Quasiprobabilistic Density Ratio Estimation with a Reverse Engineered Classification Loss Function

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.

Neural Quasiprobabilistic Likelihood Ratio Estimation with Negatively Weighted Data

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.