Gradient boosting machine for high-dimensional additive models
- The gradient boosting machine proposed by Friedman (2001) represents a fundamental advance in statistical learning. Although previous studies have shown the effectiveness of this algorithm on fitting additive models when the sample size is much bigger than the number of covariates, its properties in the high-dimensional case, where the number of covariates exceeds the sample size, are still an open area of research. We extend the application of the gradient boosting machine to a high-dimensional censored regression problem, and use simulation studies to show that this algorithm outperforms the currently used iterative regularization method. Buhlmann (2006) proved the convergence and consistency of the gradient boosting machine for high-dimensional linear models. We establish the same asymptotic theory for nonlinear additive models by showing that the set of basis functions is highly redundant. Then we discuss the properties of the 10-fold cross validation, which can be used in practice to define a criterion for choosing the number of iterations for the gradient boosting machine. We illustrate the effectiveness of the gradient boosting machine plus this stopping criterion on fitting high-dimensional additive models through numerical examples.
|Type of resource
|electronic; electronic resource; remote
|1 online resource.
|Stanford University, Institute for Computational and Mathematical Engineering.
|Lai, T. L
|Lai, T. L
|Statement of responsibility
|Submitted to the Institute for Computational and Mathematical Engineering.
|Thesis (Ph.D.)--Stanford University, 2014.
- © 2014 by Tong Xia
- This work is licensed under a Creative Commons Attribution Non Commercial 3.0 Unported license (CC BY-NC).
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