Graphical models for estimating dynamic networks

PhD ceremony: Mr. A. Abbruzzo, 11.00 uur, Academiegebouw, Broerstraat 5, Groningen

Dissertation: Graphical models for estimating dynamic networks

Promotor(s): prof. E.C. Wit, prof. A.M. Mineo

Faculty: Mathematics and Natural Sciences

Estimating dynamic networks from data is an active research area and it is one important direction in system biology. Estimating the structure of a network is about deciding the presence or absence of relationships between the nodes. Graphical models describe conditional independence relationships. Gaussian graphical models assume that the nodes follow a multivariate normal distribution. When Gaussian graphical models are applied in order to study large networks, they typically fail because the number of variables is much greater than the number of observations. Recently, penalized Gaussian graphical models have been proposed to estimate static networks in high-dimensional studies because of their statistical properties and computational tractability. We propose to use penalized Gaussian graphical models to estimate structured dynamic networks, for modeling slowly changing of dynamic networks, and to estimate particular structures such as scale-free dynamic networks in a small world setting. These models can be applied when estimating dynamic networks in high dimensional environments. When the underlying dynamic processes represented via binary, ordinal, count or otherwise non-Gaussian data, we propose to use the Gaussian copula for defining a general non-Gaussian graphical model. The Gaussian copula effectively transforms the data by means of marginal transformations or via latent Gaussian variables. This approach is very powerful and has the advantage of being able to deal with mixed types of variables of arbitrary distribution. The problem of estimating dynamic networks becomes even more challenging when latent or hidden variables are involved in larger systems. State-space models have been proposed in order to study dynamic networks with latent variables. We propose a penalized Gaussian graphical models to estimate dynamic networks with latent structures.