A practical approximation algorithm for the LTS estimator

The linear least trimmed squares (LTS) estimator is a statistical technique for fitting a linear model to a set of points. It was proposed by Rousseeuw as a robust alternative to the classical least squares estimator. Given a set of n points in Rd, the objective is to minimize the sum of the smalles...

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Published in:	Computational statistics & data analysis Vol. 99; pp. 148 - 170
Main Authors:	Mount, David M., Netanyahu, Nathan S., Piatko, Christine D., Wu, Angela Y., Silverman, Ruth
Format:	Journal Article
Language:	English
Published:	Elsevier B.V 01.07.2016
Subjects:	Accuracy Algorithms Approximation Approximation algorithms Computation Computational geometry data collection Estimators Least trimmed squares Linear estimation linear models Mathematical analysis Mathematical models probability analysis Robust estimation Slopes Least trimmed squares Computational geometry Approximation algorithms Robust estimation Linear estimation
ISSN:	0167-9473, 1872-7352
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Abstract	The linear least trimmed squares (LTS) estimator is a statistical technique for fitting a linear model to a set of points. It was proposed by Rousseeuw as a robust alternative to the classical least squares estimator. Given a set of n points in Rd, the objective is to minimize the sum of the smallest 50% squared residuals (or more generally any given fraction). There exist practical heuristics for computing the linear LTS estimator, but they provide no guarantees on the accuracy of the final result. Two results are presented. First, a measure of the numerical condition of a set of points is introduced. Based on this measure, a probabilistic analysis of the accuracy of the best LTS fit resulting from a set of random elemental fits is presented. This analysis shows that as the condition of the point set improves, the accuracy of the resulting fit also increases. Second, a new approximation algorithm for LTS, called Adaptive-LTS, is described. Given bounds on the minimum and maximum slope coefficients, this algorithm returns an approximation to the optimal LTS fit whose slope coefficients lie within the given bounds. Empirical evidence of this algorithm’s efficiency and effectiveness is provided for a variety of data sets.
AbstractList	The linear least trimmed squares (LTS) estimator is a statistical technique for fitting a linear model to a set of points. It was proposed by Rousseeuw as a robust alternative to the classical least squares estimator. Given a set of n points in Rd, the objective is to minimize the sum of the smallest 50% squared residuals (or more generally any given fraction). There exist practical heuristics for computing the linear LTS estimator, but they provide no guarantees on the accuracy of the final result. Two results are presented. First, a measure of the numerical condition of a set of points is introduced. Based on this measure, a probabilistic analysis of the accuracy of the best LTS fit resulting from a set of random elemental fits is presented. This analysis shows that as the condition of the point set improves, the accuracy of the resulting fit also increases. Second, a new approximation algorithm for LTS, called Adaptive-LTS, is described. Given bounds on the minimum and maximum slope coefficients, this algorithm returns an approximation to the optimal LTS fit whose slope coefficients lie within the given bounds. Empirical evidence of this algorithm’s efficiency and effectiveness is provided for a variety of data sets. The linear least trimmed squares (LTS) estimator is a statistical technique for fitting a linear model to a set of points. It was proposed by Rousseeuw as a robust alternative to the classical least squares estimator. Given a set of nn points in R super(d)Rd, the objective is to minimize the sum of the smallest 50% squared residuals (or more generally any given fraction). There exist practical heuristics for computing the linear LTS estimator, but they provide no guarantees on the accuracy of the final result. Two results are presented. First, a measure of the numerical condition of a set of points is introduced. Based on this measure, a probabilistic analysis of the accuracy of the best LTS fit resulting from a set of random elemental fits is presented. This analysis shows that as the condition of the point set improves, the accuracy of the resulting fit also increases. Second, a new approximation algorithm for LTS, called Adaptive-LTS, is described. Given bounds on the minimum and maximum slope coefficients, this algorithm returns an approximation to the optimal LTS fit whose slope coefficients lie within the given bounds. Empirical evidence of this algorithm's efficiency and effectiveness is provided for a variety of data sets.
