  Graphical models are widely used in scienti fic and engineering research to
represent conditional independence structures between random variables. In many
controlled experiments, environmental changes or external stimuli can often
alter the conditional dependence between the random variables, and potentially
produce significant structural changes in the corresponding graphical models.
Therefore, it is of great importance to be able to detect such structural
changes from data, so as to gain novel insights into where and how the
structural changes take place and help the system adapt to the new environment.
Here we report an effective learning strategy to extract structural changes in
Gaussian graphical model using l1-regularization based convex optimization. We
discuss the properties of the problem formulation and introduce an efficient
implementation by the block coordinate descent algorithm. We demonstrate the
principle of the approach on a numerical simulation experiment, and we then
apply the algorithm to the modeling of gene regulatory networks under different
conditions and obtain promising yet biologically plausible results.
