# Exponential Family Matrix Completion under Structural Constraints

arXiv: https://arxiv.org/abs/1509.04397 · HTML: https://mlsanity.com/paper/1509.04397/

## Key facts

- Cited by 2 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 15 Sep 2015.

## Built on by (most cited first, 2 of 2)

- [Always Valid Risk Monitoring for Online Matrix Completion](https://mlsanity.com/paper/2211.10363/) (2022)
- [DRIVE: Dynamic Rule Inference and Verified Evaluation for Constraint-Aware Autonomous Driving](https://mlsanity.com/paper/2508.04066/) (2025)

## Abstract (arXiv)

We consider the matrix completion problem of recovering a structured matrix from noisy and partial measurements. Recent works have proposed tractable estimators with strong statistical guarantees for the case where the underlying matrix is low--rank, and the measurements consist of a subset, either of the exact individual entries, or of the entries perturbed by additive Gaussian noise, which is thus implicitly suited for thin--tailed continuous data. Arguably, common applications of matrix completion require estimators for (a) heterogeneous data--types, such as skewed--continuous, count, binary, etc., (b) for heterogeneous noise models (beyond Gaussian), which capture varied uncertainty in the measurements, and (c) heterogeneous structural constraints beyond low--rank, such as block--sparsity, or a superposition structure of low--rank plus elementwise sparseness, among others. In this paper, we provide a vastly unified framework for generalized matrix completion by considering a matrix completion setting wherein the matrix entries are sampled from any member of the rich family of exponential family distributions; and impose general structural constraints on the underlying matrix, as captured by a general regularizer R(.). We propose a simple convex regularized M--estimator for the generalized framework, and provide a unified and novel statistical analysis for this general class of estimators. We finally corroborate our theoretical results on simulated datasets.