Author	Wu, Angela Y. Silverman, Ruth Piatko, Christine D. Mount, David M. Netanyahu, Nathan S.
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References	Mount, Netanyahu, Piatko, Silverman, Wu (br000095) 2014; 69 Souvaine, Steele (br000140) 1987; 82 Cormen, Leiserson, Rivest, Stein (br000015) 2009 Rousseeuw (br000115) 1991; 11 Djorgovski, Gal, Odewahn, Carvalho, Brunner, Longo, Scaramella (br000025) 1998 Hofmann, Kontoghiorghes (br000065) 2010; 54 Hofmann, Gatu, Kontoghiorghes (br000060) 2010; 19 Mount, Netanyahu, Romanik, Silverman, Wu (br000100) 2007; 51 Agulló (br000005) 2001; 36 Hawkins (br000055) 1994; 17 Mount, Netanyahu, Piatko, Silverman, Wu (br000090) 2000; 10 Torti, Perrotta, Atkinson, Riani (br000145) 2012; 56 Erickson, Har-Peled, Mount (br000035) 2006; 36 Bernholt (br000010) 2005; vol. 3480 Jaulin, Kieffer, Didrit, Walter (br000080) 2001 Rousseeuw (br000110) 1984; 79 Mount, Netanyahu, Le Moigne (br000085) 1999; 32 Huttenlocher, D.P., Rucklidge, W.J., 1993. A multi-resolution technique for comparing images using the Hausdorff distance. In: Proceedings of the IEEE Conference on Computer Vision and Pattern Recognition, New York, pp. 705–706. Edelsbrunner, Souvaine (br000030) 1990; 85 Rousseeuw, van Driessen (br000125) 2006; 12 Hössjer (br000070) 1995; 19 Friedberg, Insel, Spence (br000040) 2002 Mount, Netanyahu, Zuck (br000105) 2004 Rucklidge (br000135) 1997; 24 Golub, Loan (br000045) 1996 Rousseeuw, Leroy (br000120) 1987 Diaconis, Shahshahani (br000020) 1987; 1 Hagedoorn, Veltkamp (br000050) 1999; 31 Rucklidge (br000130) 1996; no. 1173 Hofmann (10.1016/j.csda.2016.01.016_br000060) 2010; 19 Torti (10.1016/j.csda.2016.01.016_br000145) 2012; 56 Diaconis (10.1016/j.csda.2016.01.016_br000020) 1987; 1 Rucklidge (10.1016/j.csda.2016.01.016_br000130) 1996; no. 1173 Hofmann (10.1016/j.csda.2016.01.016_br000065) 2010; 54 Rousseeuw (10.1016/j.csda.2016.01.016_br000110) 1984; 79 Rucklidge (10.1016/j.csda.2016.01.016_br000135) 1997; 24 Bernholt (10.1016/j.csda.2016.01.016_br000010) 2005; vol. 3480 Rousseeuw (10.1016/j.csda.2016.01.016_br000125) 2006; 12 Edelsbrunner (10.1016/j.csda.2016.01.016_br000030) 1990; 85 Cormen (10.1016/j.csda.2016.01.016_br000015) 2009 Friedberg (10.1016/j.csda.2016.01.016_br000040) 2002 Djorgovski (10.1016/j.csda.2016.01.016_br000025) 1998 Agulló (10.1016/j.csda.2016.01.016_br000005) 2001; 36 Mount (10.1016/j.csda.2016.01.016_br000100) 2007; 51 Erickson (10.1016/j.csda.2016.01.016_br000035) 2006; 36 Golub (10.1016/j.csda.2016.01.016_br000045) 1996 Hawkins (10.1016/j.csda.2016.01.016_br000055) 1994; 17 Mount (10.1016/j.csda.2016.01.016_br000085) 1999; 32 Mount (10.1016/j.csda.2016.01.016_br000105) 2004 Rousseeuw (10.1016/j.csda.2016.01.016_br000115) 1991; 11 Mount (10.1016/j.csda.2016.01.016_br000090) 2000; 10 Souvaine (10.1016/j.csda.2016.01.016_br000140) 1987; 82 Hagedoorn (10.1016/j.csda.2016.01.016_br000050) 1999; 31 10.1016/j.csda.2016.01.016_br000075 Rousseeuw (10.1016/j.csda.2016.01.016_br000120) 1987 Mount (10.1016/j.csda.2016.01.016_br000095) 2014; 69 Jaulin (10.1016/j.csda.2016.01.016_br000080) 2001 Hössjer (10.1016/j.csda.2016.01.016_br000070) 1995; 19
