Integer optimization in data mining
Name
53010913-MIT.pdf
Description
Full printable version
Size
3.47 MB
Format
Adobe PDF
Checksum (MD5)
38e93c0e57c8f2c6dac94b15c3a7d8ea
Author(s)
Shioda, Romy, 1977-
Advisor(s)
Dimitris Bertsimas.
Alternative Title
Data mining via integer optimization
Date Issued
2003
Publisher
Massachusetts Institute of Technology
Abstract
While continuous optimization methods have been widely used in statistics and data mining over the last thirty years, integer optimization has had very limited impact in statistical computation. Thus, our objective is to develop a methodology utilizing state of the art integer optimization methods to exploit the discrete character of data mining problems. The thesis consists of two parts: The first part illustrates a mixed-integer optimization method for classification and regression that we call Classification and Regression via Integer Optimization (CRIO). CRIO separates data points in different polyhedral regions. In classification each region is assigned a class, while in regression each region has its own distinct regression coefficients. Computational experimentation with real data sets shows that CRIO is comparable to and often outperforms the current leading methods in classification and regression. The second part describes our cardinality-constrained quadratic mixed-integer optimization algorithm, used to solve subset selection in regression and portfolio selection in asset allocation. We take advantage of the special structures of these problems by implementing a combination of implicit branch-and-bound, Lemke's pivoting method, variable deletion and problem reformulation. Testing against popular heuristic methods and CPLEX 8.0's quadratic mixed-integer solver, we see that our tailored approach to these quadratic variable selection problems have significant advantages over simple heuristics and generalized solvers.
Description
Thesis (Ph. D.)--Massachusetts Institute of Technology, Sloan School of Management, Operations Research Center, 2003.
Includes bibliographical references (p. 103-107).
Subjects
Operations Research Center.
MIT Department
Massachusetts Institute of Technology. Operations Research Center
Sloan School of Management
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