Matrix Completion with Heterogonous Cost

TL;DR

This paper investigates matrix completion when observation costs vary across entries, introducing models for heterogeneous costs and analyzing the complexity and guarantees of algorithms under these conditions.

Contribution

It proposes new models for matrix completion with non-uniform costs and provides complexity analysis and tightness guarantees for these models.

Findings

Algorithms with proven complexity bounds for heterogeneous cost models

Tightness guarantees established for the proposed algorithms

Analysis applicable to real-world scenarios with variable observation costs

Abstract

The matrix completion problem has been studied broadly under many underlying conditions. The problem has been explored under adaptive or non-adaptive, exact or estimation, single-phase or multi-phase, and many other categories. In most of these cases, the observation cost of each entry is uniform and has the same cost across the columns. However, in many real-life scenarios, we could expect elements from distinct columns or distinct positions to have a different cost. In this paper, we explore this generalization under adaptive conditions. We approach the problem under two different cost models. The first one is that entries from different columns have different observation costs, but, within the same column, each entry has a uniform cost. The second one is any two entry has different observation cost, despite being the same or different columns. We provide complexity analysis of our algorithms and provide tightness guarantees.