Wasserstein Generative Learning of Conditional Distribution
This method addresses the fundamental challenge of modeling relationships between variables for applications like sample generation and uncertainty quantification, representing a novel method for a known bottleneck in distribution learning.
The authors tackled the problem of learning conditional distributions by proposing a Wasserstein generative approach that transforms a known distribution to the target conditional distribution using a conditional generator, establishing non-asymptotic error bounds and showing it mitigates the curse of dimensionality for data on lower-dimensional sets.
Conditional distribution is a fundamental quantity for describing the relationship between a response and a predictor. We propose a Wasserstein generative approach to learning a conditional distribution. The proposed approach uses a conditional generator to transform a known distribution to the target conditional distribution. The conditional generator is estimated by matching a joint distribution involving the conditional generator and the target joint distribution, using the Wasserstein distance as the discrepancy measure for these joint distributions. We establish non-asymptotic error bound of the conditional sampling distribution generated by the proposed method and show that it is able to mitigate the curse of dimensionality, assuming that the data distribution is supported on a lower-dimensional set. We conduct numerical experiments to validate proposed method and illustrate its applications to conditional sample generation, nonparametric conditional density estimation, prediction uncertainty quantification, bivariate response data, image reconstruction and image generation.