Quasiprobabilistic Density Ratio Estimation with a Reverse Engineered Classification Loss Function

2025-12-22

AI Summary

Conventional classification losses in quasi-probability density ratio estimation induce a discontinuous, non-surjective mapping between the optimal discriminator and the target ratio. Method: We propose a novel convex and invertible classification loss, establishing a strict bijection between discriminator outputs and quasi-probability ratios; further, we define an extended sliced Wasserstein distance compatible with negative densities, providing a theoretically consistent metric for quasi-probability distributions containing negative values. Our loss is reverse-engineered to ensure estimation stability and interpretability. Results: Evaluated on the real-world particle physics task of gluon-fusion di-Higgs + jet production, our framework significantly improves density ratio estimation accuracy, achieving state-of-the-art performance.

Technology Category

• Machine Learning: Calibration & Uncertainty Quantification
• Reasoning under Uncertainty: Relational Probabilistic Models
• Search and Optimization: Learning to Search

Application Category

• Search and Retrieval-Augmented AI: Web learning to rank, online learning, and counterfactual learning for ranking
• Economics, Online Markets and Human Computation: LLM based quality controls for crowd work
• Graph Algorithms and Modeling for the Web: Graph embeddings and representation learning for Web-related graphs

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.

Problem

• Generalizes density-ratio estimation to allow negative probability densities
• Introduces a convex loss function for quasiprobabilistic density ratio estimation
• Applies method to particle physics for di-Higgs production analysis

Innovation

• Convex loss function for quasiprobabilistic density ratio estimation
• Extended Sliced-Wasserstein distance for quasiprobability distributions
• Applied to particle physics di-Higgs production with jets