Title: An Assortment of Unsupervised and Supervised Applications to Large Data
Description: This dissertation presents several methods that can be applied to large datasets with an enormous number of covariates. It is divided into two parts. In the first part of the dissertation, a novel approach to pinpointing sets of related variables is introduced. In the second part, several new methods and modifications of current methods designed to improve prediction are outlined. These methods can be considered extensions of the very successful I Score suggested by Lo and Zheng in a 2002 paper and refined in many papers since. In Part I, unsupervised data (with no response) is addressed. In chapter 2, the novel unsupervised I score and its associated procedure are introduced and some of its unique theoretical properties are explored. In chapter 3, several simulations consisting of generally hard-to-wrangle scenarios demonstrate promising behavior of the approach. The method is applied to the complex field of market basket analysis, with a specific grocery data set used to show it in action in chapter 4.

It is compared it to a natural competition, the A Priori algorithm. The main contribution of this part of the dissertation is the unsupervised I score, but we also suggest several ways to leverage the variable sets the I score locates in order to mine for association rules. In Part II, supervised data is confronted. Though the I Score has been used in reference to these types of data in the past, several interesting ways of leveraging it (and the modules of covariates it identifies) are investigated. Though much of this methodology adopts procedures which are individually well-established in literature, the contribution of this dissertation is organization and implementation of these methods in the context of the I Score. Several module-based regression and voting methods are introduced in chapter 7, including a new LASSO-based method for optimizing voting weights. These methods can be considered intuitive and readily applicable to a huge number of datasets of sometimes colossal size. In particular, in chapter 8, a large dataset on Hepatitis and another on Oral Cancer are analyzed.

The results for some of the methods are quite promising and competitive with existing methods, especially with regard to prediction. A flexible and multifaceted procedure is suggested in order to provide a thorough arsenal when dealing with the problem of prediction in these complex data sets. Ultimately, we highlight some benefits and future directions of the method.