自适应加权近邻法提升矩阵补全精度，无需交叉验证选参数。
Adaptively-weighted Nearest Neighbors for Matrix Completion
- 根据偏差-方差权衡动态调整近邻权重与半径。
- 理论证明在弱假设下仍具良好性能，合成实验验证有效。
- 适合推荐系统等缺失数据场景，尤其需避免调参的用户。
本文提出AWNN：一种用于矩阵补全的自适应加权最近邻方法。最近邻方法广泛应用于推荐系统、面板数据反事实推断等缺失数据问题，因其直观易实现且具备良好理论保障而受到青睐。然而，多数方法性能依赖于邻域半径和邻居权重的合理选择，尽管过去二十年已有诸多研究，仍缺乏不依赖交叉验证的系统性选择策略。AWNN通过精巧平衡加权最近邻回归中的偏差-方差权衡，解决了该问题。我们在最弱假设下提供了理论保证，并通过合成实验支持理论结论。
原文摘要 · Abstract (English)
In this technical note, we introduce and analyze AWNN: an adaptively weighted nearest neighbor method for performing matrix completion. Nearest neighbor (NN) methods are widely used in missing data problems across multiple disciplines such as in recommender systems and for performing counterfactual inference in panel data settings. Prior works have shown that in addition to being very intuitive and easy to implement, NN methods enjoy nice theoretical guarantees. However, the performance of majority of the NN methods rely on the appropriate choice of the radii and the weights assigned to each member in the nearest neighbor set and despite several works on nearest neighbor methods in the past two decades, there does not exist a systematic approach of choosing the radii and the weights without relying on methods like cross-validation. AWNN addresses this challenge by judiciously balancing the bias variance trade off inherent in weighted nearest-neighbor regression. We provide theoretical guarantees for the proposed method under minimal assumptions and support the theory via synthetic experiments.
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