# Distribution-Free Matrix Prediction Under Arbitrary Missing Pattern

arXiv: https://arxiv.org/abs/2305.11640 · HTML: https://mlsanity.com/paper/2305.11640/

## Key facts

- Cited by 5 papers in the map (data through 14 Oct 2026).
- Builds on 22 of its 49 references that are in the map.
- First posted on arXiv 19 May 2023.

## Builds on (most cited first, 22 of 22)

- [Distribution-Free Predictive Inference For Regression](https://mlsanity.com/paper/1604.04173/) (2016)
- [Conformalized Quantile Regression](https://mlsanity.com/paper/1905.03222/) (2019)
- [Conformal prediction beyond exchangeability](https://mlsanity.com/paper/2202.13415/) (2022)
- [Conformal Risk Control](https://mlsanity.com/paper/2208.02814/) (2022)
- [Predictive inference with the jackknife+](https://mlsanity.com/paper/1905.02928/) (2019)
- [Conformal Inference of Counterfactuals and Individual Treatment Effects](https://mlsanity.com/paper/2006.06138/) (2020)
- [Learning by Transduction](https://mlsanity.com/paper/1301.7375/) (2013)
- [Conformal Prediction: a Unified Review of Theory and New Challenges](https://mlsanity.com/paper/2005.07972/) (2020)
- [Distributional conformal prediction](https://mlsanity.com/paper/1909.07889/) (2019)
- [Conformalized Survival Analysis](https://mlsanity.com/paper/2103.09763/) (2021)
- [An Exact and Robust Conformal Inference Method for Counterfactual and Synthetic Controls](https://mlsanity.com/paper/1712.09089/) (2017)
- [Testing randomness](https://mlsanity.com/paper/1906.09256/) (2019)
- [Estimating network edge probabilities by neighborhood smoothing](https://mlsanity.com/paper/1509.08588/) (2015)
- [Network cross-validation by edge sampling](https://mlsanity.com/paper/1612.04717/) (2016)
- [Stable Conformal Prediction Sets](https://mlsanity.com/paper/2112.10224/) (2021)
- [Black-box tests for algorithmic stability](https://mlsanity.com/paper/2111.15546/) (2021)
- [Nearly-optimal Robust Matrix Completion](https://mlsanity.com/paper/1606.07315/) (2016)
- [Conformalized matrix completion](https://mlsanity.com/paper/2305.10637/) (2023)
- [Optimal Estimation and Completion of Matrices with Biclustering Structures](https://mlsanity.com/paper/1512.00150/) (2015)
- [Link prediction for partially observed networks](https://mlsanity.com/paper/1301.7047/) (2013)
- [Co-clustering of Nonsmooth Graphons](https://mlsanity.com/paper/1507.06352/) (2015)
- [Inductive Conformal Recommender System](https://mlsanity.com/paper/2109.08949/) (2021)

## Built on by (most cited first, 5 of 5)

- [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)
- [Conformal Prediction for Dyadic Regression Under Complex Missingness](https://mlsanity.com/paper/2606.11136/) (2026)
- [Joint Registration and Conformal Prediction for Partially Observed Functional Data](https://mlsanity.com/paper/2502.15000/) (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)

This paper studies the open problem of conformalized entry prediction in a row/column-exchangeable matrix. The matrix setting presents novel and unique challenges, but there exists little work on this interesting topic. We meticulously define the problem, differentiate it from closely related problems, and rigorously delineate the boundary between achievable and impossible goals. We then propose two practical algorithms. The first method provides a fast emulation of the full conformal prediction, while the second method leverages the technique of algorithmic stability for acceleration. Both methods are computationally efficient and can effectively safeguard coverage validity in presence of arbitrary missing pattern. Further, we quantify the impact of missingness on prediction accuracy and establish fundamental limit results. Empirical evidence from synthetic and real-world data sets corroborates the superior performance of our proposed methods.