BACKFITTING FOR LARGE SCALE CROSSED RANDOM EFFECTS REGRESSIONS

• 成果类型: Article
• 署名作者: Ghosh, Swarnadip; Hastie, Trevor; Owen, Art B.
• 署名单位: Stanford University
• 刊物名称: ANNALS OF STATISTICS
• ISSN/ISSBN: 0090-5364
• DOI: 10.1214/21-AOS2121
• 发表日期: 2022
• 页码: 560-583
• 关键词: inference

摘要

Regression models with crossed random effect errors can be very expensive to compute. The cost of both generalized least squares and Gibbs sampling can easily grow as N-3/2 (or worse) for N observations. Papaspiliopoulos, Roberts and Zanella (Biometrika 107 (2020) 25-40) present a collapsed Gibbs sampler that costs O(N), but under an extremely stringent sampling model. We propose a backfitting algorithm to compute a generalized least squares estimate and prove that it costs O(N). A critical part of the proof is in ensuring that the number of iterations required is O(1), which follows from keeping a certain matrix norm below 1 - delta for some delta > 0. Our conditions are greatly relaxed compared to those for the collapsed Gibbs sampler, though still strict. Empirically, the backfitting algorithm has a norm below 1 - delta under conditions that are less strict than those in our assumptions. We illustrate the new algorithm on a ratings data set from Stitch Fix.