  We study the matrix completion problem when the observation pattern is
deterministic and possibly non-uniform. We propose a simple and efficient
debiased projection scheme for recovery from noisy observations and analyze the
error under a suitable weighted metric. We introduce a simple function of the
weight matrix and the sampling pattern that governs the accuracy of the
recovered matrix. We derive theoretical guarantees that upper bound the
recovery error and nearly matching lower bounds that showcase optimality in
several regimes. Our numerical experiments demonstrate the computational
efficiency and accuracy of our approach, and show that debiasing is essential
when using non-uniform sampling patterns.
