Wasserstein Distributionally Robust Nonparametric Regression
NeutralArtificial Intelligence
In the recent paper 'Wasserstein Distributionally Robust Nonparametric Regression,' researchers delve into the application of Wasserstein distributionally robust optimization (WDRO) within nonparametric regression frameworks. This study is crucial as it addresses model uncertainty, a common challenge in statistical learning. The authors establish a structural distinction based on the order of the Wasserstein distance, where a first-order distance induces Lipschitz-type regularization, while higher orders correspond to gradient-norm regularization. They analyze the excess local worst-case risk and derive non-asymptotic error bounds for estimators constructed with norm-constrained feedforward neural networks. The proposed estimator achieves a convergence rate of n^{-2β/(d+2β)}, which is significant in high-dimensional settings, indicating minimax optimality under commonly satisfied conditions. This work not only strengthens the theoretical foundation of WDRO in nonparametric contexts but…
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