Sample Efficient Nonparametric Regression via Low-Rank Regularization

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Nonparametric regression suffers from curse of dimensionality, requiring a relatively large sample size for accurate estimation beyond the univariate case. In this article, 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. Supplementary materials for this article are available online.