Quasiprobabilistic Density Ratio Estimation with a Reverse Engineered Classification Loss Function

TL;DR

This paper introduces a convex loss function for quasiprobabilistic density ratio estimation, enabling better handling of negative densities and demonstrating state-of-the-art results in a particle physics application.

Contribution

It proposes a novel convex loss function suitable for quasiprobabilistic density ratios and extends the Sliced-Wasserstein distance for performance evaluation.

Findings

Achieved state-of-the-art results on a particle physics dataset.

Extended the Sliced-Wasserstein distance for quasiprobability distributions.

Demonstrated effectiveness in a real-world physics problem.

Abstract

We consider a generalization of the classifier-based density-ratio estimation task to a quasiprobabilistic setting where probability densities can be negative. The problem with most loss functions used for this task is that they implicitly define a relationship between the optimal classifier and the target quasiprobabilistic density ratio which is discontinuous or not surjective. We address these problems by introducing a convex loss function that is well-suited for both probabilistic and quasiprobabilistic density ratio estimation. To quantify performance, an extended version of the Sliced-Wasserstein distance is introduced which is compatible with quasiprobability distributions. We demonstrate our approach on a real-world example from particle physics, of di-Higgs production in association with jets via gluon-gluon fusion, and achieve state-of-the-art results.