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Chain Graphs and Directed Acyclic Graphs Improved by Equivalence Classes and their Essential Graphs

Departamento de Matemáticas Fundamentales
Facultad de Ciencias, UNED, Madrid, Spain

Abstract: There exists the possibility to improve the efficiency of Bayesian Network learning procedures, by selecting as search space the equivalence classes of Directed Acyclic Graphs (DAGs), or the more general of Chain Graphs (CGs), and from them we can select an essential graph as representative of each class. Furthermore, we describe and advance some new results, with efficient algebraic tools, as Imsets, Semigraphoids, Matroids and so on.

Keywords: A. I., Graph Theory, Bayesian Networks.

Angel Garrido is Full (time) Professor, belonging to the Department of Fundamental Mathematics, in the Faculty of Sciences of UNED (Universidad Nacional de Educación a Distancia), Madrid, Spain, where he imparts Mathematical Analysis for Physics to his students and does research by collaborating with the research Department of Artificial Intelligence, ETS Ingeniería Informática, also at UNED. He runs complete studies on Mathematics and Computation into the Faculty of Mathematics, at Universities Complutense, UNED and Polytechnic of Madrid; also gives lectures on different subjects of Computer Science, as Automata Theory, Complexity and Computability, A. I., Statistical Inference. Furthermore, on Mathematics in ETS of Architecture, at Polytechnic University of Madrid and distinct Institutes. Prof. Garrido runs also Summer Courses at UNED, on Art and Mathematics, with subjects as Geometry of Gaudi architectural work, or Analysis of the Cordobe Mosque and so on. Lately he’s been imparting Seminars on different research lines, as Causality, Probabilistic Graphical Models (PGMs), Essential Graphs and so on. His published works comprise until now forty-five research papers, which appeared in different prestigious international scientific journals. With active participation in more than forty international conferences, on Mathematics and Computation. Being member of Scientific Committee of many of such Congresses. And belonging to the Editorial Board of some scientific international journals, as AUA (Acta Universitatis Apulensis), IJOPMCS (International Journal of Open Problems on Mathematics and Computer Science), IJMA (International Journal of Mathematical Analysis), AS (Agora Studies), and so on. Prof. Garrido is the author of five books on  Mathematical Analysis, ODE, Physics of Sound and Acoustics. He also holds the First Birhäuser Prize to the Best Communication, at the ICM (International Congress of Mathematicians, Madrid, 2006).

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Angel GARRIDO, Improved by Equivalence Classes and their Essential Graphs, Studies in Informatics and Control, ISSN 1220-1766, vol. 18 (1), pp. 39-40, 2009.