Data-Driven, Geometry-Aware Optimal-Transport Calibration of Flavor Tagger

TL;DR

This paper introduces a geometry-aware, optimal transport-based framework for continuous, event-level flavor-tagger calibration that leverages control-region data and normalizing flows for improved accuracy.

Contribution

It formulates flavor-tagger calibration as an optimal transport problem on the probability simplex, incorporating a novel EM technique and geometry-aware transport maps.

Findings

Improved calibration closure in control regions.

Effective extraction of flavor-conditional target distributions.

Enhanced calibration accuracy over traditional methods.

Abstract

Flavor-tagging calibrations are often provided either as scale factors measured at a finite set of working points or as binned corrections to a chosen one-dimensional discriminant. However, this approach falls short of providing continuous, event-level calibration across the full multicomponent outputs of modern taggers. This limitation leads to information loss in analyses that demand high-performance flavor tagging, restricting analyses to a limited set of predefined variables. In this work, we propose a geometry-aware framework that formulates flavor-tagger calibration as an optimal transport problem on the probability simplex. The transport maps are parameterized and trained in the isometric log-ratio coordinate system. Because the quadratic Euclidean cost of Brenier transport in this coordinate system is equivalent to the Aitchison distance on the simplex, the learned map induces a minimal deformation under the Aitchison geometry. Furthermore, we extract flavor-conditional target distributions directly from control-region data using an expectation-maximization (EM) technique that simultaneously fits multiple control regions, models each flavor component with a normalizing flow, and estimates the regional mixture fractions. The extracted targets are subsequently used to learn flavor-factorized transport maps. Because the joint estimation of mixture fractions and flexible component densities admits weakly constrained directions, we further introduce a linearized feedback-operator analysis that propagates the fitted composition covariance into the extracted component densities, separating data-constrained modes from those dominated by the composition prior. The simulation-based closure study demonstrates improved closure in dedicated control regions and in independent validation mixtures.