Distributional Matrix Completion via Nearest Neighbors in the Wasserstein Space
通过 Wasserstein 空间近邻进行分布矩阵补全
We study the problem of distributional matrix completion: Given a sparsely observed matrix of empirical distributions, we seek to impute the true distributions associated with both observed and unobserved matrix entries. This is a generalization of traditional matrix completion, where the observations per matrix entry are scalar-valued. To do so, we utilize tools from optimal transport to generalize the nearest neighbors method to the distributional setting. Under a suitable…