Quasiprobabilistic Density Ratio Estimation with a Reverse Engineered Classification Loss Function
This work addresses a specific challenge in quasiprobabilistic density-ratio estimation for domains like particle physics, representing an incremental improvement with a novel method for a known bottleneck.
The paper tackles the problem of density-ratio estimation in a quasiprobabilistic setting where densities can be negative, by introducing a convex loss function and an extended Sliced-Wasserstein distance for evaluation, achieving state-of-the-art results in a particle physics application.
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.