Flows for Flows: Morphing one Dataset into another with Maximum
  Likelihood Estimation
Tobias Golling Samuel Klein Radha Mastandrea Benjamin Nachman John Andrew Raine
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