Learning new physics efficiently with nonparametric methods

Abstract

We present a machine learning approach for model-independent new physics searches. The corresponding algorithm is powered by recent large-scale implementations of kernel methods, nonparametric learning algorithms that can approximate any continuous function given enough data. Based on the original proposal by D’Agnolo and Wulzer (Phys Rev D 99(1):015014, 2019, arXiv:1806.02350 [hep-ph]), the model evaluates the compatibility between experimental data and a reference model, by implementing a hypothesis testing procedure based on the likelihood ratio. Model-independence is enforced by avoiding any prior assumption about the presence or shape of new physics components in the measurements. We show that our approach has dramatic advantages compared to neural network implementations in terms of training times and computational resources, while maintaining comparable performances. In particular, we conduct our tests on higher dimensional datasets, a step forward with respect to previous studies.

On the curse of dimensionality for Normalizing Flows

“…• Development of reliable multivariate quality metrics, including approaches based on machine learning [58,59]. New results [60][61][62] suggests that classifier-based two-sample tests have the potential to match the needs of the HEP community when paired with a careful statistical analysis. These tests can leverage different ML models to provide high flexibility and sensitivity together with short training times, especially when based on kernel methods [62].…”

A fast and flexible machine learning approach to data quality monitoring

“…By a standard computation, the learned function can be shown to approximate the likelihood ratio f ŵ ≈ f * (x) = log p(x|1) p(x|0) (see, for instance, appendix A of Ref. [5]). The log-likelihood ratio test statistics can then be easily evaluated on the measurements as…”

“…Hyper-parameters are tuned following the prescription given in Ref. [5], which includes a mix of heuristics, statistical optimality and efficiency requirements. Anomaly detection.…”

“…This work is inspired by the ML model introduced in Ref. [5] in the context of model-independent new physics searches in high-energy physics. In that work, the authors propose an algorithm based on kernel methods with clear advantages compared to similar neural network implementations in terms of training time while obtaining similar performance.…”

CURTAINs for your sliding window: Constructing unobserved regions by transforming adjacent intervals

“…These models are subsequently used to reject SM-like processes in favour of potential new physics. Other approaches are motivated from the ratio of probability densities and directly measure a test statistic from the comparison of a sample of events with respect to a set of reference distributed events (D'Agnolo and Wulzer, 2019 ; Simone and Jacques, 2019 ; D'Agnolo et al, 2021 ; Letizia et al, 2022 ). A comparison of a wide range of methods is also performed in Kasieczka et al ( 2021 ), which summarises a community challenge for anomaly detection in high energy physics.…”