# Doubly robust nearest neighbors in factor models

arXiv: https://arxiv.org/abs/2211.14297 · HTML: https://mlsanity.com/paper/2211.14297/

## Key facts

- Cited by 9 papers in the map (data through 14 Oct 2026).
- Builds on 17 of its 66 references that are in the map.
- First posted on arXiv 25 Nov 2022.

## Builds on (most cited first, 17 of 17)

- [A Tutorial on Thompson Sampling](https://mlsanity.com/paper/1707.02038/) (2017)
- [Doubly Robust Off-policy Value Evaluation for Reinforcement Learning](https://mlsanity.com/paper/1511.03722/) (2015)
- [Double Reinforcement Learning for Efficient Off-Policy Evaluation in Markov Decision Processes](https://mlsanity.com/paper/1908.08526/) (2019)
- [Optimal and Adaptive Off-policy Evaluation in Contextual Bandits](https://mlsanity.com/paper/1612.01205/) (2016)
- [Personalized HeartSteps: A Reinforcement Learning Algorithm for Optimizing Physical Activity](https://mlsanity.com/paper/1909.03539/) (2019)
- [Causal Matrix Completion](https://mlsanity.com/paper/2109.15154/) (2021)
- [Synthetic Difference in Differences](https://mlsanity.com/paper/1812.09970/) (2018)
- [Inference and Uncertainty Quantification for Noisy Matrix Completion](https://mlsanity.com/paper/1906.04159/) (2019)
- [Assessing Time-Varying Causal Effect Moderation in Mobile Health](https://mlsanity.com/paper/1601.00237/) (2016)
- [Synthetic Interventions](https://mlsanity.com/paper/2006.07691/) (2020)
- [Robust Synthetic Control](https://mlsanity.com/paper/1711.06940/) (2017)
- [Stochastic Bandits for Multi-platform Budget Optimization in Online Advertising](https://mlsanity.com/paper/2103.10246/) (2021)
- [Matrix Completion via Max-Norm Constrained Optimization](https://mlsanity.com/paper/1303.0341/) (2013)
- [Contextual Multi-Armed Bandits for Causal Marketing](https://mlsanity.com/paper/1810.01859/) (2018)
- [What Is Meant by "Missing at Random"?](https://mlsanity.com/paper/1306.2812/) (2013)
- [Uncertainty quantification for nonconvex tensor completion: Confidence intervals, heteroscedasticity and optimality](https://mlsanity.com/paper/2006.08580/) (2020)
- [Nonparametric Matrix Estimation with One-Sided Covariates](https://mlsanity.com/paper/2110.13969/) (2021)

## Built on by (most cited first, 9 of 9)

- [Doubly Robust Inference in Causal Latent Factor Models](https://mlsanity.com/paper/2402.11652/) (2024)
- [Distributional Matrix Completion via Nearest Neighbors in the Wasserstein Space](https://mlsanity.com/paper/2410.13112/) (2024)
- [Learning Counterfactual Distributions via Kernel Nearest Neighbors](https://mlsanity.com/paper/2410.13381/) (2024)
- [A Causal Inference Framework for Data Rich Environments](https://mlsanity.com/paper/2504.01702/) (2025)
- [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)
- [N2: A Unified Python Package and Test Bench for Nearest Neighbor-Based Matrix Completion](https://mlsanity.com/paper/2506.04166/) (2025)
- [Counterfactual Forecasting for Panel Data](https://mlsanity.com/paper/2511.06189/) (2025)
- [Causal Matrix Completion under Multiple Treatments via Mixed Synthetic Nearest Neighbors](https://mlsanity.com/paper/2603.11942/) (2026)

## Abstract (arXiv)

We introduce and analyze an improved variant of nearest neighbors (NN) for estimation with missing data in latent factor models. We consider a matrix completion problem with missing data, where the (i, t)-th entry, when observed, is given by its mean f(ui, vt) plus mean-zero noise for an unknown function f and latent factors ui and vt. Prior NN strategies, like unit-unit NN, for estimating the mean f(ui, vt) relies on existence of other rows j with uj ≈ ui. Similarly, time-time NN strategy relies on existence of columns t' with vt' ≈ vt. These strategies provide poor performance respectively when similar rows or similar columns are not available. Our estimate is doubly robust to this deficit in two ways: (1) As long as there exist either good row or good column neighbors, our estimate provides a consistent estimate. (2) Furthermore, if both good row and good column neighbors exist, it provides a (near-)quadratic improvement in the non-asymptotic error and admits a significantly narrower asymptotic confidence interval when compared to both unit-unit or time-time NN.