Probabilistic graphical models, by making conditional independence assumptions, can represent complex joint distributions in a factorized form. However, in large problems graphical models often run into two issues. First, in non-treelike graphs, computational issues frustrate exact inference....

This thesis presents a class of graphical models for directly representing the joint cumulative distribution function (CDF) of many random variables, called cumulative distribution networks (CDNs). Unlike graphical models for probability density and mass functions, in a CDN, the marginal...