PhD Colloquium Mathematics, Pariya Behrouzi

Abstract: The behavior of most complex systems, from the cell to the Internet, emerges from the activity of many components that pairwise interact with each other. At an abstract level, these components can be shown as a series of nodes that are connected to each other by links, where each link shows the interaction between two components. The nodes and links together form a network or, in more formal language, a graph.

The objectives of this work have been to extend graphical models for different data structures and to enlarge the applicability of graphical models in various fields, particularly in systems genetics. In this talk, we introduce our proposed method for reconstructing a conditional independence network from multivariate non-Gaussian data, in particular for ordinal and for mixed ordinal-and-continuous data. As an application of our proposed method we detect epistatic interactions network in A.thaliana where we aim to find loci on a genome that do not segregate independently conditional on other loci. In addition, we talk about an extension of the proposed method for constructing high-quality linkage maps for any biparental species. A linkage map contains important genetic information such as the number of chromosomes of a species, the number of markers inside each chromosome, and the order of markers within each chromosome. We have implemented the proposed methods as user-friendly software called netgwas, which is freely accessible for users.

Furthermore, we talk about an extension of graphical models to high-dimensional time-series data with non-Gaussian structure, where we combine directed and undirected graphical models to explore dynamic and contemporaneous interactions. We demonstrate our method on depression data from the Netherlands Study of Depression and Anxiety.