Distributionally Robust Local Non-parametric Conditional Estimation
This addresses robustness issues in non-parametric estimation for applications in engineering and sciences, though it appears incremental as it builds on existing methods with a robustness focus.
The paper tackles the problem of local conditional estimation under adversarial noise and low sample sizes by proposing a distributionally robust estimator that minimizes worst-case conditional expected loss over Wasserstein ambiguity sets, achieving competitive performance on synthetic and MNIST datasets.
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.