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.
翻译:有条件分布是描述响应和预测器之间关系的一个基本数量。我们提议了瓦森斯坦基因化方法来学习有条件分布。拟议方法使用一个有条件的发电机将已知分布转换成目标有条件分布。有条件的发电机通过将有条件的发电机与目标联合分布相匹配来估算,使用瓦塞斯坦距离作为这些联合分布的差异计量标准。我们确定了非默认错误,将拟议方法产生的有条件抽样分布捆绑在一起,并表明它能够减轻维度的诅咒,假设数据分布得到低维度数据集的支持。我们进行了数字实验,以验证拟议方法,并展示其对有条件样本生成、非参数性有条件密度估计、预测不确定性量化、双轨反应数据、图像重建与图像生成的应用。