Statistical Learning Methods for High Dimensional Genomic Data Statistical Learning Methods for High Dimensional Genomic Data Title: Statistical Learning Methods for High Dimensional Genomic Data

Due to their high-dimensionality, -omics technologies require the development of computational methods that are able to work with large number of variables. Each data type is characterized by its method of measurement and by the biological aspect under study. Understanding the data properties allows the design of sophisticated and effective computational models that are able to uncover and explain complex biological phenomena. This thesis aims at exploring the use of statistical learning methods for dealing with different high-throughput molecular data, in order to answer heterogeneous biological questions related to various diseases. We address problems at different biological levels (e.g. gene expression or genomic alteration) but exploiting different peculiarities of the data under analysis. We propose a computational framework in which biological questions can be modeled as solution of a minimization problem of a functional where data properties are described via a composition of penalties and constraints. This framework includes a wide range of regularized least squares and regularized matrix factorization methods. We focus on two main questions. First, we apply the `1`2-norms regularization to extract gene signatures from gene expression data related to neurodegenerative diseases like Alzheimer and Parkinson. Such feature selection method is nested in a pipeline where functionally related pathways are extracted from the list of relevant genes. The last step of the pipeline, moreover, plans to infer interaction network related to each pathways from the data in order to evaluate differences between different phenotypes (e.g. patients vs controls). Second, dealing with aCGH data, in the context of Dictionary Learning, we combine a set of penalties (e.g. `1-norm and Total Variation) and hard constraints in order to automatically detect common genomic alterations from a set of high risk Neuroblastoma patients. Genomic alterations identified by the regularized method are used as input of an algorithm for oncogenesis tree estimation. Finally, we present a set of well structured software modules, tools and libraries that implement the above methods and models.