Probabilistic reasoning in intelligent systems: networks of plausible inference
Probabilistic reasoning in intelligent systems: networks of plausible inference
Elements of information theory
Elements of information theory
Learning Bayesian networks from data: an information-theory based approach
Artificial Intelligence
Equivalence and synthesis of causal models
UAI '90 Proceedings of the Sixth Annual Conference on Uncertainty in Artificial Intelligence
Large-Sample Learning of Bayesian Networks is NP-Hard
The Journal of Machine Learning Research
Strong completeness and faithfulness in Bayesian networks
UAI'95 Proceedings of the Eleventh conference on Uncertainty in artificial intelligence
A kernel-based causal learning algorithm
Proceedings of the 24th international conference on Machine learning
On the classification performance of TAN and general Bayesian networks
Knowledge-Based Systems
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Cheng, Greiner, Kelly, Bell and Liu [Artificial Intelligence 137 (2002) 43-90] describe an algorithm for learning Bayesian networks that--in a domain consisting of n variables--identifies the optimal solution using O(n4) calls to a mutual-information Oracle. This result relies on (1) the standard assumption that the generative distribution is Markov and faithful to some directed acyclic graph (DAG), and (2) a new assumption about the generative distribution that the authors call monotone DAG faithfulness (MDF). The MDF assumption rests on an intuitive connection between active paths in a Bayesian-network structure and the mutual information among variables. The assumption states that the (conditional) mutual information between a pair of variables is a monotonic function of the set of active paths between those variables; the more active paths between the variables the higher he mutual information. In this paper, we demonstrate the unfortunate result that, for any realistic learning scenario, the monotone DAG faithfulness assumption is incompatible with the faithfulness assumption. Furthermore, for the class of Bayesian-network structures for which the two assumptions are compatible, we can learn the optimal solution using standard approaches that require Only O(n2) calls to an independence oracle.