Model selection over partially ordered sets

• 成果类型: Article
• 署名作者: Taeb, Armeen; Buhlmann, Peter; Chandrasekaran, Venkat
• 署名单位: University of Washington; University of Washington Seattle; California Institute of Technology; California Institute of Technology
• 刊物名称: PROCEEDINGS OF THE NATIONAL ACADEMY OF SCIENCES OF THE UNITED STATES OF AMERICA
• ISSN/ISSBN: 0027-10289
• DOI: 10.1073/pnas.2314228121
• 发表日期: 2024-02-20
• 关键词: false discovery rate; inference

摘要

In problems such as variable selection and graph estimation, models are characterized by Boolean logical structure such as the presence or absence of a variable or an edge. Consequently, false -positive error or false -negative error can be specified as the number of variables/edges that are incorrectly included or excluded in an estimated model. However, there are several other problems such as ranking, clustering, and causal inference in which the associated model classes do not admit transparent notions of false -positive and false -negative errors due to the lack of an underlying Boolean logical structure. In this paper, we present a generic approach to endow a collection of models with partial order structure, which leads to a hierarchical organization of model classes as well as natural analogs of false -positive and false -negative errors. We describe model selection procedures that provide false -positive error control in our general setting, and we illustrate their utility with numerical experiments.