BACKFITTING FOR LARGE SCALE CROSSED RANDOM EFFECTS REGRESSIONS
ANNALS OF STATISTICS(2022)
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.
更多查看译文
关键词
Collapsed Gibbs sampler, mixed effect models, generalized least squares
AI 理解论文
溯源树
样例
生成溯源树,研究论文发展脉络
Chat Paper
正在生成论文摘要