B0438
Title: R-VGAL: A sequential variational Bayes algorithm for generalized linear mixed models
Authors: David Gunawan - University of Wollongong (Australia)
Andrew Zammit Mangion - University of Wollongong (Australia)
Bao Vu - University of Wollongong (Australia)
David Gunawan - University of Wollongong (Australia) [presenting]
Abstract: Models with random effects, such as generalised linear mixed models (GLMMs), are often used for analysing clustered data. Parameter inference with these models is difficult because of the presence of cluster-specific random effects, which must be integrated when evaluating the likelihood function. A sequential variational Bayes algorithm is proposed, called recursive variational Gaussian approximation for latent variable models (R-VGAL), for estimating parameters in GLMMs. The R-VGAL algorithm operates on the data sequentially, requires only a single pass through the data, and can provide parameter updates as new data are collected without the need of re-processing the previous data. At each update, the R-VGAL algorithm requires the gradient and Hessian of a "partial" log-likelihood function evaluated at the new observation, which is generally not available in closed form for GLMMs. To circumvent this issue, an importance-sampling-based approach is proposed for estimating the gradient and Hessian via Fisher's and Louis' identities. It is found that R-VGAL can be unstable when traversing the first few data points, but this issue can be mitigated by using a variant of variational tempering in the initial steps of the algorithm. Through illustrations on both simulated and real datasets, it is shown that R-VGAL provides good approximations to the exact posterior distributions, that it can be made robust through tempering, and that it is computationally efficient.
