User Manual for Libra 1.1.2d

In Libra, each probabilistic model represents a probability distribution, P (X ), over set of discrete random variables, X = {X1, X2, . . . , Xn}. Libra supports Bayesian networks (BNs), Markov networks (MNs), dependency networks (DNs) [8], sumproduct networks (SPNs) [19], arithmetic circuits (ACs) [6], and mixtures of trees (MT) [17]. BNs and DNs represent a probability distribution as a collection of conditional probability distributions (CPDs), each denoting the conditional probability of one random variable given its parents. The most common CPD representation is a table with one entry for each joint configuration of the variable and its parents. In addition to tables, Libra also supports tree CPDs and more complex feature-based CPDs. In a tree CPD, nodes and branches specify conditions on the parent variables, and each leaf contains the probability of the target variable given the conditions on the path to that leaf. When many configurations have identical probabilities, trees can be exponentially more compact than table CPDs. Feature-based CPDs use a weighted set of conjunctive features. Each conjunctive feature represents a set of conditions on the parent variables and target variables, similar to the paths in