# Truncated Matrix Completion - An Empirical Study

arXiv: https://arxiv.org/abs/2504.09873 · HTML: https://mlsanity.com/paper/2504.09873/

## Key facts

- No citing papers in the map yet (data through 14 Oct 2026).
- Builds on 11 of its 33 references that are in the map.
- First posted on arXiv 14 Apr 2025.

## Builds on (most cited first, 11 of 11)

- [Recommendations as Treatments: Debiasing Learning and Evaluation](https://mlsanity.com/paper/1602.05352/) (2016)
- [Implicit Regularization Towards Rank Minimization in ReLU Networks](https://mlsanity.com/paper/2201.12760/) (2022)
- [Causal Matrix Completion](https://mlsanity.com/paper/2109.15154/) (2021)
- [Imputation and low-rank estimation with Missing Not At Random data](https://mlsanity.com/paper/1812.11409/) (2018)
- [Matrix completion with data-dependent missingness probabilities](https://mlsanity.com/paper/2106.02290/) (2021)
- [A Characterization of Deterministic Sampling Patterns for Low-Rank Matrix Completion](https://mlsanity.com/paper/1503.02596/) (2015)
- [Rank 2r iterative least squares: efficient recovery of ill-conditioned low rank matrices from few entries](https://mlsanity.com/paper/2002.01849/) (2020)
- [GNMR: A provable one-line algorithm for low rank matrix recovery](https://mlsanity.com/paper/2106.12933/) (2021)
- [Matrix completion with deterministic pattern - a geometric perspective](https://mlsanity.com/paper/1802.00047/) (2018)
- [TenIPS: Inverse Propensity Sampling for Tensor Completion](https://mlsanity.com/paper/2101.00323/) (2021)
- [Escaping Saddle Points in Ill-Conditioned Matrix Completion with a Scalable Second Order Method](https://mlsanity.com/paper/2009.02905/) (2020)

## Abstract (arXiv)

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.