Heterogeneous Graphical Models with Applications to Omics Data

Thanks to the advances in bioinformatics and high-throughput methodologies of the last decades, a large unprecedented amount of biological data coming from various experiments in metabolomics, genomics and proteomics is available. This has lead the researchers to conduct more and more comprehensive molecular proling of biological samples through different multiple aspects of genomic activities, thus introducing new challenges in the developments of statistical tools to integrate and model multi-omics data. The main research objective of this thesis is to develop a statistical framework for modelling the interactions between genes when their activity is measured on different domains; to do so, our approach relies on the concept of multilayer network, and how structures of this type can be combined with graphical models for mixed data, i.e., data comprising variables of different nature (e.g., continuous, categorical, skewed, to name a few). We further develop an algorithm for learning the structure of the undirected multilayer networks underlying the proposed models, showing its promising results through empirical analyses on cancer data, which was downloaded from the public TCGA consortium.