MAXIMIN EFFECTS IN INHOMOGENEOUS LARGE-SCALE DATA

• 成果类型: Article
• 署名作者: Meinshausen, Nicolai; Buehlmann, Peter
• 署名单位: Swiss Federal Institutes of Technology Domain; ETH Zurich
• 刊物名称: ANNALS OF STATISTICS
• ISSN/ISSBN: 0090-5364
• DOI: 10.1214/15-AOS1325
• 发表日期: 2015
• 页码: 1801-1830
• 关键词: regression; regret

摘要

Large-scale data are often characterized by some degree of inhomogeneity as data are either recorded in different time regimes or taken from multiple sources. We look at regression models and the effect of randomly changing coefficients, where the change is either smoothly in time or some other dimension or even without any such structure. Fitting varying-coefficient models or mixture models can be appropriate solutions but are computationally very demanding and often return more information than necessary. If we just ask for a model estimator that shows good predictive properties for all regimes of the data, then we are aiming for a simple linear model that is reliable for all possible subsets of the data. We propose the concept of maximin effects and a suitable estimator and look at its prediction accuracy from a theoretical point of view in a mixture model with known or unknown group structure. Under certain circumstances the estimator can be computed orders of magnitudes faster than standard penalized regression estimators, making computations on large-scale data feasible. Empirical examples complement the novel methodology and theory.