Categorizing events using discriminant observables is central to many high-energy physics analyses. Yet, bin boundaries are often chosen by hand. A simple, popular choice is to apply argmax projections of multi-class scores and equidistant binning of one-dimensional discriminants. We propose a binning optimization for signal significance directly in multi-dimensional discriminants. We use a Gaussian Mixture Model (GMM) to define flexible bin boundary shapes for multi-class scores, while in one dimension (binary classification) we move bin boundaries directly. On this binning model, we study two optimization strategies: a differentiable and a Bayesian optimization approach. We study two toy setups: a binary classification and a three-class problem with two signals and backgrounds. In the one-dimensional case, both approaches achieve similar gains in signal sensitivity compared to equidistant binnings for a given number of bins. In the multi-dimensional case, the GMM-based binning defines sensitive categories as well, with the differentiable approach performing best. We show that, in particular for limited separability of the signal processes, our approach outperforms argmax classification even with optimized binning in the one-dimensional projections. Both methods are released as lightweight Python plugins intended for straightforward integration into existing analyses.

翻译：利用判别可观测量对事件进行分类是高能物理分析的核心环节。然而，分箱边界通常依赖人工选择。一种简单且广泛采用的方法是对多类分类得分进行argmax投影，并对一维判别式进行等距分箱。本文提出直接在多维判别式中针对信号显著性进行分箱优化的方法。我们采用高斯混合模型定义多类分类得分的灵活分箱边界形状，而对于一维情况（二分类问题）则直接移动分箱边界。在此分箱模型基础上，我们研究了两种优化策略：可微优化方法与贝叶斯优化方法。通过两个示例场景进行验证：二分类问题以及包含两个信号与背景的三分类问题。在一维情形中，对于给定箱数，两种方法相较于等距分箱均能实现相似的信号灵敏度提升。在多维情形中，基于高斯混合模型的分箱方法同样能构建敏感的分类区间，其中可微优化方法表现最佳。研究表明，特别是在信号过程可分离性有限的情况下，即使对一维投影进行优化分箱，本方法仍优于argmax分类法。两种方法均已发布为轻量级Python插件，便于直接集成至现有分析流程。