Extra Colloquium Mathematics, Dr. Marco Grzegorczyk (Dortmund)

Join us for coffee and tea at 13.15 p.m.

Date:                          Wednesday, February 13^th 2013

Speaker:                     Dr. Marco Grzegorczyk (Dortmund)

Room:                         5161.0289 (Bernoulliborg)

Time:                           13.30 – 14.30

Title: Modelling dynamic networks – with applications in systems biology

Abstract:

The objective of systems biology research is the elucidation of the regulatory networks and signaling pathways of the cell. The ideal approach would be the deduction of a detailed mathematical description of the entire system in terms of a set of coupled non-linear differential equations. As high-throughput measurements are inherently stochastic 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-dimensional multimodal parameter spaces are not robust, and model selection is impeded by the fact that more complex pathway models would always provide a better explanation of the data than less complex ones, rendering this approach intrinsically susceptible to over-fitting.

To assist the elucidation of regulatory networks, dynamic Bayesian networks can be employed. The idea is to simplify the mathematical description of the biological system by replacing coupled differential equations by conditional probability distributions. This results in a scoring function (marginal likelihood) of closed form that depends only on the structure of the network and avoids the over-fitting problem. Markov Chain Monte Carlo (MCMC) algorithms can be applied to search the space of network structures for those that are most consistent with the data.

In the talk I will present two novel non-homogeneous dynamic Bayesian network models for sequential [1] and global [2,3] information sharing with respect to the interaction parameters.

REFERENCES:

[1] Grzegorczyk, M. and Husmeier, D. (2012a): A non-homogeneous dynamic Bayesian network model with sequentially coupled interaction parameters for applications in systems and synthetic biology. Statistical Applications in Genetics and Molecular Biology (SAGMB), vol. 11 (4), Article 7.

[2] Grzegorczyk, M. and Husmeier, D. (2012b): Bayesian regularization of non-homogeneous dynamic Bayesian networks by globally coupling interaction parameters. In: N. Lawrence and M. Girolami (editors), Proceedings of the 15th International Conference on Artifical Intelligence and Statistics (AISTATS), 467-476, vol. 22 of JMLR: W&CP 22.

[3] Grzegorczyk, M. and Husmeier, D. (2013): Regularization of Non-Homogeneous Dynamic Bayesian Networks with Global Information-Coupling based on Hierarchical Bayesian models. Machine Learning, DOI: 10.1007/s10994-012-5326-3, in press (online version published).

Colloquium coordinators are Prof.dr. A.C.D. van Enter (e-mail : A.C.D.van.Enter@rug.nl) and

Dr. A.V. Kiselev (e-mail: a.v.kiselev rug.nl)

http://www.rug.nl/wiskunde/nieuws/actueel/wiskundecolloquia