Generalized reparametrized variational Bayes with skew-symmetric normalization

Bayesian hierarchical models with high-dimensional latent structure require scalable posterior approximations that preserve key dependencies while remaining computationally tractable.

Mean-field variational inference (MFVI) is efficient, but can be unreliable when local variables are strongly correlated or tightly coupled to global variables.

We propose KNorm-RVB, a generalized reparametrized variational Bayes framework for latent Gaussian and latent non-Gaussian models with sparse local precision matrices.

KNorm-RVB maps the conditional posterior of local variables toward a standard Gaussian via normalization followed by skewness reduction, enabled by a novel K-component skew-symmetric density representation.

This reparametrization centers the transformed conditional local posterior at an optimized reflection point and decorrelates local and global variables, making MFVI much more effective.

Under symmetry conditions, we show that MFVI recovers the local posterior mean and correlation matrix exactly, motivating KNorm-RVB's normalization and symmetrization of the conditional local posterior before applying MFVI.

We combine a Gaussian variational family for reparametrized local variables with a flexible closed skew normal family for the remaining variables.

Across generalized linear mixed models, mixed multinomial logit models, spatial autoregressive models, and stochastic volatility models, KNorm-RVB improves posterior approximation accuracy over existing methods.