Data-Driven High-Dimensional Statistical Inference with Generative Models

TL;DR

HI-SIGMA introduces a data-driven, generative ML-based method for high-dimensional statistical inference in particle physics, improving sensitivity and systematic uncertainty handling over traditional classifier-based approaches.

Contribution

The paper presents HI-SIGMA, a novel generative ML approach for unbinned high-dimensional inference that directly models background distributions, unlike prior classifier-based methods.

Findings

HI-SIGMA outperforms standard classifier-based methods in sensitivity.

The approach effectively incorporates systematic uncertainties.

Demonstrated on a di-Higgs measurement in $bb\gamma\gamma$ final state.

Abstract

Crucial to many measurements at the LHC is the use of correlated multi-dimensional information to distinguish rare processes from large backgrounds, which is complicated by the poor modeling of many of the crucial backgrounds in Monte Carlo simulations. In this work, we introduce HI-SIGMA, a method to perform unbinned high-dimensional statistical inference with data-driven background distributions. In contradistinction to many applications of Simulation Based Inference in High Energy Physics, HI-SIGMA relies on generative ML models, rather than classifiers, to learn the signal and background distributions in the high-dimensional space. These ML models allow for interpretable inference while also incorporating model errors and other sources of systematic uncertainties. We showcase this methodology on a simplified version of a di-Higgs measurement in the $bb\gamma\gamma$ final state, where the di-photon resonance allows for background interpolation from sidebands into the signal region. We demonstrate that HI-SIGMA provides improved sensitivity as compared to standard classifier-based methods, and that systematic uncertainties can be straightforwardly incorporated by extending methods which have been used for histogram based analyses.