# Adaptively-weighted Nearest Neighbors for Matrix Completion

arXiv: https://arxiv.org/abs/2505.09612 · HTML: https://mlsanity.com/paper/2505.09612/

## Key facts

- Cited by 1 papers in the map (data through 14 Oct 2026).
- Builds on 13 of its 38 references that are in the map.
- First posted on arXiv 14 May 2025.

## Builds on (most cited first, 13 of 13)

- [Matrix Completion and Low-Rank SVD via Fast Alternating Least Squares](https://mlsanity.com/paper/1410.2596/) (2014)
- [Noisy Matrix Completion: Understanding Statistical Guarantees for Convex Relaxation via Nonconvex Optimization](https://mlsanity.com/paper/1902.07698/) (2019)
- [Causal Matrix Completion](https://mlsanity.com/paper/2109.15154/) (2021)
- [Provable Inductive Matrix Completion](https://mlsanity.com/paper/1306.0626/) (2013)
- [Synthetic Interventions](https://mlsanity.com/paper/2006.07691/) (2020)
- [Local nearest neighbour classification with applications to semi-supervised learning](https://mlsanity.com/paper/1704.00642/) (2017)
- [Design-based Analysis in Difference-In-Differences Settings with Staggered Adoption](https://mlsanity.com/paper/1808.05293/) (2018)
- [Matrix completion with data-dependent missingness probabilities](https://mlsanity.com/paper/2106.02290/) (2021)
- [Counterfactual inference in sequential experiments](https://mlsanity.com/paper/2202.06891/) (2022)
- [Doubly robust nearest neighbors in factor models](https://mlsanity.com/paper/2211.14297/) (2022)
- [Trust your neighbors: A comprehensive survey of neighborhood-based methods for recommender systems](https://mlsanity.com/paper/2109.04584/) (2021)
- [Nonparametric Matrix Estimation with One-Sided Covariates](https://mlsanity.com/paper/2110.13969/) (2021)
- [Two-Sided Nearest Neighbors: An adaptive and minimax optimal procedure for matrix completion](https://mlsanity.com/paper/2411.12965/) (2024)

## Built on by (most cited first, 1 of 1)

- [N2: A Unified Python Package and Test Bench for Nearest Neighbor-Based Matrix Completion](https://mlsanity.com/paper/2506.04166/) (2025)

## Abstract (arXiv)

In this technical note, we introduce and analyze AWNN: an adaptively weighted nearest neighbor method for performing matrix completion. Nearest neighbor (NN) methods are widely used in missing data problems across multiple disciplines such as in recommender systems and for performing counterfactual inference in panel data settings. Prior works have shown that in addition to being very intuitive and easy to implement, NN methods enjoy nice theoretical guarantees. However, the performance of majority of the NN methods rely on the appropriate choice of the radii and the weights assigned to each member in the nearest neighbor set and despite several works on nearest neighbor methods in the past two decades, there does not exist a systematic approach of choosing the radii and the weights without relying on methods like cross-validation. AWNN addresses this challenge by judiciously balancing the bias variance trade off inherent in weighted nearest-neighbor regression. We provide theoretical guarantees for the proposed method under minimal assumptions and support the theory via synthetic experiments.