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Computing of high breakdown regression estimators without sorting on graphics processing units

G. Beliakov, M. Johnstone, S. Nahavandi
School of Information Technology, Deakin University, 221 Burwood Hwy, Burwood 3125, Australia
Computing, Volume 94, Issue 5, pp 433-447, 2012

@article{beliakov2012computing,

   year={2012},

   issn={0010-485X},

   journal={Computing},

   volume={94},

   issue={5},

   doi={10.1007/s00607-011-0183-7},

   title={Computing of high breakdown regression estimators without sorting on graphics processing units},

   url={http://dx.doi.org/10.1007/s00607-011-0183-7},

   publisher={Springer Vienna},

   keywords={Robust regression; Median; Order statistic; Sorting; GPU; Cutting plane; 65Y05; 65Y10; 68W10; 62J05; 65K05},

   author={Beliakov, G. and Johnstone, M. and Nahavandi, S.},

   pages={433-447},

   language={English}

}

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We present an approach to computing high-breakdown regression estimators in parallel on graphics processing units (GPU). We show that sorting the residuals is not necessary, and it can be substituted by calculating the median. We present and compare various methods to calculate the median and order statistics on GPUs. We introduce an alternative method based on the optimization of a convex function, and show its numerical superiority when calculating the order statistics of very large arrays on GPUs.
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