# Adaptive Noisy Matrix Completion

arXiv: https://arxiv.org/abs/2203.08340 · HTML: https://mlsanity.com/paper/2203.08340/

## Key facts

- Cited by 3 papers in the map (data through 14 Oct 2026).
- Builds on 8 of its 20 references that are in the map.
- First posted on arXiv 16 Mar 2022.

## Builds on (most cited first, 8 of 8)

- [Efficient Representations for Life-Long Learning and Autoencoding](https://mlsanity.com/paper/1411.1490/) (2014)
- [Low-Rank Matrix and Tensor Completion via Adaptive Sampling](https://mlsanity.com/paper/1304.4672/) (2013)
- [On the Power of Adaptivity in Matrix Completion and Approximation](https://mlsanity.com/paper/1407.3619/) (2014)
- [Noise-Tolerant Life-Long Matrix Completion via Adaptive Sampling](https://mlsanity.com/paper/1612.00100/) (2016)
- [Optimal Exact Matrix Completion Under new Parametrization](https://mlsanity.com/paper/2002.02431/) (2020)
- [Adaptive Sampling Distributed Stochastic Variance Reduced Gradient for Heterogeneous Distributed Datasets](https://mlsanity.com/paper/2002.08528/) (2020)
- [Lifelong Matrix Completion with Sparsity-Number](https://mlsanity.com/paper/2203.07637/) (2022)
- [Performance of Distribution Regression with Doubling Measure under the seek of Closest Point](https://mlsanity.com/paper/2203.00155/) (2022)

## Built on by (most cited first, 3 of 3)

- [Matrix Completion with Heterogonous Cost](https://mlsanity.com/paper/2203.12120/) (2022)
- [Survey of Matrix Completion Algorithms](https://mlsanity.com/paper/2204.01532/) (2022)
- [Matrix Completion with Sparse Noisy Rows](https://mlsanity.com/paper/2204.01530/) (2022)

## Abstract (arXiv)

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 M we target to recover is composed as low-rank matrix with addition of bounded small noise. The problem has been previously studied by citenina, 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.