Inference of Gaussian graphical models and ordinary differential equations

Networks provide a simple way to visualize a system of interacting elements. For example, gene regulatory networks are complex systems whose elements are genes, proteins and other molecules. The elements of this system are represented by nodes and lines are drawn between them if they interact with each other.
In many sciences uncovering the network structure is an important and difficult problem. With a limited knowledge about the system noisy measurements on the nodes should be used to estimate the network. When we know the structure of the interactions, another major obstacle is to learn the fine dynamics of the system using the same noisy data, from describing bridges subject to strong winds to the spread of an infectious disease.
In this thesis we propose modifications of existing methods to improve the estimation of networks and dynamical systems.
Some applications of methods we develop include: predicting the number of individuals that get infected by childhood disease measles, reconstructing transcription factor activities in streptomyces coelicolor bacterium, and inferring the interaction between genes and proteins in Escherichia coli bacterium.