Streamlined Variational Inference for Linear Mixed Models with Crossed Random Effects
This work addresses computational efficiency and accuracy issues for statisticians and data scientists working with large-scale linear mixed models, representing an incremental improvement in variational inference methods.
The authors tackled the challenge of variational inference for linear mixed models with crossed random effects by deriving streamlined algorithms, achieving high inferential accuracy with the least stringent product restriction, though at the cost of increased storage and computing demands.
We derive streamlined mean field variational Bayes algorithms for fitting linear mixed models with crossed random effects. In the most general situation, where the dimensions of the crossed groups are arbitrarily large, streamlining is hindered by lack of sparseness in the underlying least squares system. Because of this fact we also consider a hierarchy of relaxations of the mean field product restriction. The least stringent product restriction delivers a high degree of inferential accuracy. However, this accuracy must be mitigated against its higher storage and computing demands. Faster sparse storage and computing alternatives are also provided, but come with the price of diminished inferential accuracy. This article provides full algorithmic details of three variational inference strategies, presents detailed empirical results on their pros and cons and, thus, guides the users on their choice of variational inference approach depending on the problem size and computing resources.