A1388
Title: Scalable computations for generalized mixed effects models with crossed random effects using Krylov subspace methods
Authors: Fabio Sigrist - ETH Zurich (Switzerland) [presenting]
Pascal Kuendig - Lucerne University of Applied Sciences and Arts (Switzerland)
Abstract: Mixed effects models are widely used for modeling data with hierarchically grouped structures and high-cardinality categorical predictor variables. However, for high-dimensional crossed random effects, current standard computations relying on Cholesky decompositions can become prohibitively slow. The aim is to present novel Krylov subspace-based methods that address several existing computational bottlenecks. Among other things, various preconditioners are theoretically analyzed and empirically evaluated for the conjugate gradient and stochastic Lanczos quadrature methods, derive new convergence results, and computationally efficient methods are developed for calculating predictive variances. Extensive experiments using simulated and real-world data sets show that the proposed methods scale much better than Cholesky-based computations, for instance, achieving a runtime reduction of approximately two orders of magnitude for both estimation and prediction. Moreover, the software implementation is up to 10'000 times faster and more stable than state-of-the-art implementations such as lme4 and glmmTMB when using default settings.
