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Gibbs ensembles for incompatible dependency networks

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In most statistical applications, the Gibbs sampler is the method of choice for inference regarding conditionally specified distributions that are compatible. Compatibility ensures that a unique Gibbs distribution exists. For machine learning of complex models such as dependency networks, the conditional models are sometimes incompatible. In this paper, we review an ensemble approach using the Gibbs sampler as the base procedure. A Gibbs ensemble consists of many joint distributions resulting from different scan orders of the same conditional model, and the solution is a weighted sum of the ensemble. The algorithm is scalable and can handle large data sets of high dimensionality. The proposed approach provides joint distributions that conform with the conditional specifications better than the solutions obtained by linear programming and by a fixed‐scan Gibbs sampler alone. Owing to incompatibility, the invariant distribution of a Gibbs sampler is scan‐order dependent. A Gibbs ensemble is the collection of joint distributions estimated from the Gibbs samples of different scan orders. WIREs Comput Stat 2013, 5:478–485. doi: 10.1002/wics.1273 This article is categorized under: Statistical and Graphical Methods of Data Analysis > Markov Chain Monte Carlo (MCMC)
(a) Bayesian network; (b) dependency network; and (c) Markov network.
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Dependency network for concerns and symptoms in cancer patients (N = 100).
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Contour plot of joint distributions for continuous example.
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Flow diagram for the Gibbs ensemble.
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Statistical and Graphical Methods of Data Analysis > Markov Chain Monte Carlo (MCMC)

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