A Deep Generative Approach to Conditional Sampling
提出一种基于噪声外包引理的深度生成方法，通过学习条件生成器从参考分布采样来逼近目标条件分布，适用于高维预测变量或响应变量，且能处理连续和离散类型。
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 transforming 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. Supplementary materials for this article are available online.