# Collective Matrix Completion

arXiv: https://arxiv.org/abs/1807.09010 · HTML: https://mlsanity.com/paper/1807.09010/

## Key facts

- Cited by 9 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 24 Jul 2018.

## Built on by (most cited first, 9 of 9)

- [Concentration properties of fractional posterior in 1-bit matrix completion](https://mlsanity.com/paper/2404.08969/) (2024)
- [Mixed Matrix Completion in Complex Survey Sampling under Heterogeneous Missingness](https://mlsanity.com/paper/2402.03954/) (2024)
- [Statistical Inference For Noisy Matrix Completion Incorporating Auxiliary Information](https://mlsanity.com/paper/2403.14899/) (2024)
- [Transductive Matrix Completion with Calibration for Multi-Task Learning](https://mlsanity.com/paper/2302.09834/) (2023)
- [Misclassification excess risk bounds for 1-bit matrix completion](https://mlsanity.com/paper/2312.12945/) (2023)
- [Misclassification excess risk bounds for PAC-Bayesian classification via convexified loss](https://mlsanity.com/paper/2408.08675/) (2024)
- [Optimal Transport with Heterogeneously Missing Data](https://mlsanity.com/paper/2505.17291/) (2025)
- [Transfer Learning for Matrix Completion](https://mlsanity.com/paper/2507.02248/) (2025)
- [Exponential-Family Tensor Completion via Nonconvex Dual Total-Variation Regularization](https://mlsanity.com/paper/2606.30958/) (2026)

## Abstract (arXiv)

Matrix completion aims to reconstruct a data matrix based on observations of a small number of its entries. Usually in matrix completion a single matrix is considered, which can be, for example, a rating matrix in recommendation system. However, in practical situations, data is often obtained from multiple sources which results in a collection of matrices rather than a single one. In this work, we consider the problem of collective matrix completion with multiple and heterogeneous matrices, which can be count, binary, continuous, etc. We first investigate the setting where, for each source, the matrix entries are sampled from an exponential family distribution. Then, we relax the assumption of exponential family distribution for the noise and we investigate the distribution-free case. In this setting, we do not assume any specific model for the observations. The estimation procedures are based on minimizing the sum of a goodness-of-fit term and the nuclear norm penalization of the whole collective matrix. We prove that the proposed estimators achieve fast rates of convergence under the two considered settings and we corroborate our results with numerical experiments.