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
Equivalence and synthesis of causal models
UAI '90 Proceedings of the Sixth Annual Conference on Uncertainty in Artificial Intelligence
Optimal structure identification with greedy search
The Journal of Machine Learning Research
Learning Bayesian Networks
A reconstruction algorithm for the essential graph
International Journal of Approximate Reasoning
Structure learning of Bayesian networks using constraints
ICML '09 Proceedings of the 26th Annual International Conference on Machine Learning
Logical inference algorithms and matrix representations for probabilistic conditional independence
UAI '09 Proceedings of the Twenty-Fifth Conference on Uncertainty in Artificial Intelligence
A geometric view on learning Bayesian network structures
International Journal of Approximate Reasoning
Efficient Algorithms for Conditional Independence Inference
The Journal of Machine Learning Research
Probabilistic Conditional Independence Structures
Probabilistic Conditional Independence Structures
On open questions in the geometric approach to structural learning Bayesian nets
International Journal of Approximate Reasoning
Efficient Structure Learning of Bayesian Networks using Constraints
The Journal of Machine Learning Research
Causal inference and causal explanation with background knowledge
UAI'95 Proceedings of the Eleventh conference on Uncertainty in artificial intelligence
Approximating discrete probability distributions with dependence trees
IEEE Transactions on Information Theory
International Journal of Approximate Reasoning
International Journal of Approximate Reasoning
Learning optimal bayesian networks: a shortest path perspective
Journal of Artificial Intelligence Research
Learning Bayesian network structure: Towards the essential graph by integer linear programming tools
International Journal of Approximate Reasoning
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The motivation for the paper is the geometric approach to learning Bayesian network (BN) structure. The basic idea of our approach is to represent every BN structure by a certain uniquely determined vector so that usual scores for learning BN structure become affine functions of the vector representative. The original proposal from Studeny et al. (2010) [26] was to use a special vector having integers as components, called the standard imset, as the representative. In this paper we introduce a new unique vector representative, called the characteristic imset, obtained from the standard imset by an affine transformation. Characteristic imsets are (shown to be) zero-one vectors and have many elegant properties, suitable for intended application of linear/integer programming methods to learning BN structure. They are much closer to the graphical description; we describe a simple transition between the characteristic imset and the essential graph, known as a traditional unique graphical representative of the BN structure. In the end, we relate our proposal to other recent approaches which apply linear programming methods in probabilistic reasoning.