E Pluribus Unum Ex Machina: Learning from Many Collider Events at Once
This work addresses a methodological question in collider physics for researchers, but it is incremental as it builds on existing proposals without demonstrating clear advantages.
The paper tackled the problem of evaluating multi-event classifiers in collider physics by showing how to build optimal multi-event classifiers from single-event ones and vice versa, finding empirically that single-event classifiers are more effective for the cases studied, with no clear benefit identified for multi-event classifiers.
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.