Flow Away your Differences: Conditional Normalizing Flows as an Improvement to Reweighting

TL;DR

This paper introduces a method using conditional normalizing flows to modify distributions for better data correction, outperforming traditional reweighting techniques by being binning-independent and providing higher statistical precision.

Contribution

The authors propose a novel approach employing conditional normalizing flows to improve distribution correction, avoiding binning and density ratio estimation, with demonstrated superior performance over reweighting.

Findings

Normalizing flows outperform reweighting in distribution matching.

The method achieves up to three times greater statistical precision.

Effective in high energy physics applications.

Abstract

We present an alternative to reweighting techniques for modifying distributions to account for a desired change in an underlying conditional distribution, as is often needed to correct for mis-modelling in a simulated sample. We employ conditional normalizing flows to learn the full conditional probability distribution from which we sample new events for conditional values drawn from the target distribution to produce the desired, altered distribution. In contrast to common reweighting techniques, this procedure is independent of binning choice and does not rely on an estimate of the density ratio between two distributions. In several toy examples we show that normalizing flows outperform reweighting approaches to match the distribution of the target.We demonstrate that the corrected distribution closes well with the ground truth, and a statistical uncertainty on the training dataset can be ascertained with bootstrapping. In our examples, this leads to a statistical precision up to three times greater than using reweighting techniques with identical sample sizes for the source and target distributions. We also explore an application in the context of high energy particle physics.