# Matrix Completion with Sparse Noisy Rows

arXiv: https://arxiv.org/abs/2204.01530 · HTML: https://mlsanity.com/paper/2204.01530/

## Key facts

- No citing papers in the map yet (data through 14 Oct 2026).
- Builds on 7 of its 15 references that are in the map.
- First posted on arXiv 1 Apr 2022.

## Builds on (most cited first, 7 of 7)

- [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)
- [Lifelong Matrix Completion with Sparsity-Number](https://mlsanity.com/paper/2203.07637/) (2022)
- [Adaptive Noisy Matrix Completion](https://mlsanity.com/paper/2203.08340/) (2022)
- [Matrix Completion with Heterogonous Cost](https://mlsanity.com/paper/2203.12120/) (2022)

## Abstract (arXiv)

Exact matrix completion and low rank matrix estimation problems has been studied in different underlying conditions. In this work we study exact low-rank completion under non-degenerate noise model. Non-degenerate random noise model has been previously studied by many researchers under given condition that the noise is sparse and existing in some of the columns. In this paper, we assume that each row can receive random noise instead of columns and propose an interactive algorithm that is robust to this noise. We show that we use a parametrization technique to give a condition when the underlying matrix could be recoverable and suggest an algorithm which recovers the underlying matrix.