12/18/06

Welcome to Thomas's Web site!

Thomas Shih is an Industrial Engineering Ph.D. at UTA. The title of his dissertation is "Convex Versions of Multivariate Adaptive Regression Splines and Implementations for Complex Optimizations Problems," co-supervised by Dr. Chen and Dr. Kim.

Multivariate Adaptive Regression Splines (MARS) provide a flexible statistical modeling method that employs forward and backward search algorithms to identify the combination of basis functions that best fits the data.  In optimization, MARS has been used successfully to estimate the value function in stochastic dynamic programming, and MARS could be potentially useful in many real world optimization problems where objective (or other) functions need to be estimated from data, such as in simulation optimization.  Many optimization methods depend on convexity, but a nonconvex MARS approximation is inherently possible.  In his dissertation, convex versions of MARS are proposed.  In order to ensure MARS convexity, two major modifications are made: (1) coefficients are constrained such that pairs of basis functions are guaranteed to jointly form convex functions; (2) The form of interaction terms is appropriately changed.

The implementation of MARS for approximating complex optimization functions can involve thousands of state or decision variables.  In particular, his research studies application to an inventory forecasting stochastic dynamic programming problem and an airline fleet assignment problem. Although one can simply attempt a MARS approximation over all the variables, prior research on the fleet assignment application indicates that many variables have little effect on the objective. Thus, a data mining step to conduct variable selection is needed. This step separates potentially critical variables from clearly redundant ones. In his dissertation, variants of two data mining tools are explored separately and in combination for variable selection: regression trees and multiple testing procedures based on false discovery rate.

Mr. Shih's primary research interests use statistical approaches to develop new methods for operations research problems in engineering and science. He has expertise in statistical modeling and data mining, particularly employed for computer experiments and optimization. He has studied applications in inventory forecasting, airline optimization, and air quality. Through his statistics-based methodology, he has developed computationally-tractable methods for complex optimization problems. The other project he has been working on is the one sponsored by DFW International Airport. This funded project is joint with Dr. Victoria C. P. Chen, Dr. Seoung Bum Kim, Dr. Jay M. Rosenberger and other colleagues in Center on Stochastic Modeling, Optimization, & Statistics. Data mining approaches such as regression trees have been explored to identify the important variables to predict dissolved oxygen in the receiving water of interest.

This site was last updated 12/18/06