A geometric theory of outliers and perturbation
Name
50594675-MIT.pdf
Description
Full printable version
Size
6.88 MB
Format
Adobe PDF
Checksum (MD5)
25caedffb8943684c59a75975172bef9
Author(s)
Dunagan, John D. (John David), 1976-
Advisor(s)
Santosh Vempala.
Date Issued
2002
Publisher
Massachusetts Institute of Technology
Abstract
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.
Description
Thesis (Ph. D.)--Massachusetts Institute of Technology, Dept. of Mathematics, 2002.
Includes bibliographical references (p. 91-94).
Subjects
Mathematics.
MIT Department
Massachusetts Institute of Technology. Department of Mathematics
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