Distribution Regression Network

We introduce our Distribution Regression Network (DRN) which performs regression from input probability distributions to output probability distributions. Compared to existing methods, DRN learns with fewer model parameters and easily extends to multiple input and multiple output distributions. On synthetic and real-world datasets, DRN performs similarly or better than the state-of-the-art. The field of regression analysis is largely established with methods ranging from linear least squares to multilayer perceptrons. However, the scope of the regression is mostly limited to real valued inputs and outputs (Fiori et al., 2015; Marquardt, 1963). In this paper, we perform distribution-to- distribution regression where one regresses from input probability distributions to output probability distributions. Distribution-to-distribution regression (see work by Oliva et al. (2013)) has not been as widely studied compared to the related task of functional regression (Ferraty & Vieu, 2006). Nevertheless, regression on distributions has many relevant applications. In the study of human populations, probability distributions capture the collective characteristics of the people.