Normalizing Flow Regression

In this letter we propose a convex approach to learning expressive scalar conditional distributions. The model denoted by Normalizing Flow Regression (NFR) is inspired by deep normalizing flow networks but is convex due to the use of a dictionary of pre-defined transformations. By defining a rich enough dictionary, NFR generalizes the Gaussian posterior associated with linear regression to an arbitrary conditional distribution. In the special case of piece wise linear dictionary, we also provide a closed form solution for the conditional mean. We demonstrate the advantages of NFR over competitors using synthetic data as well as real world data.