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

TL;DR

This paper introduces a novel binning optimization method for multi-dimensional discriminants in high-energy physics, improving signal sensitivity over traditional methods using differentiable and Bayesian approaches with GMM-based bin boundaries.

Contribution

It presents a new binning optimization technique using GMMs and differentiable/Bayesian methods, enhancing event categorization in high-energy physics analyses.

Findings

Both methods outperform equidistant binning in signal sensitivity.

Differentiable approach performs best in multi-dimensional binning.

Outperforms argmax classification with optimized binning in limited separability scenarios.

Abstract

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.