A Deep Generative Approach to Conditional Sampling

TL;DR

This paper introduces a deep generative method for conditional sampling that leverages neural networks to learn a generator capable of producing samples from complex conditional distributions, handling high-dimensional data.

Contribution

It presents a novel neural network-based conditional generator framework that unifies conditional distribution estimation with nonparametric regression, allowing for high-dimensional and mixed data types.

Findings

Outperforms existing conditional density estimation methods in experiments.

Ensures convergence of the generator to the true conditional distribution.

Handles both continuous and discrete predictors and responses.

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 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.