Bayesian Nonparametric Structural Learning

With nowadays high availability of complex data, more statistical techniques aimed at understanding the underlying dependence structures are needed. Data complexity refers to two separate issues: (i) complex interactions occurring among the random variables object of study, for instance in large networks of protein-protein interactions; (ii) complex data type, for instance Twitter text posts and gene regulatory networks. The huge statistical literature on graphical models has extensively dealt with the first kind of complexity, interaction complexity, by assuming multivariate Gaussian data with graph-driven dependencies. The wider and wider set of statistical models on relational data, high-dimensional data, up to infinite-dimensional parameters, has attacked the second kind of complexity, type complexity, though random network models, sparsity-based inferential methods and random probability measures. In particular, the Bayesian nonparametric literature has proposed several well-motivated prior distributions on random measures, with the purpose of detaching from over-simplified base models often justified by mathematical convenience.