Conformalized matrix completion

TL;DR

This paper introduces conformalized matrix completion (cmc), a distribution-free method that provides robust, valid uncertainty quantification for matrix completion, regardless of model correctness, outperforming existing methods under misspecification.

Contribution

The paper develops a novel conformal prediction-based approach for matrix completion that guarantees predictive coverage without relying on low-rank assumptions.

Findings

Cmc provides valid coverage under model misspecification.

Cmc matches existing methods when the model is correct.

Empirical results show robustness and accuracy on real and simulated data.

Abstract

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.