A Generative Approach to Conditional Sampling

• Activity Number: 440 - SLDS CSpeed 8
• Type: Contributed
• Date/Time: Thursday, August 12, 2021 : 4:00 PM to 5:50 PM
• Sponsor: Section on Statistical Learning and Data Science
• Author(s): Xingyu Zhou* and Jian Huang and Yuling Jiao and Jin Liu
• Companies: Department of statistics and actuarial Science, The university of Iowa and Department of statistics and actuarial science, The university of Iowa and School of Mathematics and Statistics, Wuhan University and Duke-NUS Medical School, Health Service & Systems Research
• Keywords: Distribution matching; Generative learning; f-divergence; High-dimensional data; Nonparametric estimation; Neural networks

Abstract

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 $f$-divergence. An appealing aspect of our method is that it allows either or both of 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 generated conditional samples converge in distribution to the underlying conditional distribution. Our numerical experiments with simulated and benchmark image data validate the proposed method and demonstrate that it outperforms several existing conditional density estimation methods.