Solving weakly supervised multi-output regression

Abstract

We propose a solution to the multi-output weakly supervised regression problem. In the studied setting the observed data is partly labeled, and known labels are considered to be the probability distribution to represent possible uncertainty in labeling due to noise. The proposed solution consists in minimizing the Wasserstein distance between multivariate normal distributions, and approximation of matrices having a low-rank format. In the experimental part of the paper we provide the results, which are shown to be superior to the previous methods on Monte-Carlo simulations and a real dataset