References_xml	– year: 2009 ident: br000015 article-title: Introduction to Algorithms – volume: 36 start-page: 425 year: 2001 end-page: 439 ident: br000005 article-title: New algorithms for computing the least trimmed squares regression estimator publication-title: Comput. Statist. Data Anal. – start-page: 207 year: 2004 end-page: 219 ident: br000105 article-title: Analyzing the number of samples required for an approximate Monte-Carlo LMS line estimator publication-title: Theory and Applications of Recent Robust Methods, Statistics for Industry and Technology – year: 1987 ident: br000120 article-title: Robust Regression and Outlier Detection – year: 2001 ident: br000080 article-title: Applied Interval Analysis – volume: no. 1173 year: 1996 ident: br000130 publication-title: Efficient Visual Recognition Using the Hausdorff Distance – volume: 51 start-page: 2461 year: 2007 end-page: 2486 ident: br000100 article-title: A practical approximation algorithm for the LMS line estimator publication-title: Comput. Statist. Data Anal. – volume: 19 start-page: 265 year: 1995 end-page: 282 ident: br000070 article-title: Exact computation of the least trimmed squares estimate in simple linear regression publication-title: Comput. Statist. Data Anal. – reference: Huttenlocher, D.P., Rucklidge, W.J., 1993. A multi-resolution technique for comparing images using the Hausdorff distance. In: Proceedings of the IEEE Conference on Computer Vision and Pattern Recognition, New York, pp. 705–706. – volume: 17 start-page: 185 year: 1994 end-page: 196 ident: br000055 article-title: The feasible solution algorithm for least trimmed squares regression publication-title: Comput. Statist. Data Anal. – volume: 31 start-page: 103 year: 1999 end-page: 115 ident: br000050 article-title: Reliable and efficient pattern matching using an affine invariant metric publication-title: Int. J. Comput. Vis. – volume: vol. 3480 start-page: 697 year: 2005 end-page: 706 ident: br000010 article-title: Computing the least median of squares estimator in time publication-title: Proc. Intl. Conf. on Computational Science and Its Applications – volume: 1 start-page: 15 year: 1987 end-page: 32 ident: br000020 article-title: The subgroup algorithm for generating uniform random variables publication-title: Prob. Eng. Inf. Sci. – volume: 32 start-page: 17 year: 1999 end-page: 38 ident: br000085 article-title: Efficient algorithms for robust point pattern matching publication-title: Pattern Recognit. – volume: 85 start-page: 115 year: 1990 end-page: 119 ident: br000030 article-title: Computing median-of-squares regression lines and guided topological sweep publication-title: J. Amer. Statist. Assoc. – volume: 24 start-page: 251 year: 1997 end-page: 270 ident: br000135 article-title: Efficiently locating objects using the Hausdorff distance publication-title: Int. J. Comput. Vis. – start-page: 89 year: 1998 ident: br000025 article-title: The Palomar digital sky survey (DPOSS) publication-title: Wide Field Surveys in Cosmology (14th IAP meeting) – volume: 69 start-page: 148 year: 2014 end-page: 183 ident: br000095 article-title: On the least trimmed squares estimator publication-title: Algorithmica – volume: 36 start-page: 593 year: 2006 end-page: 607 ident: br000035 article-title: On the least median square problem publication-title: Discrete Comput. Geom. – volume: 82 start-page: 794 year: 1987 end-page: 801 ident: br000140 article-title: Time- and space- efficient algorithms for least median of squares regression publication-title: J. Amer. Statist. Assoc. – year: 2002 ident: br000040 article-title: Linear Algebra – year: 1996 ident: br000045 article-title: Matrix Computations – volume: 79 start-page: 871 year: 1984 end-page: 880 ident: br000110 article-title: