Bayesian Networks in the Presence of Temporal Information - Bayesian Networks in R: With Applications in Systems Biology - page 69

3.3.4 Modular Networks

The Statistical Inference for MOdular NEtworks (SIMoNe) by Chiquet et al. ( 2009 )
implements various learning algorithms based on the LASSO, with an additional
grouping effect for multiple data.
SIMoNe follows a score-based approach; it searches for a latent clustering of
the network to drive the selection of arcs through an adaptive L 1 penalization of the
model likelihood, in particular for VAR(1) processes. The penalization of individual
arcs may be weighted according to a predefined latent clustering of the network,
thus adapting the inference of the network to a particular topology. The optimal L 1
penalty level can be chosen by minimizing the BIC criterion.
Note that this procedure can deal with samples collected in different experimental
conditions and therefore not identically distributed.

3.4 Non-homogeneous Dynamic Bayesian Network Learning

Homogeneity (Assumption 4 in Sect. 2 ) is a strong assumption which may not be
satisfied for real-world data. For example, the coordination of molecular and bio-
chemical processes inside a cell requires highly dynamic gene regulation networks.
Different interactions between cellular components can occur across time depend-
ing, for instance, on the developmental program of the cell or on physiological and
environmental changes. In order to model such data, the ARTIVA approach from
Lebre et al. ( 2010 )usesan Auto-Regressive TIme VArying model and the associated
learning and inference procedures.
ARTIVA performs an analysis of time-course measurements to identify poten-
tial interactions between two sets of variables referred to as targets and parents ,re-
spectively. When considering gene regulation networks, parents are variables whose
functions agree with regulatory controls of other genes. Typically these are genes
coding for transcription factors. In ARTIVA, each target variable is analyzed inde-
pendently while searching for dependencies with the parents. As a result, ARTIVA
identifies temporal segments in the time-course measurements (Fig. 3.3 ,dashed
lines) for which different interaction models occur between parent and target vari-
ables. The time points that delimit the different temporal segments are referred to
as changepoints (CPs) and define homogeneous phases , i.e., sets of time points for
which the local network topology (interactions between parent and target genes)
remains unchanged.
ARTIVA's probabilistic model is a particular case of a VAR process. Within a
temporal phase h , each random variable X i (

is assumed to depend on its p putative
parents, through an auto-regressive model which takes into account a time delay d
between the expression values of parent and target genes. The model is defined as

t )

A h B h

h

X ( t )= X ( t − 1 )+ + ε ( t ) , (3.16)