Transformation Models for Flexible Posteriors in Variational Bayes
This addresses the problem of limited flexibility in Gaussian variational inference for Bayesian practitioners, offering a more accurate approximation method.
The paper tackles the challenge of approximating complex posterior distributions in Bayesian models by introducing transformation model-based variational inference (TM-VI), which accurately approximates posteriors in single-parameter models and works in a mean-field fashion for multi-parameter models like neural networks.
The main challenge in Bayesian models is to determine the posterior for the model parameters. Already, in models with only one or few parameters, the analytical posterior can only be determined in special settings. In Bayesian neural networks, variational inference is widely used to approximate difficult-to-compute posteriors by variational distributions. Usually, Gaussians are used as variational distributions (Gaussian-VI) which limits the quality of the approximation due to their limited flexibility. Transformation models on the other hand are flexible enough to fit any distribution. Here we present transformation model-based variational inference (TM-VI) and demonstrate that it allows to accurately approximate complex posteriors in models with one parameter and also works in a mean-field fashion for multi-parameter models like neural networks.