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Published February 20, 2024 | Published
Journal Article Open

Model selection over partially ordered sets

  • 1. ROR icon California Institute of Technology


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.

Copyright and License

© 2024 the Author(s). Published by PNAS. This article is distributed under Creative Commons Attribution-NonCommercial-NoDerivatives License 4.0 (CC BY-NC-ND).


We thank Marina Meila and Lior Pachter for insightful conversations. A.T. received funding from the Royalty Research Fund at the University of Washington. P.B. received funding from the European Research Council under the European Union’s Horizon 2020 research and innovation program (grant agreement No. 786461). V.C. was supported in part by Air Force Office of Scientific Research grants FA9550-22-1-0225 and FA9550-23-1-0204 and by NSF grant DMS 2113724.


A.T., P.B., and V.C. designed research; performed research; and wrote the paper.

Data Availability

All study data are included in the article. The code for implementing our methods is available at https://github.com/armeentaeb/model-selection-over-posets (30).

Conflict of Interest

The authors declare no competing interest.


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Additional details

February 21, 2024
February 21, 2024