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Extra Colloquium Mathematics, Marco Grzegorczyk Dept. of Statistics TU Dortmund University, Germany

29 April 2013

Date:                           Monday, April 29th 2013
Speaker:                     Marco Grzegorczyk (Dept. of Statistics TU Dortmund University, Germany )
Room:                         5161.0293 (Bernoulliborg)
Time:                           11.00

Title: Bayesian regularization of non-homogeneous dynamic Bayesian network models


The objective of systems biology research is the elucidation
of the regulatory networks and signalling 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.

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. However, the assumption of prior independence
is unrealistic in many real-world applications, where the majority of
segment-specific regulatory relationships among the interdependent
quantities tend to undergo minor and gradual adaptations. Moreover, for
sparse time series, as typically available in many systems biology
applications, inference suffers from vague posterior distributions, and
could borrow strength from a systematic mechanism of information

There are two approaches to information coupling in time series
segmented by multiple changepoints: sequential information coupling, and
global information coupling. In the former, information is shared between
adjacent segments. In the latter, segments are treated as
interchangeable units, and information is shared globally. Sequential
information coupling is appropriate for a system in the process of
development, e.g. in morphogenesis. Global information coupling, on the
other hand, is more appropriate when time series segments are related to
different experimental scenarios or environmental conditions. These
coupling schemes have been applied to the regularization of DBNs with
time-varying network structures, by penalizing network structure changes
sequentially or globally. However, these approaches do not address the
information coupling with respect to the interaction parameters and
assume complete parameter independence among time segments.

In my 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 network interaction parameters.

Last modified:06 June 2018 2.05 p.m.

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