Multiple testing for signal-agnostic searches of new physics with machine learning
NSF AI Institute for Artificial Intelligence and Fundamental Interactions（NSF人工智能与基础相互作用AI研究所）；MIT Laboratory for Nuclear Science（麻省理工学院核科学实验室）；School of Engineering and Applied Sciences, Harvard University（哈佛大学工程与应用科学学院）；University of Genoa（热那亚大学）；INFN, Sezione di Genova（意大利核物理研究所热那亚分所）
本文研究利用多重检验策略增强机器学习中的信号不可知搜索，通过结合不同超参数的检验并聚合 p 值或统计量，在避免模型偏差的同时实现与最佳检验相当且对异常响应更均匀的性能。
摘要：
在这项工作中，我们探讨了如何利用多重检验策略来增强信号不可知搜索。具体而言，我们考虑了依赖机器学习的假设检验，其中模型选择可能会引入对特定新物理信号族的偏差。我们表明，结合由不同超参数选择所表征的不同检验是有益的，通常能实现与现有最佳检验相当的性能，同时对各种类型的异常提供更均匀的响应。以 New Physics Learning Machine（一种执行信号不可知似然比检验的方法论）为重点，我们探索了多种多重检验方法，例如合并 p 值和聚合检验统计量。
英文摘要：
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. We 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 providing a more uniform response to various types of anomalies. 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 combining p-values and aggregating test statistics.
Searches for unknown physics and decisions between competing astrophysical models to explain data both rely on statistical hypothesis testing. The usual approach in searches for new physical phenomena is based on the statistical Likelihood Ratio Test (LRT) and its asymptotic properties. In the common situation, when neither of the two models under comparison is a special case of the other i.e., when the hypotheses are non-nested, this test is not applicable. In astrophysics, this problem occurs when two models that reside in different parameter spaces are to be compared. An important example i…
Despite its common practice, statistical hypothesis testing presents challenges in interpretation. For instance, in the standard frequentist framework there is no control of the type II error. As a result, the non-rejection of the null hypothesis cannot reasonably be interpreted as its acceptance. We propose that this dilemma can be overcome by using agnostic hypothesis tests, since they can control the type I and II errors simultaneously. In order to make this idea operational, we show how to obtain agnostic hypothesis in typical models. For instance, we show how to build (unbiased) uniformly…
University of California Santa Barbara（加州大学圣巴巴拉分校）
Machine learning models are known to be susceptible to adversarial attacks which can cause misclassification by introducing small but well designed perturbations. In this paper, we consider a classical hypothesis testing problem in order to develop fundamental insight into defending against such adversarial perturbations. We interpret an adversarial perturbation as a nuisance parameter, and propose a defense based on applying the generalized likelihood ratio test (GLRT) to the resulting composite hypothesis testing problem, jointly estimating the class of interest and the adversarial perturbat…
The search for new significant peaks over a energy spectrum often involves a statistical multiple hypothesis testing problem. Separate tests of hypothesis are conducted at different locations producing an ensemble of local p-values, the smallest of which is reported as evidence for the new resonance. Unfortunately, controlling the false detection rate (type I error rate) of such procedures may lead to excessively stringent acceptance criteria. In the recent physics literature, two promising statistical tools have been proposed to overcome these limitations. In 2005, a method to "find needles i…
University of Granada（格拉纳达大学）；University of Cambridge（剑桥大学）
In the 70s a novel branch of statistics emerged focusing its effort in selecting a function in the pattern recognition problem, which fulfils a definite relationship between the quality of the approximation and its complexity. These data-driven approaches are mainly devoted to problems of estimating dependencies with limited sample sizes and comprise all the empirical out-of sample generalization approaches, e.g. cross validation (CV) approaches. Although the latter are \emph{not designed for testing competing hypothesis or comparing different models} in neuroimaging, there are a number of the…
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We study a stylized multiple testing problem where the test statistics are independent and assumed to have the same distribution under their respective null hypotheses. We first show that, in the normal means model where the test statistics are normal Z-scores, the well-known method of (Benjamini and Hochberg, 1995) is optimal in some asymptotic sense. We then show that this is also the case of a recent distribution-free method proposed by Foygel-Barber and Candès (2015). The method is distribution-free in the sense that it is agnostic to the null distribution - it only requires that the null …
A Three-Way Testing Framework for Quantifying Epistemic Calibration Uncertainty in SBI
DEs, ICMC（数学与统计系，计算与应用数学研究所）；Federal Univ. of São Carlos（圣卡洛斯联邦大学）；Univ. of São Paulo（圣保罗大学）；Brazil（巴西）；Univ. Grenoble Alpes（格勒诺布尔阿尔卑斯大学）；Inria（法国国家数字科学研究所）；CNRS（法国国家科学研究中心）；Grenoble INP（格勒诺布尔国立理工学院）；LJK（拉格朗日计算与分析实验室）
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Direct constraints on the agnostic $ν$SMEFT from heavy-neutrino searches at the LHC
Instituto de Física, Facultad de Ciencias, Universidad de la República（乌拉圭共和国大学理学院物理研究所）；Instituto de Física, Facultad Ingeniería, Universidad de la República（乌拉圭共和国大学工程学院物理研究所）
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Sapienza Università di Roma（罗马第一大学）；INFN, Sezione di Roma（意大利国家核物理研究所罗马分部）；Universitat de les Illes Balears（巴利阿里群岛大学）；University of Birmingham（伯明翰大学）；Max-Planck-Institut für Gravitationsphysik (Albert-Einstein-Institut)（马克斯·普朗克引力物理学研究所（阿尔伯特·爱因斯坦研究所））；Leibniz Universität Hannover（汉诺威莱布尼茨大学）
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