Date: Monday, April 29th 2013
Marco Grzegorczyk (Dept. of Statistics TU Dortmund University, Germany
Room: 5161.0293 (Bernoulliborg)
Bayesian regularization of non-homogeneous dynamic Bayesian network models
The objective of systems biology research is the elucidationof the regulatory networks and signalling pathways of the cell. Theideal approach would be the deduction of a detailed mathematicaldescription of the entire system in terms of a set of coupled non-lineardifferential equations. As high-throughput measurements are inherentlystochastic and most kinetic rate constants cannot be measured directly,the parameters of the system would have to be estimated from the data.Unfortunately, standard optimization techniques in high-dimensionalmultimodal parameter spaces are not robust, and model selection isimpeded by the fact that more complex pathway models would alwaysprovide a better explanation of the data than less complex ones,rendering this approach intrinsically susceptible to over-fitting. Toassist the elucidation of regulatory networks, dynamic Bayesian networkscan be employed. The idea is to simplify the mathematical description ofthe biological system by replacing coupled differential equations byconditional probability distributions. This results in a scoringfunction (marginal likelihood) of closed form that depends only on thestructure of the network and avoids the over-fitting problem. MarkovChain Monte Carlo (MCMC) algorithms can be applied to search the spaceof network structures for those that are most consistent with the data.
To relax the homogeneity assumption of classical dynamic Bayesiannetworks (DBNs), various recent studies have combined DBNs with multiplechangepoint processes. The underlying assumption is that the parametersassociated with time series segments delimited by multiple changepointsare a priori independent. However, the assumption of prior independenceis unrealistic in many real-world applications, where the majority ofsegment-specific regulatory relationships among the interdependentquantities tend to undergo minor and gradual adaptations. Moreover, forsparse time series, as typically available in many systems biologyapplications, inference suffers from vague posterior distributions, andcould borrow strength from a systematic mechanism of informationcoupling.
There are two approaches to information coupling in time seriessegmented by multiple changepoints: sequential information coupling, andglobal information coupling. In the former, information is shared betweenadjacent segments. In the latter, segments are treated asinterchangeable units, and information is shared globally. Sequentialinformation coupling is appropriate for a system in the process ofdevelopment, e.g. in morphogenesis. Global information coupling, on theother hand, is more appropriate when time series segments are related todifferent experimental scenarios or environmental conditions. Thesecoupling schemes have been applied to the regularization of DBNs withtime-varying network structures, by penalizing network structure changessequentially or globally. However, these approaches do not address theinformation coupling with respect to the interaction parameters andassume complete parameter independence among time segments.
In my talk I will present two novel non-homogeneous dynamic Bayesiannetwork models for sequential  and global [2,3] information sharingwith respect to the network interaction parameters.
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