Truncated Matrix Completion - An Empirical Study

2022-08-29

European Signal Processing Conference

AI Summary

This work addresses the practical efficacy of low-rank matrix completion (LRMC) under data-dependent sampling—common in sensing, recommendation, and sequential decision-making—challenging the standard assumption that sampling is independent of the underlying matrix. Through the first systematic empirical evaluation of mainstream algorithms (e.g., Soft-Impute, AltMin, nuclear norm minimization) on both synthetic and real-world datasets, we demonstrate substantial performance degradation under value-dependent truncated sampling. Crucially, we identify coupling between sampling bias direction and intrinsic matrix structure—particularly singular vector alignment—as the primary cause of failure, and derive an interpretable performance decay law grounded in this coupling. Our study bridges a critical gap between theoretical assumptions and practical deployment, providing an empirical foundation and diagnostic framework for designing robust LRMC methods in realistic, non-i.i.d. sampling scenarios.

Technology Category

• Machine Learning: Matrix & Tensor Methods
• Reasoning under Uncertainty: Stochastic Optimization
• Search and Optimization: Sampling/Simulation-based Search

Application Category

• Graph Algorithms and Modeling for the Web: Algorithms and analysis for incomplete, noisy, or partially observed Web-related graphs
• Search and Retrieval-Augmented AI: Web learning to rank, online learning, and counterfactual learning for ranking
• Web Mining and Content Analysis: Robustness and generalizability of Web mining methods

Abstract

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.

Problem

• Recover missing entries in low-rank matrices
• Address data-dependent sampling mask issues
• Compare LRMC algorithms for real-world applications

Innovation

• Truncated Matrix Completion for data-dependent sampling
• Empirical study of LRMC algorithms
• Comparison of performance in various settings