Title: Graphical models based on trees
Authors: Anna Gottard - University of Firenze (Italy) [presenting]
Abstract: Graphical models have been utilised in a wide range of problems to characterise the conditional independence structure among random variables. Particularly interesting are applications in genomics and omics science. A better understanding of the association among gene/protein/metabolite molecular signatures potentially offers new insights for complex diseases. With continuous random variable, most of this research traditionally focuses on Gaussian graphical models, assuming linear relationships. However, the assumptions of multivariate Gaussianity and linearity in the dependence structure are often evidently erroneous. Recent literature explores graphical models with non-linear relations. We investigate pairwise graphical models on a set of random variables, with distributions in which dependence occurs through the expected value. We study the utility of tree based models to detect interactions and non-linearities in these distributions and compare different algorithm for searching a tree or a sum of trees. A particular case of quasi-linear systems is analysed, embedding linear and nonlinear effects.