Learning Mixtures of Low-Rank Models

We study the problem of learning mixtures low-rank models, i.e. reconstructing multiple matrices from unlabelled linear measurements each. This enriches two widely studied settings - matrix sensing and mixed regression by bringing latent variables (i.e. unknown labels) structural priors structures) into consideration. To cope with non-convexity issues arising heterogeneous data low-complexity structure, we develop a three-stage meta-algorithm that is guaranteed to recover near-optimal sample computational complexities under Gaussian designs. In addition, proposed algorithm provably stable against random noise. complement theoretical studies empirical evidence confirms efficacy our algorithm.