# Distributionally Robust Local Non-parametric Conditional Estimation

arXiv: https://arxiv.org/abs/2010.05373 · HTML: https://mlsanity.com/paper/2010.05373/

## Key facts

- Cited by 13 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 12 Oct 2020.

## Built on by (most cited first, 13 of 13)

- [A Survey of Contextual Optimization Methods for Decision Making under Uncertainty](https://mlsanity.com/paper/2306.10374/) (2023)
- [Statistical Analysis of Wasserstein Distributionally Robust Estimators](https://mlsanity.com/paper/2108.02120/) (2021)
- [Holistic Robust Data-Driven Decisions](https://mlsanity.com/paper/2207.09560/) (2022)
- [Data-Driven Sample Average Approximation with Covariate Information](https://mlsanity.com/paper/2207.13554/) (2022)
- [Semi-Discrete Optimal Transport: Hardness, Regularization and Numerical Solution](https://mlsanity.com/paper/2103.06263/) (2021)
- [Robustifying Conditional Portfolio Decisions via Optimal Transport](https://mlsanity.com/paper/2103.16451/) (2021)
- [Wasserstein Robust Classification with Fairness Constraints](https://mlsanity.com/paper/2103.06828/) (2021)
- [Adversarial for Good? How the Adversarial ML Community's Values Impede Socially Beneficial Uses of Attacks](https://mlsanity.com/paper/2107.10302/) (2021)
- [Adversarial Regression with Doubly Non-negative Weighting Matrices](https://mlsanity.com/paper/2109.14875/) (2021)
- [Distributionally Robust Prescriptive Analytics with Wasserstein Distance](https://mlsanity.com/paper/2106.05724/) (2021)
- [Generative Conditional Distributions by Neural (Entropic) Optimal Transport](https://mlsanity.com/paper/2406.02317/) (2024)
- [Invariant Probabilistic Prediction](https://mlsanity.com/paper/2309.10083/) (2023)
- [Distributionally Robust Recovery of Omitted Factors from Forecast Residuals with Application to Interest Rate Risk Management](https://mlsanity.com/paper/2601.04608/) (2026)

## Abstract (arXiv)

Conditional estimation given specific covariate values (i.e., local conditional estimation or functional estimation) is ubiquitously useful with applications in engineering, social and natural sciences. Existing data-driven non-parametric estimators mostly focus on structured homogeneous data (e.g., weakly independent and stationary data), thus they are sensitive to adversarial noise and may perform poorly under a low sample size. To alleviate these issues, we propose a new distributionally robust estimator that generates non-parametric local estimates by minimizing the worst-case conditional expected loss over all adversarial distributions in a Wasserstein ambiguity set. We show that despite being generally intractable, the local estimator can be efficiently found via convex optimization under broadly applicable settings, and it is robust to the corruption and heterogeneity of the data. Experiments with synthetic and MNIST datasets show the competitive performance of this new class of estimators.