Graphical models for estimating dynamic networks

Abstract

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 random variables. Graphical models describe conditional independence relationships. Gaussian graphical models are graphical models where it is assumed that the random variables 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 multivariate dynamic data are binary or ordinal random variables, transformations based on probability distribution with fixed marginal can be used to do inference. We propose the Gaussian copula for non-Gaussian graphical models to overcome the assumption of Gaussianity. 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.