Least median-of-squares regression publication-title: J. Amer. Statist. Assoc. – volume: 12 start-page: 29 year: 2006 end-page: 45 ident: br000125 article-title: Computing LTS regression for large data sets publication-title: Data Min. Knowl. Discov. – volume: 11 start-page: 127 year: 1991 end-page: 129 ident: br000115 article-title: A diagnostic plot for regression outliers and leverage points publication-title: Comput. Statist. Data Anal. – volume: 54 start-page: 3392 year: 2010 end-page: 3403 ident: br000065 article-title: Matrix strategies for computing the least trimmed squares estimation of the general linear and sur models publication-title: Comput. Statist. Data Anal. – volume: 10 start-page: 593 year: 2000 end-page: 608 ident: br000090 article-title: Quantile approximation for robust statistical estimation and publication-title: Internat. J. Comput. Geom. Appl. – volume: 56 start-page: 2501 year: 2012 end-page: 2512 ident: br000145 article-title: Benchmark testing of algorithms for very robust regression: FS, LMS and LTS publication-title: Comput. Statist. Data Anal. – volume: 19 start-page: 191 year: 2010 end-page: 204 ident: br000060 article-title: An exact least trimmed squares algorithm for a range of coverage values publication-title: J. Comput. Graph. Statist. – volume: 54 start-page: 3392 year: 2010 ident: 10.1016/j.csda.2016.01.016_br000065 article-title: Matrix strategies for computing the least trimmed squares estimation of the general linear and sur models publication-title: Comput. Statist. Data Anal. doi: 10.1016/j.csda.2010.04.023 – volume: 36 start-page: 425 year: 2001 ident: 10.1016/j.csda.2016.01.016_br000005 article-title: New algorithms for computing the least trimmed squares regression estimator publication-title: Comput. Statist. Data Anal. doi: 10.1016/S0167-9473(00)00056-6 – ident: 10.1016/j.csda.2016.01.016_br000075 doi: 10.1109/CVPR.1993.341019 – volume: 51 start-page: 2461 year: 2007 ident: 10.1016/j.csda.2016.01.016_br000100 article-title: A practical approximation algorithm for the LMS line estimator publication-title: Comput. Statist. Data Anal. doi: 10.1016/j.csda.2006.08.033 – volume: 56 start-page: 2501 year: 2012 ident: 10.1016/j.csda.2016.01.016_br000145 article-title: Benchmark testing of algorithms for very robust regression: FS, LMS and LTS publication-title: Comput. Statist. Data Anal. doi: 10.1016/j.csda.2012.02.003 – start-page: 207 year: 2004 ident: 10.1016/j.csda.2016.01.016_br000105 article-title: Analyzing the number of samples required for an approximate Monte-Carlo LMS line estimator – volume: 82 start-page: 794 year: 1987 ident: 10.1016/j.csda.2016.01.016_br000140 article-title: Time- and space- efficient algorithms for least median of squares regression publication-title: J. Amer. Statist. Assoc. doi: 10.1080/01621459.1987.10478500 – year: 1996 ident: 10.1016/j.csda.2016.01.016_br000045 – volume: 19 start-page: 265 year: 1995 ident: 10.1016/j.csda.2016.01.016_br000070 article-title: Exact computation of the least trimmed squares estimate in simple linear regression publication-title: Comput. Statist. Data Anal. doi: 10.1016/0167-9473(95)92697-V – year: 2001 ident: 10.1016/j.csda.2016.01.016_br000080 – volume: 10 start-page: 593 year: 2000 ident: 10.1016/j.csda.2016.01.016_br000090 article-title: Quantile approximation for robust statistical estimation and k-enclosing problems publication-title: Internat. J. Comput. Geom. Appl. doi: 