Adaptive Noisy Matrix Completion

TL;DR

This paper introduces an adaptive approach for noisy low-rank matrix completion that estimates the subspace bounds iteratively, requiring fewer observations than previous fixed sampling methods.

Contribution

It presents a novel adaptive matrix completion algorithm that efficiently estimates the low-rank subspace with bounded noise, outperforming fixed sampling techniques.

Findings

Requires fewer observations than fixed sampling methods.

Effectively estimates the subspace bounds in the presence of noise.

Improves efficiency of noisy matrix completion algorithms.

Abstract

Low-rank matrix completion has been studied extensively under various type of categories. The problem could be categorized as noisy completion or exact completion, also active or passive completion algorithms. In this paper we focus on adaptive matrix completion with bounded type of noise. We assume that the matrix $\mathbf{M}$ we target to recover is composed as low-rank matrix with addition of bounded small noise. The problem has been previously studied by \cite{nina}, in a fixed sampling model. Here, we study this problem in adaptive setting that, we continuously estimate an upper bound for the angle with the underlying low-rank subspace and noise-added subspace. Moreover, the method suggested here, could be shown requires much smaller observation than aforementioned method.