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Front. Appl. Math. Stat. | doi: 10.3389/fams.2018.00063

A Tree-based Multiscale Regression Method

  • 1University of Missouri–St. Louis, United States

A tree-based method for regression is proposed. In a high dimensional feature space,
the method has the ability to adapt to the lower intrinsic dimension of data if the data
possess such a property so that reliable statistical estimates can be performed without
being hindered by the “curse of dimensionality”. The method is also capable of
producing a smoother estimate for a regression function than those from standard tree methods like CART in the region where the function is smooth and also being more sensitive to discontinuities of the function than smoothing splines or other kernel methods. The estimation process in this method consists of three components: a random projection procedure that generates partitions of the feature space, a wavelet-like orthogonal system defined on a tree that allows for a thresholding estimation of the regression function based on that tree and, finally, an averaging process that averages a number of estimates from independently generated random projection trees.

Keywords: regression, non-linear, High dimension data, Tree methods, multiscale (MS) modeling, Manifold Learning

Received: 07 Oct 2018; Accepted: 07 Dec 2018.

Edited by:

Xiaoming Huo, Georgia Institute of Technology, United States

Reviewed by:

Shao-Bo Lin, Wenzhou University, China
Don Hong, Middle Tennessee State University, United States  

Copyright: © 2018 Cai and Jiang. This is an open-access article distributed under the terms of the Creative Commons Attribution License (CC BY). The use, distribution or reproduction in other forums is permitted, provided the original author(s) and the copyright owner(s) are credited and that the original publication in this journal is cited, in accordance with accepted academic practice. No use, distribution or reproduction is permitted which does not comply with these terms.

* Correspondence: Prof. Haiyan Cai, University of Missouri–St. Louis, St. Louis, United States,