Dimension reduction boosting

ABSTRACT

L₂Boosting is an effective method for constructing model. In the case of high-dimensional setting, Bühlmann and Yu (2003) proposed the componentwise L₂Boosting, but componentwise L₂Boosting can only fit a special limited model. In this paper, by combining a boosting and sufficient dimension reduction method, e.g., sliced inverse regression (SIR), we propose a new method for regression, called dimension reduction boosting (DRBoosting). Compared with L₂Boosting, the computation of DRBoosting is less intensive and its prediction is better, especially for high-dimensional data. Simulations confirm the advantage of the new method.

KEYWORDS:

• Conjugate direction boosting
• dimension reduction
• L₂Boosting
• sliced inverse regression

MATHEMATICS SUBJECT CLASSIFICATION:

• Primary 62H20; Secondary 62G05

Funding

This work is supported by National Science Foundation of China (No. 11471030) and the Fundamental Research Funds for Central Universities.