Distances and Stability in Biological Network Theory

In this thesis we introduce, define and quantitatively assess the stability of the algorithms for the econstruction of networks. We will focus on theory, development and implementation of operative procedures and algorithms for the assessment of stability in complex networks for biological systems, with gene regulatory networks as the key example. A major issue affecting network inference is indeed the high variability of network reconstruction and network topology inferred after data perturbation, different parameter choices and alternative methods. Network stability will thus be used to measure reliability of inferred topology, also obtaining confidence intervals for the outcomes. The methods will be employed to introduce a new approach to reproducibility in the study of complex networks. It will also be coupled with statistical machine learning models, in order to integrate feature selection and network inference within a pathway profiling approach. The evaluation of similarity between networks will be the first and central operative procedure of the developed pipelines, the key point being the identification of distances that can compare network structures improving over classical measures based on the confusion matrix, too coarse for this task. A combination of spectral and edit distances especially tailored for biological networks will be investigated and applied to several high-throughput biological datasets of different nature and with different tasks in oncogenomics, neurogenomics and exposomics.