Borgelt C., Steinbrecher M., Kruse R. Graphical Models. Representations for Learning, Reasoning and Data Mining

Second Edition. — John Wiley, 2009. — 397 p. — ISBN: 978-0-470-72210-7.Although the origins of graphical models can be traced back to the beginning of the 20th century, they have become truly popular only since the mid-eighties, when several researchers started to use Bayesian networks in expert systems. But as soon as this start was made, the interest in graphical models grew rapidly and is still growing to this day. The reason is that graphical models, due to their explicit and sound treatment of (conditional) dependences and independences, proved to be clearly superior to naive approaches like certainty factors attached to if-then-rules, which had been tried earlier.
Data Mining, also called Knowledge Discovery in Databases, is a another relatively young area of research, which has emerged in response to the flood of data we are faced with nowadays. It has taken up the challenge to develop techniques that can help humans discover useful patterns in their data. In industrial applications patterns found with these methods can often be exploited to improve products and processes and to increase turnover.
This book is positioned at the boundary between these two highly important research areas, because it focuses on learning graphical models from data, thus exploiting the recognized advantages of graphical models for learning and data analysis. Its special feature is that it is not restricted to probabilistic models like Bayesian and Markov networks. It also explores relational graphical models, which provide excellent didactical means to explain the ideas underlying graphical models. In addition, possibilistic graphical models are studied, which are worth considering if the data to analyze contains imprecise information in the form of sets of alternatives instead of unique values.
Looking back, this book has become longer than originally intended. However, although it is true that, as C.F. von Weizsäcker remarked in a lecture, anything ultimately understood can be said briefly, it is also evident that anything said too briefly is likely to be incomprehensible to anyone who has not yet understood completely. Since our main aim was comprehensibility, we hope that a reader is remunerated for the length of this book by an exposition that is clear and self-contained and thus easy to read.Imprecision and Uncertainty
Decomposition
Graphical Representation
Computing Projections
Naive Classifiers
Learning Global Structure
Learning Local Structure
Inductive Causation
Visualization
Applications
A: Proofs of Theorems
B: Software Tools