Sample Efficient Nonparametric Regression via Low-Rank Regularization
提出一种基于低秩假设的非参数回归降维方法，通过级数估计和张量回归处理高维数据，在近似低秩情形下收敛速度更快，模拟和真实数据表明其均方根误差低于现有方法。
Nonparametric regression suffers from curse of dimensionality, requiring a relatively large sample size for accurate estimation beyond the univariate case. In this paper, we consider a simple method of dimension reduction in nonparametric regression via series estimation, based on the concept of low-rankness which was previously studied in parametric multivariate reduced-rank regression and matrix regression. For d>2, the low-rank assumption is realized via tensor regression. We establish a faster convergence rate of the estimator in the (approximate) low-rank case. Limitations of the model are also discussed. Through simulation studies and real data analysis, we compare the estimation accuracy of the proposed method with that of existing approaches. The results demonstrate that the proposed method yields estimates with lower RMSE compared to existing methods.