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We study the matrix completion problem when the observation pattern isdeterministic and possibly non-uniform. We propose a simple and efficientdebiased projection scheme for recovery from noisy observations and analyze theerror under a suitable weighted metric. We introduce a simple function of theweight matrix and the sampling pattern that governs the accuracy of therecovered matrix. We derive theoretical guarantees that upper bound therecovery error and nearly matching lower bounds that showcase optimality inseveral regimes. Our numerical experiments demonstrate the computationalefficiency and accuracy of our approach, and show that debiasing is essentialwhen using non-uniform sampling patterns.

Weighted matrix completion from non-random, non-uniform sampling patterns