model the covariance function with a finite Fourier series approximation and treat it as a random va...

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

Gaussian variational approximation with a factor covariance structure

Variational approximation methods have proven to be useful for scaling Bayesian computations to large data sets and highly parametrized models. Applying variational methods involves solving an optimization problem, and recent research in this area has focused on stochastic gradient ascent methods as a general approach to implementation. Here variational approximation is considered for a posteri...

Stochastic Variational Inference for Gaussian Process Latent Variable Models using Back Constraints

Gaussian process latent variable models (GPLVMs) are a probabilistic approach to modelling data that employs Gaussian process mapping from latent variables to observations. This paper revisits a recently proposed variational inference technique for GPLVMs and methodologically analyses the optimality and different parameterisations of the variational approximation. We investigate a structured va...