Date of Award
Doctor of Philosophy
Kenneth Gilbert, Hamila Bensmail, Chanaka Edirisinghe
This dissertation develops new computationally e±cient algorithms for identifying the subset of variables that minimizes any desired information criteria in model selection.
In recent years, the statistical literature has placed more and more empha- sis on information theoretic model selection criteria. A model selection crite- rion chooses model that \closely" approximates the true underlying model. Recent years have also seen many exciting developments in the model se- lection techniques. As demand increases for data mining of massive data sets with many variables, the demand for model selection techniques are be- coming much stronger and needed. To this end, we introduce a new Implicit Enumeration (IE) algorithm and a hybridized IE with the Genetic Algorithm (GA) in this dissertation.
The proposed Implicit Enumeration algorithm is the ¯rst algorithm that explicitly uses an information criterion as the objective function. The algo- rithm works with a variety of information criteria including some for which the existing branch and bound algorithms developed by Furnival and Wil- son (1974) and Gatu and Kontoghiorghies (2003) are not applicable. It also ¯nds the \best" subset model directly without the need of ¯nding the \best" subset of each size as the branch and bound techniques do.
The proposed methods are demonstrated in multiple, multivariate, logis- tic regression and discriminant analysis problems. The implicit enumeration algorithm converged to the optimal solution on real and simulated data sets v with up to 80 predictors, thus having 280 = 1; 208; 925; 819; 614; 630; 000; 000; 000 possible subset models in the model portfolio. To our knowledge, none of the existing exact algorithms have the capability of optimally solving such problems of this size.
Bao, Xinli, "Com- putational Subset Model Selection Algorithms and Applications. " PhD diss., University of Tennessee, 2004.