E Pluribus Unum Ex Machina: Learning from Many Collider Events at Once

TL;DR

This paper investigates the theoretical and empirical aspects of combining multiple collider events into classifiers, showing how single-event classifiers relate to multi-event classifiers and evaluating their effectiveness in collider physics tasks.

Contribution

It provides a formal framework connecting single- and multi-event classifiers, demonstrating how to construct optimal classifiers in both cases, and empirically compares their performance.

Findings

Single-event classifiers generally outperform multi-event classifiers in studied cases.

Optimal multi-event classifiers can be derived from single-event classifiers under IID assumptions.

No clear advantage of multi-event classifiers was observed in collider physics applications.

Abstract

There have been a number of recent proposals to enhance the performance of machine learning strategies for collider physics by combining many distinct events into a single ensemble feature. To evaluate the efficacy of these proposals, we study the connection between single-event classifiers and multi-event classifiers under the assumption that collider events are independent and identically distributed (IID). We show how one can build optimal multi-event classifiers from single-event classifiers, and we also show how to construct multi-event classifiers such that they produce optimal single-event classifiers. This is illustrated for a Gaussian example as well as for classification tasks relevant for searches and measurements at the Large Hadron Collider. We extend our discussion to regression tasks by showing how they can be phrased in terms of parametrized classifiers. Empirically, we find that training a single-event (per-instance) classifier is more effective than training a multi-event (per-ensemble) classifier, as least for the cases we studied, and we relate this fact to properties of the loss function gradient in the two cases. While we did not identify a clear benefit from using multi-event classifiers in the collider context, we speculate on the potential value of these methods in cases involving only approximate independence, as relevant for jet substructure studies.