  We study the problem of matrix estimation and matrix completion under a
general framework. This framework includes several important models as special
cases such as the gaussian mixture model, mixed membership model, bi-clustering
model and dictionary learning. We consider the optimal convergence rates in a
minimax sense for estimation of the signal matrix under the Frobenius norm and
under the spectral norm. As a consequence of our general result we obtain
minimax optimal rates of convergence for various special models.
