Fusion, propagation, and structuring in belief networks
Artificial Intelligence
Probabilistic reasoning in intelligent systems: networks of plausible inference
Probabilistic reasoning in intelligent systems: networks of plausible inference
Gibbs and Markov properties of graphs
Annals of Mathematics and Artificial Intelligence
Advances in the understanding and use of conditional independence
Annals of Mathematics and Artificial Intelligence
On Stochastic Conditional Independence: the Problems of Characterization and Description
Annals of Mathematics and Artificial Intelligence
CMSB '03 Proceedings of the First International Workshop on Computational Methods in Systems Biology
Handbook of data mining and knowledge discovery
On deducing conditional independence from d-separation in causal graphs with feedback
Journal of Artificial Intelligence Research
Modeling discrete interventional data using directed cyclic graphical models
UAI '09 Proceedings of the Twenty-Fifth Conference on Uncertainty in Artificial Intelligence
Introduction to Causal Inference
The Journal of Machine Learning Research
An alternative Markov property for chain graphs
UAI'96 Proceedings of the Twelfth international conference on Uncertainty in artificial intelligence
A discovery algorithm for directed cyclic graphs
UAI'96 Proceedings of the Twelfth international conference on Uncertainty in artificial intelligence
A polynomial-time algorithm for deciding Markov equivalence of directed cyclic graphical models
UAI'96 Proceedings of the Twelfth international conference on Uncertainty in artificial intelligence
Learning linear cyclic causal models with latent variables
The Journal of Machine Learning Research
Cyclic causal models with discrete variables: Markov Chain equilibrium semantics and sample ordering
IJCAI'13 Proceedings of the Twenty-Third international joint conference on Artificial Intelligence
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The use of directed acyclic graphs (DAGs) to represent conditional independence relations among random variables has proved fruitful in a variety of ways. Recursive structural equation models are one kind of DAG model. However, non-recursive structural equation models of the kinds used to model economic processes are naturally represented by directeed cyclic graphs (DCG). For linear systems associated with DCGs with independent errors, a characterisation of conditional independence constraints is obtained, and it is shown that the result generalizes in a natural way to systems in which the error variables or noises are statistically dependent. For non-linear systems with independent errors a sufficient condition for conditional independence of variables in associated distributions is obtained.