A deep generative approach to conditional distribution estimation and its applications

A fundamental problem in statistics and machine learning is how to model the relationship between a response and a predictor. Such a model can be used for predicting the values of the response based on the new observations of the predictor and for assessing the variation in the response for a given value of the predictor. The familiar regression models that focus on estimating the conditional mean or median of the response given the predictor have been widely used for such purposes in applications. However, in problems when the conditional distribution is multimodal or asymmetrical, conditional mean and median are no longer adequate for modeling the relationship between the response and predictor. In general, to completely understand how the response depends on the predictor, it becomes necessary to learn the conditional distribution, which provides a full description of the relationship between the response variable and the predictor. Conditional distribution is widely used in scientific research and engineering for describing the relationship between two factors. This thesis proposes a deep generative approach to learning a conditional distribution. The proposed approach is inspired by the recently developed generative adversarial networks in deep learning. Instead of estimating the functional form of the conditional distribution, the proposed approach seeks to estimate a conditional generator that can sample from the target conditional distribution. The basis of the proposed method is a unified formulation of the conditional density estimation and the generalized nonparametric regression. The thesis also includes illustrations of the use the proposed method in a wide range of applications, including conditional sample generation, prediction with uncertainty quantification, image generation, image reconstruction, and survival analysis in biostatistics.