Gene association networks and higher-order interactions: Algorithms and statistical models

This thesis presents new statistical tools to address the question of how genes interact in a cell. It has been challenging to study genetic interactions for two reasons. First, computational time is an issue. Second, higher order interactions between genes and gene messages are recognized with increasingly complexity. New statistical tools are continuously in need in order to describe various types of interactions that are observed.;The computational issue is addressed first. I proposed new statistical procedure called "network partition and re-assembly search (nPars)" to circumvent the issue of high-dimensional network spaces. Second, new statistical tools for detecting various types of interactions among genes are introduced. I proposed the novel "generalized liquid association measure" for quantifying a specific type of three-way interaction named "liquid association". Finally, a new computer software program called "LiquidAssociation" was presented. This software can be freely obtained through the website: http://www.bioconductor.org.;The contribution of this thesis work rests with its providing better statistical tools for the analysis of large-scale genetic data while capturing gene interactions of various natures. It is our hope that these methods would lead to a better understanding of the interactions of genes and their connections to outcomes, such as cell behavior, cancer treatment and various human disorders.