From Conditional Independences to Factorization Constraints with Discrete Random Variables
Annals of Mathematics and Artificial Intelligence
On Axiomatizing Probabilistic Conditional Independencies in Bayesian Networks
WI '01 Proceedings of the First Asia-Pacific Conference on Web Intelligence: Research and Development
Triangulation of Bayesian Networks: A Relational Database Perspective
TSCTC '02 Proceedings of the Third International Conference on Rough Sets and Current Trends in Computing
A Method for Detecting Context-Specific Independence in Conditional Probability Tables
TSCTC '02 Proceedings of the Third International Conference on Rough Sets and Current Trends in Computing
Properties of Weak Conditional Independence
TSCTC '02 Proceedings of the Third International Conference on Rough Sets and Current Trends in Computing
Construction of a Non-redundant Cover for Conditional Independencies
AI '02 Proceedings of the 15th Conference of the Canadian Society for Computational Studies of Intelligence on Advances in Artificial Intelligence
On the Role of Contextual Weak Independence in Probabilistic Inference
AI '02 Proceedings of the 15th Conference of the Canadian Society for Computational Studies of Intelligence on Advances in Artificial Intelligence
The membership problem for probabilistic and data dependencies
Technologies for constructing intelligent systems
A Web-Based Intelligent Tutoring System for Computer Programming
WI '04 Proceedings of the 2004 IEEE/WIC/ACM International Conference on Web Intelligence
A web-based bayesian intelligent tutoring system for computer programming
Web Intelligence and Agent Systems
Maximal prime subgraph decomposition of Bayesian networks: A relational database perspective
International Journal of Approximate Reasoning
Information Sciences: an International Journal
A simple graphical approach for understanding probabilistic inference in Bayesian networks
Information Sciences: an International Journal
On Inferences ofWeak Multivalued Dependencies
Fundamenta Informaticae
Conditional independence structure and its closure: Inferential rules and algorithms
International Journal of Approximate Reasoning
Acyclic Directed Graphs to Represent Conditional Independence Models
ECSQARU '09 Proceedings of the 10th European Conference on Symbolic and Quantitative Approaches to Reasoning with Uncertainty
A join tree probability propagation architecture for semantic modeling
Journal of Intelligent Information Systems
A new inference axiom for probabilistic conditional independence
AI'03 Proceedings of the 16th Canadian society for computational studies of intelligence conference on Advances in artificial intelligence
Critical remarks on the maximal prime decomposition of Bayesian networks
RSFDGrC'03 Proceedings of the 9th international conference on Rough sets, fuzzy sets, data mining, and granular computing
A web-based interface for hiding Bayesian network inference
ISMIS'08 Proceedings of the 17th international conference on Foundations of intelligent systems
Acyclic directed graphs representing independence models
International Journal of Approximate Reasoning
Constructing the Bayesian network structure from dependencies implied in multiple relational schemas
Expert Systems with Applications: An International Journal
Exploiting independencies to compute semigraphoid and graphoid structures
International Journal of Approximate Reasoning
Join tree propagation utilizing both arc reversal and variable elimination
International Journal of Approximate Reasoning
Finding P-maps and I-maps to represent conditional independencies
ECSQARU'11 Proceedings of the 11th European conference on Symbolic and quantitative approaches to reasoning with uncertainty
Evaluating probabilistic inference techniques: a question of "When," not "Which"
SUM'11 Proceedings of the 5th international conference on Scalable uncertainty management
The computational complexity of inference using rough set flow graphs
RSFDGrC'05 Proceedings of the 10th international conference on Rough Sets, Fuzzy Sets, Data Mining, and Granular Computing - Volume Part I
Incorporating evidence in bayesian networks with the select operator
AI'05 Proceedings of the 18th Canadian Society conference on Advances in Artificial Intelligence
An efficient algorithm for inference in rough set flow graphs
Transactions on Rough Sets V
Characterisations of multivalued dependency implication over undetermined universes
Journal of Computer and System Sciences
An improved LAZY-AR approach to bayesian network inference
AI'06 Proceedings of the 19th international conference on Advances in Artificial Intelligence: Canadian Society for Computational Studies of Intelligence
ACM Transactions on Database Systems (TODS)
On Inferences ofWeak Multivalued Dependencies
Fundamenta Informaticae
Probabilistic conditional independence under schema certainty and uncertainty
SUM'12 Proceedings of the 6th international conference on Scalable Uncertainty Management
Reasoning about functional and full hierarchical dependencies over partial relations
Information Sciences: an International Journal
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The implication problem is to test whether a given set of independencies logically implies another independency. This problem is crucial in the design of a probabilistic reasoning system. We advocate that Bayesian networks are a generalization of standard relational databases. On the contrary, it has been suggested that Bayesian networks are different from the relational databases because the implication problem of these two systems does not coincide for some classes of probabilistic independencies. This remark, however, does not take into consideration one important issue, namely, the solvability of the implication problem. In this comprehensive study of the implication problem for probabilistic conditional independencies, it is emphasized that Bayesian networks and relational databases coincide on solvable classes of independencies. The present study suggests that the implication problem for these two closely related systems differs only in unsolvable classes of independencies. This means there is no real difference between Bayesian networks and relational databases, in the sense that only solvable classes of independencies are useful in the design and implementation of these knowledge systems. More importantly, perhaps, these results suggest that many current attempts to generalize Bayesian networks can take full advantage of the generalizations made to standard relational databases