10.1142/S0218195900000334 – volume: 19 start-page: 191 year: 2010 ident: 10.1016/j.csda.2016.01.016_br000060 article-title: An exact least trimmed squares algorithm for a range of coverage values publication-title: J. Comput. Graph. Statist. doi: 10.1198/jcgs.2009.07091 – year: 2009 ident: 10.1016/j.csda.2016.01.016_br000015 – volume: 17 start-page: 185 year: 1994 ident: 10.1016/j.csda.2016.01.016_br000055 article-title: The feasible solution algorithm for least trimmed squares regression publication-title: Comput. Statist. Data Anal. doi: 10.1016/0167-9473(92)00070-8 – year: 1987 ident: 10.1016/j.csda.2016.01.016_br000120 – volume: vol. 3480 start-page: 697 year: 2005 ident: 10.1016/j.csda.2016.01.016_br000010 article-title: Computing the least median of squares estimator in time O(nd) – volume: 36 start-page: 593 year: 2006 ident: 10.1016/j.csda.2016.01.016_br000035 article-title: On the least median square problem publication-title: Discrete Comput. Geom. doi: 10.1007/s00454-006-1267-6 – volume: 11 start-page: 127 year: 1991 ident: 10.1016/j.csda.2016.01.016_br000115 article-title: A diagnostic plot for regression outliers and leverage points publication-title: Comput. Statist. Data Anal. doi: 10.1016/0167-9473(91)90059-B – volume: 32 start-page: 17 year: 1999 ident: 10.1016/j.csda.2016.01.016_br000085 article-title: Efficient algorithms for robust point pattern matching publication-title: Pattern Recognit. doi: 10.1016/S0031-3203(98)00086-7 – volume: 85 start-page: 115 year: 1990 ident: 10.1016/j.csda.2016.01.016_br000030 article-title: Computing median-of-squares regression lines and guided topological sweep publication-title: J. Amer. Statist. Assoc. doi: 10.1080/01621459.1990.10475313 – volume: no. 1173 year: 1996 ident: 10.1016/j.csda.2016.01.016_br000130 – volume: 1 start-page: 15 year: 1987 ident: 10.1016/j.csda.2016.01.016_br000020 article-title: The subgroup algorithm for generating uniform random variables publication-title: Prob. Eng. Inf. Sci. doi: 10.1017/S0269964800000255 – volume: 12 start-page: 29 year: 2006 ident: 10.1016/j.csda.2016.01.016_br000125 article-title: Computing LTS regression for large data sets publication-title: Data Min. Knowl. Discov. doi: 10.1007/s10618-005-0024-4 – year: 2002 ident: 10.1016/j.csda.2016.01.016_br000040 – volume: 69 start-page: 148 year: 2014 ident: 10.1016/j.csda.2016.01.016_br000095 article-title: On the least trimmed squares estimator publication-title: Algorithmica doi: 10.1007/s00453-012-9721-8 – volume: 24 start-page: 251 year: 1997 ident: 10.1016/j.csda.2016.01.016_br000135 article-title: Efficiently locating objects using the Hausdorff distance publication-title: Int. J. Comput. Vis. doi: 10.1023/A:1007975324482 – volume: 31 start-page: 103 year: 1999 ident: 10.1016/j.csda.2016.01.016_br000050 article-title: Reliable and efficient pattern matching using an affine invariant metric publication-title: Int. J. Comput. Vis. doi: 10.1023/A:1008022116857 – start-page: 89 year: 1998 ident: 10.1016/j.csda.2016.01.016_br000025 article-title: The Palomar digital sky survey (DPOSS) – volume: 79 start-page: 871 year: 1984 ident: 10.1016/j.csda.2016.01.016_br000110 article-title: Least median-of-squares regression publication-title: J. Amer. Statist. Assoc. doi: 10.1080/01621459.1984.10477105
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Title	A practical approximation algorithm for the LTS estimator
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