Variable grouping by CART and combination of marginal models for large scale modelling

Abstract

These days we are exposed to huge data, some of which has relations each other. But it is different to find them. Data mining is a series of procedure which extracts information by exploring and modelling the relationships within such data and CART is one of the most popular tools for Data Mining. It develops for us a classification tree for categorical response variables and a regression tree for continuous response variables. The trees are developed in such a way that predictor variables are selected one after another in the order of the information amount that a predictor variable has for the response variable, where the information amount is computed conditional on the outcome of the predictor variables that are already selected in the tree construction process. Our goal in this thesis is finding a model structure for a large set of random variables, some of which are continuous and the rest are categorical. While CART is useful for a supervised learning, log-linear modelling is an unsupervised learning. We use CART at an initial stage of large scale modelling for the purpose of selecting subgroups of the random variables that are involved in the whole data set. Since CART is available to a data set of many random variables of mixed type, easy to apply, and easy to interpret the result of analysis, we can easily group the variables so that the variables in a group are associated highly with each other. Once groups of random variables are obtained, we then apply log-linear modelling to individual groups and obtain graphical log-linear models whose model structures are rep-resentable via graphs of vertices and edges. From each graphical model, we find particular types of graph separators called "prime separators", which are each defined as a graph separator which separates cliques or irreducible cycles. The prime separators have a nice property that they remain as prime separators both in a graphical model and its marginal model. This property is used in comb...