Weighted Matrix Completion From Non-Random, Non-Uniform Sampling Patterns

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