Adaptively Weighted Nearest Neighbors for Matrix Completion
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This document introduces and analyzes AWNN (Adaptively Weighted Nearest Neighbors), a novel matrix completion method. Traditional Nearest Neighbor (NN) methods struggle with selecting the appropriate number of neighbors and their weights, often relying on computationally expensive techniques like cross-validation. AWNN addresses this by formulating weight selection as a convex optimization problem, balancing bias-variance tradeoffs and providing a data-driven approach for tuning without manual intervention. The authors present theoretical guarantees for AWNN, demonstrating its performance advantages over unweighted NN methods, particularly in handling missing data, and support these claims with empirical results from synthetic experiments. AWNN offers a principled and efficient alternative for matrix completion in various applications.
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