The Discrete Acyclic Digraph Markov Model in Data Mining
Year: 2002
Type: dissertation
Abstract: Graphical Markov models are a powerful tool for the description of \ncomplex interactions between the variables of a domain. They provide a \nsuccinct description of the joint distribution of the variables. This \nfeature has led to the most successful application of graphical Markov \nmodels, that is as the core component of probabilistic expert systems. \nThe fascinating theory behind this type of models arises from three \ndifferent disciplines, viz., Statistics, Graph Theory and Artificial \nIntelligence. This interdisciplinary origin has given rich insight from \ndifferent perspectives. \nThere are two main ways to find the qualitative structure of graphical \nMarkov models. Either the structure is specified by a domain expert or \n``structural learning'' is applied, i.e., the structure is automatically \nrecovered from data. For structural learning, one has to compare how \nwell different models describe the data. This is easy for, e.g., acyclic \ndigraph Markov models. However, structural learning is still a hard \nproblem because the number of possible models grows exponentially with \nthe number of variables. \nThe main contributions of this thesis are as follows. Firstly, a new \nclass of graphical Markov models, called TCI models, is introduced. \nThese models can be represented by labeled trees and form the \nintersection of two previously well-known classes. Secondly, the \ninclusion order of graphical Markov models is studied. From this study, \ntwo new learning algorithms are derived. One for heuristic search and \nthe other for the Markov Chain Monte Carlo Method. Both algorithms \nimprove the results of previous approaches without compromising the \ncomputational cost of the learning process. Finally, new diagnostics for \nconvergence assessment of the Markov Chain Monte Carlo Method in \nstructural learning are introduced. The results of this thesis are \nillustrated using both synthetic and real world datasets.
Author: J.R. Castelo Valdueza
Language: English
Subfield: Artificial Intelligence
Field: Computer Science
Domain: Physical Sciences
Open Access status: green
OpenAlex ID: W1510976864