  There is emerging interest in performing regression between distributions. In
contrast to prediction on single instances, these machine learning methods can
be useful for population-based studies or on problems that are inherently
statistical in nature. The recently proposed distribution regression network
(DRN) has shown superior performance for the distribution-to-distribution
regression task compared to conventional neural networks. However, in Kou et
al. (2018) and some other works on distribution regression, there is a lack of
comprehensive comparative study on both theoretical basis and generalization
abilities of the methods. We derive some mathematical properties of DRN and
qualitatively compare it to conventional neural networks. We also perform
comprehensive experiments to study the generalizability of distribution
regression models, by studying their robustness to limited training data, data
sampling noise and task difficulty. DRN consistently outperforms conventional
neural networks, requiring fewer training data and maintaining robust
performance with noise. Furthermore, the theoretical properties of DRN can be
used to provide some explanation on the ability of DRN to achieve better
generalization performance than conventional neural networks.
