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。