Domain-Specific Nonparametric Regression for Domain Generalization
提出一种领域特定回归方法，通过非参数估计领域指标函数和回归函数，处理多源数据异质性，提升目标域预测性能，并证明能缓解维度灾难。
We propose a domain-specific regression approach for domain generalization, taking into account possible heterogeneity among the datasets from different sources. In the proposed model, the domain-specific features are characterized through linear functionals of the marginal source distributions. The predictors are combined with the domain-specific linear functionals as inputs in the model. Using the source data sets, we estimate the domain-index function and the regression function nonparametrically based on neural network approximation. The resulting estimated domain-specific regression function can be used for prediction when future unlabeled data from a target domain arrives. We establish the convergence rates at which the cross-domain prediction error of the estimated domain-specific predictive function converges to that of the true one under suitable conditions. Specifically, we derive a general nonasymptotic bound characterized by the hierarchical variation of the proposed model. In addition, we prove that the proposed method can mitigate the curse of dimensionality under some low-dimensional structure assumption. We demonstrate the performance of the proposed method through numerical experiments with simulated and real data. The numerical results show that, our method outperforms several existing methods in terms of the prediction accuracy or computational efficiency, and is robust to model assumptions.