提出新型快速算法，解决高维交叉随机效应模型计算慢问题
Scalable Krylov Subspace Methods for Generalized Mixed-Effects Models with Crossed Random Effects
- 用克里洛夫子空间方法替代传统分解，突破计算瓶颈
- 实测速度提升最高达一万倍，数值更稳定
- 适合处理大规模分类变量的混合效应模型研究者
混合效应模型广泛用于具有层级结构和高基数分类预测变量的数据建模。然而，当涉及高维交叉随机效应时，依赖楚列斯基分解的标准计算方法会变得极其缓慢。本文提出基于克里洛夫子空间的方法，有效解决现有计算瓶颈，并从理论与实证两方面进行分析。特别地，我们推导了预条件随机兰佐斯求积与共轭梯度法在混合效应模型中的收敛性与精度新结果，并开发了可扩展的预测方差计算方法。在模拟数据与真实世界数据上的实验表明，所提方法速度提升最高可达约10,000倍，且数值稳定性优于楚列斯基方法。
原文摘要 · Abstract (English)
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.
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