Orthogonalizing EM: A design-based least squares algorithm

View Researcher's Other Codes

Disclaimer: The provided code links for this paper are external links. Science Nest has no responsibility for the accuracy, legality or content of these links. Also, by downloading this code(s), you agree to comply with the terms of use as set out by the author(s) of the code(s).

Authors Shifeng Xiong, Bin Dai, Jared D Huling, Peter Z. G. Qian
Journal/Conference Name Technometrics
Paper Category
Paper Abstract We introduce an efficient iterative algorithm, intended for various least squares problems, based on a design of experiments perspective. The algorithm, called orthogonalizing EM (OEM), works for ordinary least squares and can be easily extended to penalized least squares. The main idea of the procedure is to orthogonalize a design matrix by adding new rows and then solve the original problem by embedding the augmented design in a missing data framework. We establish several attractive theoretical properties concerning OEM. For the ordinary least squares with a singular regression matrix, an OEM sequence converges to the Moore-Penrose generalized inverse-based least squares estimator. For ordinary and penalized least squares with various penalties, it converges to a point having grouping coherence for fully aliased regression matrices. Convergence and the convergence rate of the algorithm are examined. Finally, we demonstrate that OEM is highly efficient for large-scale least squares and penalized least squares problems, and is considerably faster than competing methods when n is much larger than p. Supplementary materials for this article are available online.
Date of publication 2016
Code Programming Language R
Comment

Copyright Researcher 2021