Thesis (Ph. D.)--Massachusetts Institute of Technology, Dept. of Mathematics, 2002. / Includes bibliographical references (p. 91-94). / We develop a new understanding of outliers and the behavior of linear programs under perturbation. Outliers are ubiquitous in scientific theory and practice. We analyze a simple algorithm for removal of outliers from a high-dimensional data set and show the algorithm to be asymptotically good. We extend this result to distributions that we can access only by sampling, and also to the optimization version of the problem. Our results cover both the discrete and continuous cases. This is joint work with Santosh Vempala. The complexity of solving linear programs has interested researchers for half a century now. We show that an arbitrary linear program subject to a small random relative perturbation has good condition number with high probability, and hence is easy to solve. This is joint work with Avrim Blum, Daniel Spielman, and Shang-Hua Teng. This result forms part of the smoothed analysis project initiated by Spielman and Teng to better explain mathematically the observed performance of algorithms. / by John D. Dunagan. / Ph.D.
| Identifer | oai:union.ndltd.org:MIT/oai:dspace.mit.edu:1721.1/8396 |
| Date | January 2002 |
| Creators | Dunagan, John D. (John David), 1976- |
| Contributors | Santosh Vempala., Massachusetts Institute of Technology. Dept. of Mathematics., Massachusetts Institute of Technology. Dept. of Mathematics. |
| Publisher | Massachusetts Institute of Technology |
| Source Sets | M.I.T. Theses and Dissertation |
| Language | English |
| Detected Language | English |
| Type | Thesis |
| Format | 94 p., 7211412 bytes, 7211171 bytes, application/pdf, application/pdf, application/pdf |
| Rights | M.I.T. theses are protected by copyright. They may be viewed from this source for any purpose, but reproduction or distribution in any format is prohibited without written permission. See provided URL for inquiries about permission., http://dspace.mit.edu/handle/1721.1/7582 |
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