Flows for Flows: Morphing one Dataset into another with Maximum Likelihood Estimation
This addresses a common data analysis challenge in high energy physics and other fields by providing a novel morphing technique, though it appears incremental as it builds on existing normalizing flow methods.
The paper tackles the problem of morphing one dataset into another without explicit probability densities, proposing a protocol called flows for flows that uses normalizing flows trained with maximum likelihood estimation, and demonstrates it on toy examples and a collider physics case with dijet events, showing it enables a morphing strategy that statistically matches datasets. The result is a method that shifts data points instead of reweighting, preserving weights and allowing conditioning on features for varied morphing functions.
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