提出新损失函数，实现负概率密度比的稳定估计
Quasiprobabilistic Density Ratio Estimation with a Reverse Engineered Classification Loss Function
- 设计凸损失函数，解决传统方法中分类器与目标不匹配问题
- 在粒子物理真实数据上实现当前最优密度比估计效果
- 适用于需要负概率分布的前沿科学建模任务
我们研究了将基于分类器的密度比估计推广到允许负值的概率密度的准概率设定。现有损失函数隐含地导致最优分类器与目标准概率密度比之间存在不连续或非满射关系。为此，我们提出一种凸损失函数，适用于概率和准概率密度比估计。为评估性能，引入一种兼容准概率分布的广义切片沃瑟斯坦距离。我们在粒子物理中的真实案例——胶子-胶子融合产生双希格斯玻色子并伴随喷注——上验证该方法，取得了当前最优结果。
原文摘要 · Abstract (English)
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.
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