Title: A hierarchical nonparametric approach for robust graphical modelling
Authors: Andrea Cremaschi - Universitetet i Oslo (Norway) [presenting]
Raffaele Argiento - University of Torino (Italy)
Abstract: Useful tools for exploring multivariate network structures are Gaussian graphical models. However, alternative models are needed when data are strongly non-Gaussian. The t-Student distribution, obtained by dividing each component of the data vector by a gamma random variable, is the straightforward generalisation to accommodate such issue. The Dirichlet t-Student distribution is obtained when the law of the divisors is the Dirichlet process. In the latter, conditionally to a shared mass parameter, a Dirichlet process is introduced for every multivariate observation, so that one can cluster the components of each data point according to their deviation from the Normal distribution (outlier clustering). We consider a more general class of nonparametric distributions, namely the class of normalised completely random measures (NormCRM), which yields a more flexible component clustering. Moreover, in order to borrow more information across the data, we model the dependence among the NormCRM through a nonparametric hierarchical structure. At data level, each NormCRM is centred on the same base measure, which is a NormCRM itself. The discreteness of the shared base measure implies that the processes at data level share the same atoms. This desired feature allows to cluster together components of different data.An application to a bio-medical dataset is described for illustrative purposes.