A Phase-Space Inclusive Figure of Merit Based in Optimal Transport for Validating Monte Carlo Reweightings

Abstract

Validating whether the underlying physics of a model has been retained after a full phase-space reweighting poses a unique challenge. Often, validation relies on comparing histograms of 1D observables; however, this can mask correlations and biases in the complete prediction. We present a novel, unbinned approach to comparing the performance of such reweighting schemes based on the "Cross-Section-Mover's Distance", an application of Optimal Transport that quantifies the work required to transform one theoretical prediction into another and enables an interpretation of results in terms of metric spaces. We demonstrate its utility when benchmarking various reweighting schemes that mitigate the effects of negative weights in a Monte Carlo simulation. This approach can be broadly applied in other scenarios where biases in full phase-space reweighting schemes should be studied in an unbinned way.