Experiments using machine learning to approximate likelihood ratios for mixture models

17th International Workshop on Advanced Computing and Analysis Techniques in Physics Research

物理学;计算机科学

Cranmer, K.^1 ; Pavez, J.^2 ; Louppe, G.^1 ; Brooks, W.K.^3

Physics Department, New York University, New York

NY

10003, United States^1

Informatics Department, Universidad Técnica Federico Santa María, 1680 Av. España, Valparaíso, Chile^2

Physics Department, Universidad Técnica Federico Santa María, Center for Science and Technology of Valparaíso, 1680 Av. España, Valparaíso, Chile^3

关键词: Complex simulation;    Discriminative classifiers;    Likelihood functions;    Likelihood ratio tests;    Likelihood ratios;    Signal contribution;    Underlying distribution;    Unknown coefficients;   

Others  :  https://iopscience.iop.org/article/10.1088/1742-6596/762/1/012034/pdf
DOI  :  10.1088/1742-6596/762/1/012034

学科分类：计算机科学（综合）

来源: IOP

【 摘 要 】

Likelihood ratio tests are a key tool in many fields of science. In order to evaluate the likelihood ratio the likelihood function is needed. However, it is common in fields such as High Energy Physics to have complex simulations that describe the distribution while not having a description of the likelihood that can be directly evaluated. In this setting it is impossible or computationally expensive to evaluate the likelihood. It is, however, possible to construct an equivalent version of the likelihood ratio that can be evaluated by using discriminative classifiers. We show how this can be used to approximate the likelihood ratio when the underlying distribution is a weighted sum of probability distributions (e.g. signal plus background model). We demonstrate how the results can be considerably improved by decomposing the ratio and use a set of classifiers in a pairwise manner on the components of the mixture model and how this can be used to estimate the unknown coefficients of the model, such as the signal contribution.