Rusnák, Radovan (2025) Bayesian Coupled Scheme for Network Modelling with Application to the Raf Signalling Pathway. Master's Thesis / Essay, Applied Mathematics.
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Abstract
In many fields involving network modelling, particularly molecular biology, data is often collected under varying experimental conditions. We assume that such data arises from gentle mutations of an underlying network that can be modelled as a Directed Acyclic Graph (DAG). Previous work proposed a Bayesian framework that couples related DAGs through a shared “hypernetwork,” effectively capturing features common across all experimental conditions. To not penalize DAGs that encode the same conditional dependencies and independencies, we develop two new coupling mechanisms: one compares DAGs based on their equivalence classes using Completed Partially Directed Acyclic Graphs (CPDAGs), and the other operates with their underlying skeleton structures. Inference is performed via Markov Chain Monte Carlo (MCMC) sampling, and simulation studies demonstrate that our method recovers underlying networks more accurately in a statistically significant manner. A major hurdle in Bayesian network learning is that the number of DAGs grows superexponentially with the number of nodes. This particularly complicates the evaluation of the network prior distribution and forces us to employ approximation techniques. We develop a deterministic mechanism that further enhances the well-known Perfect Gas Approximation, which is often used when the prior distribution over network structures is obtained in the form of a Gibbs distribution. We report a solid improvement in computational efficiency, which allows us to use spare CPU time for additional MCMC iterations and thus further enhance inference accuracy. We demonstrate our model by reconstructing the Raf signalling pathway, an intracellular cascade important in cancer research and drug discovery.
| Item Type: | Thesis (Master's Thesis / Essay) |
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| Supervisor name: | Grzegorczyk, M.A. and Trapman, J.P. |
| Degree programme: | Applied Mathematics |
| Thesis type: | Master's Thesis / Essay |
| Language: | English |
| Date Deposited: | 22 Jul 2025 10:47 |
| Last Modified: | 22 Jul 2025 10:47 |
| URI: | https://fse.studenttheses.ub.rug.nl/id/eprint/36478 |
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