0000000000748866
AUTHOR
E. Wit
Dynamic factorial graphical models for dynamic networks
Dynamic networks models describe a growing number of important scientific processes, from cell biology and epidemiology to sociology and finance. Estimating dynamic networks from noisy time series data is a difficult task since the number of components involved in the system is very large. As a result, the number of parameters to be estimated is typically larger than the number of observations. However, a characteristic of many real life networks is that they are sparse. For example, the molec- ular structure of genes make interactions with other components a highly-structured and, therefore, a sparse process. Penalized Gaussian graphical models have been used to estimate sparse networks. H…
Generalizing LARS algorithm using differential geometry
We propose a path following algorithm for generalized linear models that can be considered a differential geometric generalization of the LARS algorithm. In our approach we use differential geometry to generalize the equiangular condition on which is based the LARS algorithm and then we use a predictor-corrector method to compute the solution path of the coefficients.
Sparse model-based network inference using Gaussian graphical models
We consider the problem of estimating a sparse dynamic Gaussian graphical model with L1 penalized maximum likelihood of structured precision matrix. The structure can consist of specific time dynamics, known presence or absence of links in the graphical model or equality constraints on the parameters. The model is defined on the basis of partial correlations, which results in a specific class precision matrices. A priori L1 penalized maximum likelihood estimation in this class is extremely difficult, because of the above mentioned constraints, the computational complexity of the L1 constraint on the side of the usual positive-definite constraint. The implementation is non-trivial, but we sh…
Inferring slowly changing dynamic gene-regulatory networks
Dynamic gene-regulatory networks are complex since the interaction patterns between its components mean that it is impossible to study parts of the network in separation. This holistic character of gene-regulatory networks poses a real challenge to any type of modelling. Graphical models are a class of models that connect the network with a conditional independence relationships between the random variables. By interpreting the random variables as gene activities and the conditional independence relationships as functional non-relatedness, graphical models have been used to describe gene-regulatory networks. Whereas the literature has been focused on static networks, most time-course experi…