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- Title
Bayesian learning of graphical vector autoregressions with unequal lag-lengths.
- Authors
Marttinen, Pekka; Corander, Jukka
- Abstract
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.
- Subjects
GRAPHIC methods for multivariate analysis; GRAPHICAL modeling (Statistics); STOCHASTIC processes; MARKOV processes; RANDOM walks; ESTIMATION theory
- Publication
Machine Learning, 2009, Vol 75, Issue 2, p217
- ISSN
0885-6125
- Publication type
Article
- DOI
10.1007/s10994-009-5101-2