The Impact of Equal Weighting of Low- and High-Confidence Observations on Robust Linear Regression Computations |
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Authors: | Venansius Baryamureeba |
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Institution: | (1) Institute of Computer Science, Makerere University, P.O. Box 7062, Kampala, Uganda |
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Abstract: | Equal weighting of low- and high-confidence observations occurs for Huber, Talwar, and Barya weighting functions when Newton's method is used to solve robust linear regression problems. This leads to easy updates and/or downdates of existing matrix factorizations or easy computation of coefficient matrices in linear systems from previous ones. Thus Newton's method based on these functions has been shown to be computationally cheap. In this paper we show that a combination of Newton's method and an iterative method is a promising approach for solving robust linear regression problems. We show that Newton's method based on the Talwar function is an active set method. Further we show that it is possible to obtain improved estimates of the solution vector by combining a line search method like Newton's method with an active set method.This revised version was published online in October 2005 with corrections to the Cover Date. |
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Keywords: | Robust linear regression Newton's method conjugate gradient least squares method LSQR preconditioner basis identification techniques |
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