Modeling cumulative biological phenomena with Suppes-Bayes Causal Networks

Noname manuscript No. (will be inserted by the editor) Abstract Several diseases related to cell proliferation are characterized by the accumulation of somatic DNA changes, with respect to wildtype conditions. Cancer and HIV are two common examples of such diseases, where the mutational load in the cancerous/viral population increases over time. In these cases, selective pressures are often observed along with competition, cooperation and parasitism among distinct cellular clones. Recently, we presented a mathematical framework to model these phenomena, based on a combination of Bayesian inference and Suppes' theory of probabilistic causation, depicted in graphical structures dubbed Suppes-Bayes Causal Networks ( SBCNs). SBCNs are generative probabilistic graphical models that recapitulate the potential ordering of accumulation of such DNA changes during the progression of the disease. Such models can be inferred from data by exploiting likelihood-based model-selection strategies with regularization. In this paper we discuss the theoretical foundations of our approach and we investigate in depth the influence on the model-selection task of: (i) the poset based on Suppes' theory and (ii) different regularization strategies. Furthermore, we provide an example of application of our framework to HIV genetic data high-Daniele Ramazzotti Department of Pathology, Stanford University, Stanford, CA 94305, USA Email: daniele.ramazzotti@stanford.edu Alex Graudenzi Department of Informatics, Systems and Communication, University of Milan-Bicocca, Milan, Italy Giulio Caravagna School of Informatics, University of Edinburgh, Edinburgh, UK Marco Antoniotti Department of Informatics, Systems and Communication, University of Milan-Bicocca, Milan, Italy Keywords Cumulative Phenomena· Bayesian Graphical Models· Probabilistic Causality 1 Introduction A number of diseases are characterized by the accumulation of genomic lesions in the DNA of a population of cells. Such lesions are often classified as mutations, if they involve one or few nucleotides, or chromosomal alterations, if they involve wider regions of a chromosome.