# Robust Matrix Estimation with Side Information

arXiv: https://arxiv.org/abs/2603.24833 · HTML: https://mlsanity.com/paper/2603.24833/

## Key facts

- No citing papers in the map yet (data through 14 Oct 2026).
- Builds on 3 of its 29 references that are in the map.
- First posted on arXiv 25 Mar 2026.

## Builds on (most cited first, 3 of 3)

- [Provable Inductive Matrix Completion](https://mlsanity.com/paper/1306.0626/) (2013)
- [Entrywise Inference for Missing Panel Data: A Simple and Instance-Optimal Approach](https://mlsanity.com/paper/2401.13665/) (2024)
- [Provable Inductive Robust PCA via Iterative Hard Thresholding](https://mlsanity.com/paper/1704.00367/) (2017)

## Abstract (arXiv)

We introduce a flexible framework for high-dimensional matrix estimation to incorporate side information for both rows and columns. Existing approaches, such as inductive matrix completion, often impose restrictive structure-for example, an exact low-rank covariate interaction term, linear covariate effects, and limited ability to exploit components explained only by one side (row or column) or by neither-and frequently omit an explicit noise component. To address these limitations, we propose to decompose the underlying matrix as the sum of four complementary components: (possibly nonlinear) interaction between row and column characteristics; row characteristic-driven component, column characteristic-driven component, and residual low-rank structure unexplained by observed characteristics. By combining sieve-based projection with nuclear-norm penalization, each component can be estimated separately and these estimated components can then be aggregated to yield a final estimate. We derive convergence rates that highlight robustness across a range of model configurations depending on the informativeness of the side information. We further extend the method to partially observed matrices under both missing-at-random and missing-not-at-random mechanisms, including block-missing patterns motivated by causal panel data. Simulations and a real-data application to tobacco sales show that leveraging side information improves imputation accuracy and can enhance treatment-effect estimation relative to standard low-rank and spectral-based alternatives.