Abstract
To relax the homogeneity assumption of classical dynamic Bayesian networks (DBNs), various recent studies have combined DBNs with multiple changepoint processes. The underlying assumption is that the parameters associated with time series segments delimited by multiple changepoints are a priori independent. Under weak regularity conditions, the parameters can be integrated out in the likelihood, leading to a closed-form expression of the marginal likelihood. However, the assumption of prior independence is unrealistic in many real-world applications, where the segment-specific regulatory relationships among the interdependent quantities tend to undergo gradual evolutionary adaptations. We therefore propose a Bayesian coupling scheme to introduce systematic information sharing among the segment-specific interaction parameters. We investigate the effect this model improvement has on the network reconstruction accuracy in a reverse engineering context, where the objective is to learn the structure of a gene regulatory network from temporal gene expression profiles. The objective of the present paper is to expand and improve an earlier conference paper in six important aspects. Firstly, we offer a more comprehensive and self-contained exposition of the methodology. Secondly, we extend the model by introducing an extra layer to the model hierarchy, which allows for information-sharing among the network nodes, and we compare various coupling schemes for the noise variance hyperparameters. Thirdly, we introduce a novel collapsed Gibbs sampling step, which replaces a less efficient uncollapsed Gibbs sampling step of the original MCMC algorithm. Fourthly, we show how collapsing and blocking techniques can be used for developing a novel advanced MCMC algorithm with significantly improved convergence and mixing. Fifthly, we systematically investigate the influence of the (hyper-)hyperparameters of the proposed model. Sixthly, we empirically compare the proposed global information coupling scheme with an alternative paradigm based on sequential information sharing.
Highlights
There is considerable interest in structure learning of dynamic Bayesian networks (DBNs), with a variety of applications in computational systems biology
In a first step we select the level-3 hyperparameters such that the level-2 hyperparameters are equal in prior expectation to those imposed in earlier studies for simpler versions of these non-homogeneous dynamic Bayesian networks (NH-DBNs) models without level-3 hyperpriors
For the low signal-to-noise ratio (SNR = 1) there is no significant difference between the three dynamic Bayesian network models
Summary
There is considerable interest in structure learning of dynamic Bayesian networks (DBNs), with a variety of applications in computational systems biology. While there have been various efforts to relax the homogeneity assumption for undirected graphical models (Talih and Hengartner 2005; Xuan and Murphy 2007), relaxing this restriction in DBNs is a more recent research topic (Lèbre 2007; Robinson and Hartemink 2009, 2010; Ahmed and Xing 2009; Kolar et al 2009; Lèbre et al 2010; Dondelinger et al 2010, 2012; Husmeier et al 2010; Grzegorczyk and Husmeier 2011). The inference task reduces to sampling the network structure as well as the number and location of changepoints from the posterior distribution, which can be effected with reversible jump Markov chain Monte Carlo (RJMCMC) (Green 1995), e.g., as in Lèbre et al (2010) or Robinson and Hartemink (2010), or with dynamic programming (Fearnhead 2006), as in Grzegorczyk and Husmeier (2011)
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