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.

Below are the frequent questions about Shih’s dissertation:

Q1: What is Multivariate Adaptive Regression Splines (MARS) ?

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. 

Q2: How is MARS used in optimization?

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. 

Q3: What is Convex version of MARS?

Many optimization methods depend on convexity, but a nonconvex MARS approximation is inherently possible.  In my dissertation, convex versions of MARS are proposed. 

Q4: What kind of modification is necessary to ensure convexity of MARS?

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.

Q5: What are the applications in this dissertation?

This research studies application to an inventory forecasting stochastic dynamic programming problem and an airline fleet assignment problem.

Q6: Why is data mining important to the problems in your dissertation?

The implementation of MARS for approximating complex optimization functions can involve thousands of state or decision variables.  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.

Q7: What kind of data mining tool is used to select important variables in the dissertation?

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.

Q8: What are your primary research interests?

My interests include using statistical approaches to develop new methods for operations research problems in engineering and science.

Q9: What are your strengths? Are there any particular applications?

My expertise lies in statistical modeling and data mining, particularly employed for computer experiments and optimization. I have studied applications in inventory forecasting, airline optimization, and air quality.

Q10: What is the contribution of this dissertation?

Through the statistics-based methodology, I have developed computationally tractable methods for complex optimization problems.

Q11: Is there any other project other than the dissertation?

The other project I worked 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.

Q12: What is your contribution with respect to the DFW project?

An integrated relational database has been constructed, and various data sets can be obtained through relevant queries. Statistical data analyses such as multiple linear regressions, regression trees models, and MARS models have been explored.

Q13: What kind of analysis have you done in the DFW project?

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