Two-sample inference for graphical models

One of the main goals of transcriptomics is the identification of genes that show a significant difference between two conditions. Biological processes underlying the basic functions of a cell involve complex interactions between genes, that can be represented through a graph where genes and their connections are, respectively, nodes and edges. The main research objective of this thesis is to improve some aspects of differential network analysis, accounting for the nature of the data and the network structure. To this aim, we propose a correction for the likelihood ratio test, with application to two-sample inference in decomposable Gaussian graphical models. We prove that the adjusted statistic leads to valid inference at different dimensionality regimes. Moreover, we study the necessary and sufficient conditions for the existence of the estimate in the Kullback-Leibler importance estimation procedure, with the aim of guiding the practitioner on the use of this tool in real data analyses and posing the basis for future works in the context of count data.