We investigate sample-based learning of conditional distributions on multi-dimensional unit boxes, allowing for different dimensions of the feature and target spaces. Our approach involves clustering data near varying query points in the feature space to create empirical measures in the target space. We employ two distinct clustering schemes: one based on a fixed-radius ball and the other on nearest neighbors. We establish upper bounds for the convergence rates of both methods and, from these bounds, deduce optimal configurations for the radius and the number of neighbors. We propose to incorporate the nearest neighbors method into neural network training, as our empirical analysis indicates it has better performance in practice. For efficiency, our training process utilizes approximate nearest neighbors search with random binary space partitioning. Additionally, we employ the Sinkhorn algorithm and a sparsity-enforced transport plan. Our empirical findings demonstrate that, with a suitably designed structure, the neural network has the ability to adapt to a suitable level of Lipschitz continuity locally. For reproducibility, our code is available at \url{https://github.com/zcheng-a/LCD_kNN}.
Deep conditional distribution learning via conditional Föllmer flow
Joint Laboratory of Data Science and Business Intelligence（数据科学与商务智能联合实验室）；Southwestern University of Finance and Economics（西南财经大学）；State Key Laboratory of Mathematical Sciences（数学科学国家重点实验室）；Academy of Mathematics and Systems Science（数学与系统科学学院）；Chinese Academy of Sciences（中国科学院）；School of Mathematics and Statistics（数学与统计学学院）；Wuhan University（武汉大学）；Hubei Key Laboratory of Computational Science（湖北省计算科学重点实验室）
Learning about an exponential amount of conditional distributions
Facebook AI Research（脸书人工智能研究院）；Montréal Institute for Learning Algorithms (MILA), University of Montréal（蒙特利尔学习算法研究所（米拉），蒙特利尔大学）
我们介绍了神经调节器（NC），一个自我监督的机器，能够学习一个随机向量$X$的所有条件分布。NC是一个函数$NC(x \cdot a, a, r)$，它利用对抗训练来匹配每个条件分布$P(X_r|X_a=x_a)$。在训练之后，NC从从未见过的条件分布中推广样本，包括联合分布。NC还能够自动编码示例，为下游分类任务提供有用的数据表示。总而言之，NC将不同的自我监督任务（每个任务都是对条件分布的估计）和监督级别（部分观察数据）无缝集成到单个学习体验中。
