Communicating Likelihoods with Normalising Flows

TL;DR

This paper introduces a machine learning workflow that models unbinned likelihoods from samples, validated by rigorous statistical tests, facilitating reliable communication of likelihoods in high-energy physics analyses.

Contribution

It presents a novel method for modeling and validating unbinned likelihoods using normalizing flows, with an open-source implementation for broader adoption.

Findings

Effective modeling of likelihoods demonstrated in three high-energy physics case studies.

Validation of learned likelihoods using statistical tests like Kolmogorov-Smirnov.

Open-source tool 'nabu' supports implementation and adoption.

Abstract

We present a machine-learning-based workflow to model an unbinned likelihood from its samples. A key advancement over existing approaches is the validation of the learned likelihood using rigorous statistical tests of the joint distribution, such as the Kolmogorov-Smirnov test of the joint distribution. Our method enables the reliable communication of experimental and phenomenological likelihoods for subsequent analyses. We demonstrate its effectiveness through three case studies in high-energy physics. To support broader adoption, we provide an open-source reference implementation, nabu.