# Conformalized matrix completion

arXiv: https://arxiv.org/abs/2305.10637 · HTML: https://mlsanity.com/paper/2305.10637/

## Key facts

- Cited by 13 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 18 May 2023.

## Built on by (most cited first, 13 of 13)

- [Conformal prediction for multi-dimensional time series by ellipsoidal sets](https://mlsanity.com/paper/2403.03850/) (2024)
- [Adaptive conformal classification with noisy labels](https://mlsanity.com/paper/2309.05092/) (2023)
- [Conformal Prediction: A Data Perspective](https://mlsanity.com/paper/2410.06494/) (2024)
- [Conformal link prediction for false discovery rate control](https://mlsanity.com/paper/2306.14693/) (2023)
- [Distribution-Free Matrix Prediction Under Arbitrary Missing Pattern](https://mlsanity.com/paper/2305.11640/) (2023)
- [Distributionally robust risk evaluation with an isotonic constraint](https://mlsanity.com/paper/2407.06867/) (2024)
- [Structured Learning of Compositional Sequential Interventions](https://mlsanity.com/paper/2406.05745/) (2024)
- [HI-PMK: A Data-Dependent Kernel for Incomplete Heterogeneous Data Representation](https://mlsanity.com/paper/2501.04300/) (2025)
- [Elements of Conformal Prediction](https://mlsanity.com/paper/2603.23923/) (2026)
- [Matrix Completion via Residual Spectral Matching](https://mlsanity.com/paper/2412.10005/) (2024)
- [Joint Registration and Conformal Prediction for Partially Observed Functional Data](https://mlsanity.com/paper/2502.15000/) (2025)
- [Optimal Transport with Heterogeneously Missing Data](https://mlsanity.com/paper/2505.17291/) (2025)
- [Weighted Conformal Prediction Provides Adaptive and Valid Mask-Conditional Coverage for General Missing Data Mechanisms](https://mlsanity.com/paper/2512.14221/) (2025)

## Abstract (arXiv)

Matrix completion aims to estimate missing entries in a data matrix, using the assumption of a low-complexity structure (e.g., low rank) so that imputation is possible. While many effective estimation algorithms exist in the literature, uncertainty quantification for this problem has proved to be challenging, and existing methods are extremely sensitive to model misspecification. In this work, we propose a distribution-free method for predictive inference in the matrix completion problem. Our method adapts the framework of conformal prediction, which provides confidence intervals with guaranteed distribution-free validity in the setting of regression, to the problem of matrix completion. Our resulting method, conformalized matrix completion (cmc), offers provable predictive coverage regardless of the accuracy of the low-rank model. Empirical results on simulated and real data demonstrate that cmc is robust to model misspecification while matching the performance of existing model-based methods when the model is correct.