# Fitting Graphical Interaction Models to Multivariate Time Series

@inproceedings{Eichler2006FittingGI, title={Fitting Graphical Interaction Models to Multivariate Time Series}, author={Michael Eichler}, booktitle={UAI}, year={2006} }

Graphical interaction models have become an important tool for analysing multivariate time series. In these models, the interrelationships among the components of a time series are described by undirected graphs in which the vertices depict the components while the edges indictate possible dependencies between the components. Current methods for the identification of the graphical structure are based on nonparametric spectral estimation, which prevents application of common model selection…

## 17 Citations

### Bayesian learning of graphical vector autoregressions with unequal lag-lengths

- Computer ScienceMachine Learning
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This work considers structural learning of vector autoregressive processes instead of unstructured models using 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.

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This paper develops a theoretical framework and an optimization procedure which is applied to the identification problem of estimating the ARMA parameters as well as the topology of the graph from statistical data.

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A semidefinite relaxation is presented, and it is proved that the relaxation is exact when the sample covariance matrix is block-Toeplitz, and the estimation method can be used for topology selection.

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This paper takes the problem to fit an autoregressive moving-average (ARMA) model to the same data one step further and develops a theoretical framework which also spreads further light on previous approaches and results.

### Topology Selection in Graphical Models of Autoregressive Processes

- Computer Science, MathematicsJ. Mach. Learn. Res.
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An algorithm is presented for topology selection in graphical models of autoregressive Gaussian time series that reduces to a convex optimization problem and is described as a large-scale algorithm that solves the dual problem via the gradient projection method.

### Conditional independence graphs for multivariate autoregressive models by convex optimization: Efficient algorithms

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A two-stage approach for fitting sparse VAR (sVAR) models in which many of the AR coefficients are zero is proposed, based on an estimate of the partial spectral coherence (PSC) together with the use of BIC.

### Maximum-likelihood estimation of autoregressive models with conditional independence constraints

- Computer Science, Mathematics2009 IEEE International Conference on Acoustics, Speech and Signal Processing
- 2009

A convex relaxation is formulated and it is proved that it is exact when the sample covariance matrix is block-Toeplitz, and in practice the relaxation is exact under much weaker conditions.

### Graphical Gaussian Process Models for Highly Multivariate Spatial Data

- Mathematics, Computer Science
- 2020

A class of multivariate "graphical Gaussian Processes" is proposed using a general construction called "stitching" that crafts cross-covariance functions from graphs and ensure process-level conditional independence among variables.

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