Joint Probability Trees

Joint probability distributions offer a wide range of highpotential applications in engineering, science, and technology (Chater et al., 2006; Griffiths et al., 2008; Knill & Pouget, 2004). Besides families of continuous distributions, introducing strong independence assumptions that must be probabilistic graphical models (PGMs), such as Bayesian known prior to learning and may turn out to be too great networks and Markov random fields (Koller & Friedman, simplifications of a model to be of practical use (Besag, 2009), are the de-facto standard in probabilistic knowledge 1975; Jain, 2012). As a simple example, consider a probability representation. They provide graph-based languages to space X, Y, C of two numeric variables, X and Y, model dependencies and independencies of variables, and and one symbolic variable C, dom(C) = {Red, Blue} as local joint or conditional distributions that quantify the statistical illustrated in Figures 1a and 1b. Let the symbolic values Red dependencies. However, the practical applicability of and Blue demaracate two clusters that are approximately PGMs suffers from the representational and computational normally distributed.