  We propose a deep generative approach to sampling from a conditional
distribution based on a unified formulation of conditional distribution and
generalized nonparametric regression function using the noise-outsourcing
lemma. The proposed approach aims at learning a conditional generator so that a
random sample from the target conditional distribution can be obtained by the
action of the conditional generator on a sample drawn from a reference
distribution. The conditional generator is estimated nonparametrically with
neural networks by matching appropriate joint distributions using the
Kullback-Liebler divergence. An appealing aspect of our method is that it
allows either of or both the predictor and the response to be high-dimensional
and can handle both continuous and discrete type predictors and responses. We
show that the proposed method is consistent in the sense that the conditional
generator converges in distribution to the underlying conditional distribution
under mild conditions. Our numerical experiments with simulated and benchmark
image data validate the proposed method and demonstrate that it outperforms
several existing conditional density estimation methods.
