# Nonparametric Matrix Estimation with One-Sided Covariates

arXiv: https://arxiv.org/abs/2110.13969 · HTML: https://mlsanity.com/paper/2110.13969/

## Key facts

- Cited by 5 papers in the map (data through 14 Oct 2026).
- Builds on 6 of its 38 references that are in the map.
- First posted on arXiv 26 Oct 2021.

## Builds on (most cited first, 6 of 6)

- [Matrix Completion has No Spurious Local Minimum](https://mlsanity.com/paper/1605.07272/) (2016)
- [Provable Inductive Matrix Completion](https://mlsanity.com/paper/1306.0626/) (2013)
- [Rates of Convergence of Spectral Methods for Graphon Estimation](https://mlsanity.com/paper/1709.03183/) (2017)
- [Matrix Completion on Graphs](https://mlsanity.com/paper/1408.1717/) (2014)
- [Optimal Estimation and Completion of Matrices with Biclustering Structures](https://mlsanity.com/paper/1512.00150/) (2015)
- [Why are Big Data Matrices Approximately Low Rank?](https://mlsanity.com/paper/1705.07474/) (2017)

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

- [Doubly robust nearest neighbors in factor models](https://mlsanity.com/paper/2211.14297/) (2022)
- [Tackling Combinatorial Distribution Shift: A Matrix Completion Perspective](https://mlsanity.com/paper/2307.06457/) (2023)
- [Two-Sided Nearest Neighbors: An adaptive and minimax optimal procedure for matrix completion](https://mlsanity.com/paper/2411.12965/) (2024)
- [Adaptively-weighted Nearest Neighbors for Matrix Completion](https://mlsanity.com/paper/2505.09612/) (2025)
- [Radial Neighborhood Smoothing Recommender System](https://mlsanity.com/paper/2507.09952/) (2025)

## Abstract (arXiv)

Consider the task of matrix estimation in which a dataset X ∈ ℝn× m is observed with sparsity p, and we would like to estimate mathbbE[X], where mathbbE[Xui] = f(αu, βi) for some Holder smooth function f. We consider the setting where the row covariates α are unobserved yet the column covariates β are observed. We provide an algorithm and accompanying analysis which shows that our algorithm improves upon naively estimating each row separately when the number of rows is not too small. Furthermore when the matrix is moderately proportioned, our algorithm achieves the minimax optimal nonparametric rate of an oracle algorithm that knows the row covariates. In simulated experiments we show our algorithm outperforms other baselines in low data regimes.