Iterative Collaborative Filtering for Sparse Matrix Estimation
提出一种在稀疏数据中通过比较扩展局部邻域来计算相似度的协同过滤算法，适用于低秩矩阵估计，提供逐项误差界，算法可解释、可扩展且易于分布式实现。
Matrix estimation or completion has served as a canonical mathematical model for recommendation systems. More recently, it has emerged as a fundamental building block for data analysis as a first step to denoise the observations and predict missing values. Since the dawn of e-commerce, similarity-based collaborative filtering has been used as a heuristic for matrix etimation. At its core, it encodes typical human behavior: you ask your friends to recommend what you may like or dislike. Algorithmically, friends are similar “rows” or “columns” of the underlying matrix. The traditional heuristic for computing similarities between rows has costly requirements on the density of observed entries. In “Iterative Collaborative Filtering for Sparse Matrix Estimation” by Christian Borgs, Jennifer T. Chayes, Devavrat Shah, and Christina Lee Yu, the authors introduce an algorithm that computes similarities in sparse datasets by comparing expanded local neighborhoods in the associated data graph: in effect, you ask friends of your friends to recommend what you may like or dislike. This work provides bounds on the max entry-wise error of their estimate for low rank and approximately low rank matrices, which is stronger than the aggregate mean squared error bounds found in classical works. The algorithm is also interpretable, scalable, and amenable to distributed implementation.