Truncated Matrix Completion - An Empirical Study
This work addresses a practical limitation in matrix completion for applications where sampling is data-dependent, though it is incremental as it empirically tests existing methods rather than proposing new ones.
The paper investigates the performance of low-rank matrix completion algorithms when the sampling mask depends on underlying data values, a common scenario in real-world applications like sensing and recommender systems, and finds that existing methods originally designed for data-independent sampling show varied effectiveness.
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.