Metropolized Knockoff Sampling
成果类型：
Article
署名作者：
Bates, Stephen; Candes, Emmanuel; Janson, Lucas; Wang, Wenshuo
署名单位：
Stanford University; Stanford University; Harvard University
刊物名称：
JOURNAL OF THE AMERICAN STATISTICAL ASSOCIATION
ISSN/ISSBN：
0162-1459
DOI：
10.1080/01621459.2020.1729163
发表日期：
2021
页码：
1413-1427
关键词：
摘要：
Model-X knockoffs is a wrapper that transforms essentially any feature importance measure into a variable selection algorithm, which discovers true effects while rigorously controlling the expected fraction of false positives. A frequently discussed challenge to apply this method is to construct knockoff variables, which are synthetic variables obeying a crucial exchangeability property with the explanatory variables under study. This article introduces techniques for knockoff generation in great generality: we provide a sequential characterization of all possible knockoff distributions, which leads to a Metropolis-Hastings formulation of an exact knockoff sampler. We further show how to use conditional independence structure to speed up computations. Combining these two threads, we introduce an explicit set of sequential algorithms and empirically demonstrate their effectiveness. Our theoretical analysis proves that our algorithms achieve near-optimal computational complexity in certain cases. The techniques we develop are sufficiently rich to enable knockoff sampling in challenging models including cases where the covariates are continuous and heavy-tailed, and follow a graphical model such as the Ising model. for this article are available online.