This project is on designing a model and algorithm that would impute matrix missing values using kernels. Here each matrix entries are assigned a distribution which is not accessible but its multiple samples are, and these samples are not observed for some entries. Imputation here means approximation of underlying distribution using neighboring observed samples. This setup is a generalization of traditional matrix completion problem. Our algorithm regards multiple measurements for each cell as an empirical distribution and use Maximum Mean Discrepency(kernel motivated metric) to quantify distance between empirical distributions for the purpose of identifying nearest neighbors. Then barycenters of empirical distributions within neighbor is returned. We show that our nearest neighbor algorithm successfully imputes matrix entries even when entries are missing with certain confounders and when some proportion of entries are deterministically not observed.