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Abstract In this work, we address the question of how to enhance signal-agnostic searches by leveraging multiple testing strategies. Specifically, we consider hypothesis tests relying on machine learning, where model selection can introduce a bias towards specific families of new physics signals. Focusing on the New Physics Learning Machine, a methodology to perform a signal-agnostic likelihood-ratio test, we explore a number of approaches to multiple testing, such as combiningp-values and aggregating test statistics. Our findings show that it is beneficial to combine different tests, characterised by distinct choices of hyperparameters, and that performances comparable to the best available test are generally achieved, while also providing a more uniform response to various types of anomalies. This study proposes a methodology that is valid beyond machine learning approaches and could in principle be applied to a larger class model-agnostic analyses based on hypothesis testing.
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A generalized hypothesis test for community structure in networks
Abstract Researchers theorize that many real-world networks exhibit community structure where within-community edges are more likely than between-community edges. While numerous methods exist to cluster nodes into different communities, less work has addressed this question: given some network, does it exhibitstatistically meaningfulcommunity structure? We answer this question in a principled manner by framing it as a statistical hypothesis test in terms of a general and model-agnostic community structure parameter. Leveraging this parameter, we propose a simple and interpretable test statistic used to formulate two separate hypothesis testing frameworks. The first is an asymptotic test against a baseline value of the parameter while the second tests against a baseline model using bootstrap-based thresholds. We prove theoretical properties of these tests and demonstrate how the proposed method yields rich insights into real-world datasets.
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- Award ID(s):
- 2413327
- PAR ID:
- 10590431
- Publisher / Repository:
- Cambridge University Press
- Date Published:
- Journal Name:
- Network Science
- Volume:
- 12
- Issue:
- 2
- ISSN:
- 2050-1242
- Page Range / eLocation ID:
- 122 to 138
- Format(s):
- Medium: X
- Sponsoring Org:
- National Science Foundation
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- Free Publicly Accessible Full Text
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Accepted Manuscript1.0
- Journal Article:
- https://doi.org/10.1017/nws.2024.1
