Scalable Krylov Subspace Methods for Generalized Mixed-Effects Models with Crossed Random Effects
Fuente:
arXiv
Enregistré dans:
| Auteurs principaux: | , |
|---|---|
| Format: | Preprint |
| Publié: |
2025
|
| Sujets: | |
| Accès en ligne: | |
| Tags: |
Ajouter un tag
Pas de tags, Soyez le premier à ajouter un tag!
|
| _version_ | 1866913124813111296 |
|---|---|
| author | Kündig, Pascal Sigrist, Fabio |
| author_facet | Kündig, Pascal Sigrist, Fabio |
| contents | Mixed-effects models are widely used to model data with hierarchical 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 by factors of up to about 10,000 and are numerically more stable than Cholesky-based computations. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2505_09552 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Scalable Krylov Subspace Methods for Generalized Mixed-Effects Models with Crossed Random Effects Kündig, Pascal Sigrist, Fabio Methodology Machine Learning Mixed-effects models are widely used to model data with hierarchical 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 by factors of up to about 10,000 and are numerically more stable than Cholesky-based computations. |
| title | Scalable Krylov Subspace Methods for Generalized Mixed-Effects Models with Crossed Random Effects |
| topic | Methodology Machine Learning |
| url | https://arxiv.org/abs/2505.09552 |