Learning conditional distributions is challenging because the desired outcome
is not a single distribution but multiple distributions that correspond to
multiple instances of the covariates. We introduce a novel neural entropic
optimal transport method designed to effectively learn generative models of
conditional distributions, particularly in scenarios characterized by limited
sample sizes. Our method relies on the minimax training of two neural networks:
a generative network parametrizing the inverse cumulative distribution
functions of the conditional distributions and another network parametrizing
the conditional Kantorovich potential. To prevent overfitting, we regularize
the objective function by penalizing the Lipschitz constant of the network
output. Our experiments on real-world datasets show the effectiveness of our
algorithm compared to state-of-the-art conditional distribution learning
techniques. Our implementation can be found at
this https URL

学习条件分布是具有挑战性的，因为所需的结果不是单个分布，而是与协变量的多个实例对应的多个分布。我们引入一种新颖的神经自由最优输运方法，旨在有效地学习条件分布的生成模型，特别是在样本量有限的情况下。我们的方法依赖于两个神经网络的极小极大训练：一个生成网络参数化条件分布的逆累积分布函数，另一个网络参数化条件 Kantorovich 势。为防止过拟合，我们通过惩罚网络输出的 Lipschitz 常数来正则化目标函数。我们在真实数据集上的实验结果显示了我们的算法相对于最先进的条件分布学习技术的有效性。我们的实现可以在 https URL 找到。

神经（熵）最优输运的生成条件分布

Generative Conditional Distributions by Neural (Entropic) Optimal  Transport

In this paper, we propose a new and unified approach for nonparametric
regression and conditional distribution learning. Our approach simultaneously
estimates a regression function and a conditional generator using a generative
learning framework, where a conditional generator is a function that can
generate samples from a conditional distribution. The main idea is to estimate
a conditional generator that satisfies the constraint that it produces a good
regression function estimator. We use deep neural networks to model the
conditional generator. Our approach can handle problems with multivariate
outcomes and covariates, and can be used to construct prediction intervals. We
provide theoretical guarantees by deriving non-asymptotic error bounds and the
distributional consistency of our approach under suitable assumptions. We also
perform numerical experiments with simulated and real data to demonstrate the
effectiveness and superiority of our approach over some existing approaches in
various scenarios.

提出一种新的非参数回归和条件分布学习的统一方法，该方法可以通过生成学习框架同时估计回归函数和条件生成器，使用深度神经网络模型来构建条件生成器，并能够处理多元结果和协变量问题，可以用于构建预测区间，并提供了理论保证以及在模拟和真实数据上的数值实验结果。