Theory of linear and integer programming
Theory of linear and integer programming
Probabilistic reasoning in intelligent systems: networks of plausible inference
Probabilistic reasoning in intelligent systems: networks of plausible inference
Bayesian Networks and Decision Graphs
Bayesian Networks and Decision Graphs
Probabilistic Networks and Expert Systems
Probabilistic Networks and Expert Systems
d-Separation: From Theorems to Algorithms
UAI '89 Proceedings of the Fifth Annual Conference on Uncertainty in Artificial Intelligence
Optimal structure identification with greedy search
The Journal of Machine Learning Research
Probabilistic Conditional Independence Structures: With 42 Illustrations (Information Science and Statistics)
Learning Bayesian Networks
Racing algorithms for conditional independence inference
International Journal of Approximate Reasoning
Three counter-examples on semi-graphoids
Combinatorics, Probability and Computing
Logical inference algorithms and matrix representations for probabilistic conditional independence
UAI '09 Proceedings of the Twenty-Fifth Conference on Uncertainty in Artificial Intelligence
Logical and algorithmic properties of stable conditional independence
International Journal of Approximate Reasoning
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
On open questions in the geometric approach to structural learning Bayesian nets
International Journal of Approximate Reasoning
Characteristic imsets for learning Bayesian network structure
International Journal of Approximate Reasoning
Hi-index | 0.01 |
The topic of the paper is computer testing of (probabilistic) conditional independence (CI) implications by an algebraic method of structural imsets. The basic idea is to transform (sets of) CI statements into certain integral vectors and to verify by a computer the corresponding algebraic relation between the vectors, called the independence implication. We interpret the previous methods for computer testing of this implication from the point of view of polyhedral geometry. However, the main contribution of the paper is a new method, based on linear programming (LP). The new method overcomes the limitation of former methods to the number of involved variables. We recall/describe the theoretical basis for all four methods involved in our computational experiments, whose aim was to compare the efficiency of the algorithms. The experiments show that the LP method is clearly the fastest one. As an example of possible application of such algorithms we show that testing inclusion of Bayesian network structures or whether a CI statement is encoded in an acyclic directed graph can be done by the algebraic method.