1 research outputs found
The Discrete Acyclic Digraph Markov Model in Data Mining
Graphical Markov models are a powerful tool for the description of
complex interactions between the variables of a domain. They provide a
succinct description of the joint distribution of the variables. This
feature has led to the most successful application of graphical Markov
models, that is as the core component of probabilistic expert systems.
The fascinating theory behind this type of models arises from three
different disciplines, viz., Statistics, Graph Theory and Artificial
Intelligence. This interdisciplinary origin has given rich insight from
different perspectives.
There are two main ways to find the qualitative structure of graphical
Markov models. Either the structure is specified by a domain expert or
``structural learning'' is applied, i.e., the structure is automatically
recovered from data. For structural learning, one has to compare how
well different models describe the data. This is easy for, e.g., acyclic
digraph Markov models. However, structural learning is still a hard
problem because the number of possible models grows exponentially with
the number of variables.
The main contributions of this thesis are as follows. Firstly, a new
class of graphical Markov models, called TCI models, is introduced.
These models can be represented by labeled trees and form the
intersection of two previously well-known classes. Secondly, the
inclusion order of graphical Markov models is studied. From this study,
two new learning algorithms are derived. One for heuristic search and
the other for the Markov Chain Monte Carlo Method. Both algorithms
improve the results of previous approaches without compromising the
computational cost of the learning process. Finally, new diagnostics for
convergence assessment of the Markov Chain Monte Carlo Method in
structural learning are introduced. The results of this thesis are
illustrated using both synthetic and real world datasets