Flows for Flows: Morphing one Dataset into another with Maximum Likelihood Estimation

TL;DR

This paper introduces a novel method called flows for flows, enabling the morphing of one dataset into another using normalizing flows trained with maximum likelihood, even without explicit knowledge of data densities, with applications in physics.

Contribution

It proposes a new protocol for training normalizing flows for dataset morphing without explicit density knowledge, including conditioning capabilities and practical demonstrations.

Findings

Effective dataset morphing demonstrated on toy examples.

Conditioned flows enable feature-specific morphing.

Method outperforms traditional reweighting approaches.

Abstract

Many components of data analysis in high energy physics and beyond require morphing one dataset into another. This is commonly solved via reweighting, but there are many advantages of preserving weights and shifting the data points instead. Normalizing flows are machine learning models with impressive precision on a variety of particle physics tasks. Naively, normalizing flows cannot be used for morphing because they require knowledge of the probability density of the starting dataset. In most cases in particle physics, we can generate more examples, but we do not know densities explicitly. We propose a protocol called flows for flows for training normalizing flows to morph one dataset into another even if the underlying probability density of neither dataset is known explicitly. This enables a morphing strategy trained with maximum likelihood estimation, a setup that has been shown to be highly effective in related tasks. We study variations on this protocol to explore how far the data points are moved to statistically match the two datasets. Furthermore, we show how to condition the learned flows on particular features in order to create a morphing function for every value of the conditioning feature. For illustration, we demonstrate flows for flows for toy examples as well as a collider physics example involving dijet events