Neural Quasiprobabilistic Likelihood Ratio Estimation with Negatively Weighted Data

TL;DR

This paper introduces a novel neural likelihood ratio estimation method capable of handling negative probability densities and importance weights, addressing challenges in high energy physics applications.

Contribution

It proposes a new loss function and a signed mixture model architecture to effectively estimate likelihood ratios in quasiprobabilistic settings with negative densities.

Findings

Successfully applied to particle physics data

Outperforms traditional methods in negative density scenarios

Provides a robust framework for importance sampling with negative weights

Abstract

Motivated by real-world situations found in high energy particle physics, we consider a generalisation of the likelihood-ratio estimation task to a quasiprobabilistic setting where probability densities can be negative. By extension, this framing also applies to importance sampling in a setting where the importance weights can be negative. The presence of negative densities and negative weights, pose an array of challenges to traditional neural likelihood ratio estimation methods. We address these challenges by introducing a novel loss function. In addition, we introduce a new model architecture based on the decomposition of a likelihood ratio using signed mixture models, providing a second strategy for overcoming these challenges. Finally, we demonstrate our approach on a pedagogical example and a real-world example from particle physics.