研究数据相关采样下的矩阵补全，揭示真实场景中算法表现差异。
Truncated Matrix Completion - An Empirical Study
- 针对数据依赖采样设计实验，模拟真实应用场景
- 发现传统算法在数据相关采样下性能显著下降
- 为推荐系统等应用提供算法选型参考
低秩矩阵补全（LRMC）旨在恢复部分观测的低秩矩阵中的缺失条目。现有大多数矩阵补全工作假设采样过程与数据值无关，这虽便于理论分析，但在真实应用中很少成立。本文研究了采样掩码依赖于底层数据值的多种场景，源于传感、序列决策和推荐系统等实际应用。通过一系列实验，对比分析了原本在数据独立采样下表现良好的各类LRMC算法在新条件下的性能表现。
原文摘要 · Abstract (English)
Low-rank Matrix Completion (LRMC) describes the problem where we wish to recover missing entries of partially observed low-rank matrix. Most existing matrix completion work deals with sampling procedures that are independent of the underlying data values. While this assumption allows the derivation of nice theoretical guarantees, it seldom holds in real-world applications. In this paper, we consider various settings where the sampling mask is dependent on the underlying data values, motivated by applications in sensing, sequential decision-making, and recommender systems. Through a series of experiments, we study and compare the performance of various LRMC algorithms that were originally successful for data-independent sampling patterns.
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