Semi-Parametric Dimension Reduction Models Using Orthogonality Constrained Optimization.

orthoDr

The goal of orthoDr is to use an orthogonality constrained optimization algorithm to solve a variety of dimension reduction problems in the semiparametric framework.

Installation

You can install the released version of orthoDr from CRAN with:

  install.packages("orthoDr")

Implemented Methods

This package implements the orthogonality constrained (Stiefel manifold) optimization approach proposed by Wen & Yin (2013). A drop-in solver ortho_optim() works just the same as the optim() function. Relying on this optimization approach, we also implemented a collection of dimension reduction models for survival analysis, regression, and personalized medicine.

• CP-SIR, Forward, IR-CP and IR-Semi methods in Sun, Zhu, Wang & Zeng (2019)
• semi-SIR and semi-PHD in Ma & Zhu (2012)
• Direct and pseudo-Direct methods in Zhou, Zhu & Zeng (2021)

We also implemented several methods and functions for comparison, testing and utilization purposes

• hMave: This is a direct R translation of the hMave MATLAB code by Xia, Zhang & Xu (2010)
• pSAVE: partial-SAVE in Feng, Wen, Yu & Zhu (2013)
• dist_cross(): kernel distances matrix between two sets of data, as an extension of dist()
• distance(): distance correlation between two linear spaces
• silverman(): Silverman's rule of thumb bandwidth.