Learning to bin: differentiable and Bayesian optimization for multi-dimensional discriminants in high-energy physics

The European Physical Journal C, vol. 86

Abstract

Abstract Categorizing events using discriminant observables is central to many high-energy physics analyses. Yet, bin boundaries are often chosen manually. A simple, popular choice in multi-classification tasks is to assign events according to the largest per-class score (“argmax”) and to apply equidistant binning to the resulting 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 regions in the score space, which can be interpreted either as bins or as analysis categories. While this GMM-based strategy is applicable in both one and multiple dimensions, we also study a direct bin-boundary optimization in one dimension as a simpler alternative for binary discriminants. 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 binning for a given number of bins, while in the multi-dimensional case the differentiable approach performs best. We show that the GMM-based optimization can outperform argmax classification even after optimized binning is applied to the one-dimensional projections. We further study the performance of our methods on the FAIR Universe $$H\rightarrow \tau \tau $$ H → τ τ dataset, where the GMM-based optimization gives the highest signal significance. Both methods are released as lightweight Python plugins intended for straightforward integration into existing analyses.

Authors 3

1. Johannes Erdmann Aachen

   RWTH Aachen University

   Affiliation as printed

   RWTH Aachen University

2. Nitish Kumar corresponding Aachen

   RWTH Aachen University

   Affiliation as printed

   RWTH Aachen University

3. Florian Mausolf Aachen

   RWTH Aachen University

   Affiliation as printed

   RWTH Aachen University