Probabilistic reasoning in intelligent systems: networks of plausible inference
Probabilistic reasoning in intelligent systems: networks of plausible inference
Probabilistic Networks and Expert Systems
Probabilistic Networks and Expert Systems
Improved learning of Bayesian networks
UAI '01 Proceedings of the 17th Conference in Uncertainty in Artificial Intelligence
Learning equivalence classes of bayesian-network structures
The Journal of Machine Learning Research
Learning equivalence classes of Bayesian network structures
UAI'96 Proceedings of the Twelfth international conference on Uncertainty in artificial intelligence
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
A reconstruction algorithm for the essential graph
International Journal of Approximate Reasoning
Characterization of inclusion neighbourhood in terms of the essential graph
International Journal of Approximate Reasoning
Efficiently approximating Markov tree bagging for high-dimensional density estimation
ECML PKDD'11 Proceedings of the 2011 European conference on Machine learning and knowledge discovery in databases - Volume Part III
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The problem of learning Markov equivalence classes of Bayesian network structures may be solved by searching for the maximum of a scoring metric in a space of these classes. This paper deals with the definition and analysis of one such search space. We use a theoretically motivated neighbourhood, the inclusion boundary, and represent equivalence classes by essential graphs. We show that this search space is connected and that the score of the neighbours can be evaluated incrementally. We devise a practical way of building this neighbourhood for an essential graph that is purely graphical and does not explicitely refer to the underlying independences. We find that its size can be intractable, depending on the complexity of the essential graph of the equivalence class. The emphasis is put on the potential use of this space with greedy hillclimbing search.