Scalable inference for crossed random effects models
This addresses a computational bottleneck for statisticians and data analysts using crossed random effects models, offering a scalable inference method.
The authors tackled the scalability problem of Gibbs samplers for crossed random effects models, showing that the standard Gibbs sampler has worse-than-proportional complexity to parameters and data, and proposed a collapsed Gibbs sampler that is provably scalable and outperforms state-of-the-art algorithms in simulations and real datasets.
We analyze the complexity of Gibbs samplers for inference in crossed random effect models used in modern analysis of variance. We demonstrate that for certain designs the plain vanilla Gibbs sampler is not scalable, in the sense that its complexity is worse than proportional to the number of parameters and data. We thus propose a simple modification leading to a collapsed Gibbs sampler that is provably scalable. Although our theory requires some balancedness assumptions on the data designs, we demonstrate in simulated and real datasets that the rates it predicts match remarkably the correct rates in cases where the assumptions are violated. We also show that the collapsed Gibbs sampler, extended to sample further unknown hyperparameters, outperforms significantly alternative state of the art algorithms.