A reconstruction algorithm for the essential graph

Authors:
Milan Studený;Jiří Vomlel
Affiliations:
Instititute of Information Theory and Automation of the ASCR, Pod vodárenskou věží 4, Prague, CZ 182 08, Czech Republic;Instititute of Information Theory and Automation of the ASCR, Pod vodárenskou věží 4, Prague, CZ 182 08, Czech Republic
Venue:
International Journal of Approximate Reasoning
Year:
2009

Citing 10
Cited 4

Probabilistic Networks and Expert Systems

Probabilistic Networks and Expert Systems
Equivalence and synthesis of causal models

UAI '90 Proceedings of the Sixth Annual Conference on Uncertainty in Artificial Intelligence
Improved learning of Bayesian networks

UAI '01 Proceedings of the 17th Conference in Uncertainty in Artificial Intelligence
Optimal structure identification with greedy search

The Journal of Machine Learning Research
Characterization of essential graphs by means of the operation of legal merging of components

International Journal of Uncertainty, Fuzziness and Knowledge-Based Systems - New trends in probabilistic graphical models
Probabilistic Conditional Independence Structures: With 42 Illustrations (Information Science and Statistics)

Probabilistic Conditional Independence Structures: With 42 Illustrations (Information Science and Statistics)
Racing algorithms for conditional independence inference

International Journal of Approximate Reasoning
Characterization of inclusion neighbourhood in terms of the essential graph

International Journal of Approximate Reasoning
On the construction of the inclusion boundary neighbourhood for markov equivalence classes of bayesian network structures

UAI'02 Proceedings of the Eighteenth conference on Uncertainty in artificial intelligence
Causal inference and causal explanation with background knowledge

UAI'95 Proceedings of the Eleventh conference on Uncertainty in artificial intelligence

A geometric view on learning Bayesian network structures

International Journal of Approximate Reasoning
On open questions in the geometric approach to structural learning Bayesian nets

International Journal of Approximate Reasoning
Improved algorithm based on mutual information for learning Bayesian network structures in the space of equivalence classes

Multimedia Tools and Applications
Characteristic imsets for learning Bayesian network structure

International Journal of Approximate Reasoning

Quantified Score

Hi-index	0.00

Visualization

Abstract

A standard graphical representative of a Bayesian network structure is a special chain graph, known as an essential graph. An alternative algebraic approach to the mathematical description of this statistical model uses instead a certain integer-valued vector, known as a standard imset. We give a direct formula for the translation of any chain graph describing a Bayesian network structure into the standard imset. Moreover, we present a two-stage algorithm which makes it possible to reconstruct the essential graph on the basis of the standard imset. The core of this paper is the proof of the correctness of the algorithm.