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False discovery and its control in low rank estimation
The Journal of the Royal Statistical Society, Series B (Statistical Methodology) ( IF 5.8 ) Pub Date : 2020-07-18 , DOI: 10.1111/rssb.12387
Armeen Taeb 1 , Parikshit Shah 2 , Venkat Chandrasekaran 1
Affiliation  

Models specified by low rank matrices are ubiquitous in contemporary applications. In many of these problem domains, the row–column space structure of a low rank matrix carries information about some underlying phenomenon, and it is of interest in inferential settings to evaluate the extent to which the row–column spaces of an estimated low rank matrix signify discoveries about the phenomenon. However, in contrast with variable selection, we lack a formal framework to assess true or false discoveries in low rank estimation; in particular, the key source of difficulty is that the standard notion of a discovery is a discrete notion that is ill suited to the smooth structure underlying low rank matrices. We address this challenge via a geometric reformulation of the concept of a discovery, which then enables a natural definition in the low rank case. We describe and analyse a generalization of the stability selection method of Meinshausen and Bühlmann to control for false discoveries in low rank estimation, and we demonstrate its utility compared with previous approaches via numerical experiments.

中文翻译:

虚假发现及其在低秩估计中的控制

低阶矩阵指定的模型在当代应用中无处不在。在许多这些问题域中,低秩矩阵的行-列空间结构携带有关某些潜在现象的信息,并且在推论设置中,评估估计的低秩矩阵的行-列空间的程度很有意义表示有关该现象的发现。但是,与变量选择相反,我们缺乏在低秩估计中评估真实或错误发现的正式框架。特别是,困难的关键来源是发现的标准概念是离散的概念,它不适合作为低秩矩阵基础的平滑结构。我们通过几何学来应对这一挑战重新定义发现的概念,然后在低等级情况下实现自然定义。我们描述并分析了Meinshausen和Bühlmann的稳定性选择方法的一般性,以控制低秩估计中的错误发现,并通过数值实验证明了其与先前方法相比的实用性。
更新日期:2020-08-10
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