Probabilistic reasoning in intelligent systems: networks of plausible inference
Probabilistic reasoning in intelligent systems: networks of plausible inference
On the Optimality of the Simple Bayesian Classifier under Zero-One Loss
Machine Learning - Special issue on learning with probabilistic representations
Machine Learning - Special issue on learning with probabilistic representations
Learnability of Augmented Naive Bayes in Nonimal Domains
ICML '01 Proceedings of the Eighteenth International Conference on Machine Learning
Geometric implications of the naive Bayes assumption
UAI'96 Proceedings of the Twelfth international conference on Uncertainty in artificial intelligence
Bayesian Networks for Knowledge-Based Authentication
IEEE Transactions on Knowledge and Data Engineering
A Formal Analysis of Fault Diagnosis with D-matrices
Journal of Electronic Testing: Theory and Applications
On the classification performance of TAN and general Bayesian networks
Knowledge-Based Systems
UniDis: a universal discretization technique
Journal of Intelligent Information Systems
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One of the most important fundamental properties of Bayesian networks is the representational power, reflecting what kind of functions they can or cannot represent. In this paper, we establish an association between the structural complexity of Bayesian networks and their representational power. We use the maximum number of nodes' parents as the measure for the structural complexity of Bayesian networks, and the maximum XOR contained in a target function as the measure for the function complexity. A representational upper bound is established and proved. Roughly speaking, discrete Bayesian networks with each node having at most k parents cannot represent any function containing (k+1)-XORs. Our theoretical results help us to gain a deeper understanding on the capacities and limitations of Bayesian networks.