Work

Scalable Krylov Subspace Methods for Generalized Mixed-Effects Models with Crossed Random Effects

Year: 2026

Type: article

Abstract: Mixed-effects models are widely used to model data with complex grouping 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. In this work, we present Krylov subspace-based methods that address existing computational bottlenecks, and we analyze them both theoretically and empirically. In particular, we derive new results on the convergence and accuracy of the preconditioned stochastic Lanczos quadrature and conjugate gradient methods for mixed-effects models, and we develop scalable methods for calculating predictive variances. In experiments with simulated and real-world data, the proposed methods yield speedups of several orders of magnitude and are more computationally robust than Cholesky-based computations, while maintaining essentially the same accuracy.

Source: Journal of Computational and Graphical Statistics

DOI: 10.1080/10618600.2026.2759707

Authors: Pascal Kündig, Fabio Sigrist

Institutions: University of Basel, Lucerne University of Applied Sciences and Arts, ETH Zurich, Seminar for Statistics

Language: English

Topic: Matrix Theory and Algorithms

Subfield: Computational Theory and Mathematics

Field: Computer Science

Domain: Physical Sciences

Open Access status: hybrid

Funder: Innosuisse - Schweizerische Agentur für Innovationsförderung

Award: G1394773076