Optimal decomposition by clique separators
Discrete Mathematics
Causality and model abstraction
Artificial Intelligence
Causality: models, reasoning, and inference
Causality: models, reasoning, and inference
Introduction to Algorithms
Bayesian graphical model determination using decision theory
Journal of Multivariate Analysis
Exact Bayesian Structure Discovery in Bayesian Networks
The Journal of Machine Learning Research
Beyond independent components: trees and clusters
The Journal of Machine Learning Research
Monte Carlo Statistical Methods (Springer Texts in Statistics)
Monte Carlo Statistical Methods (Springer Texts in Statistics)
Handbook of Mathematical Functions, With Formulas, Graphs, and Mathematical Tables,
Handbook of Mathematical Functions, With Formulas, Graphs, and Mathematical Tables,
International Journal of Intelligent Systems - Uncertainty Processing
Bayesian Model Learning Based on Predictive Entropy
Journal of Logic, Language and Information
Learning the structure of dynamic probabilistic networks
UAI'98 Proceedings of the Fourteenth conference on Uncertainty in artificial intelligence
Learning graphical models for stationary time series
IEEE Transactions on Signal Processing
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Graphical modelling strategies have been recently discovered as a versatile tool for analyzing multivariate stochastic processes. Vector autoregressive processes can be structurally represented by mixed graphs having both directed and undirected edges between the variables representing process components. To allow for more expressive vector autoregressive structures, we consider models with separate time dynamics for each directed edge and non-decomposable graph topologies for the undirected part of the mixed graph.Contrary to static graphical models, the number of possible mixed graphs is extremely large even for small systems, and consequently, standard Bayesian computation based on Markov chain Monte Carlo is not in practice a feasible alternative for model learning. To obtain a numerically efficient approach we utilize a recent Bayesian information theoretic criterion for model learning, which has attractive properties when the potential model complexity is large relative to the size of the observed data set. The performance of our method is illustrated by analyzing both simulated and real data sets. Our simulation experiments demonstrate the gains in predictive accuracy which can obtained by considering structural learning of vector autoregressive processes instead of unstructured models. The analysis of the real data also shows that the understanding of the dynamics of a multivariate process can be improved significantly by considering more flexible model classes.