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 establish 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.
"Structured matrix estimation and completion." Bernoulli 25 (4B) 3883 - 3911, November 2019. https://doi.org/10.3150/19-BEJ1114