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Belief Propagation Algorithm
Exact message-passing algorithm for trees and approximate for graphs with cycles, calculating marginal beliefs by propagating information between neighboring nodes.
Bayesian Networks
Directed probabilistic graphical models representing conditional dependencies between random variables, used for reasoning under uncertainty and decision making.
Markov Networks
Undirected probabilistic graphical models where edges represent mutual dependencies, characterized by Gibbs distributions and global Markov properties.
Evidence
Observed information about certain model variables, used to condition inference calculations and update probability distributions of unobserved variables.
Marginal Computation
Fundamental operation consisting of calculating the probability distribution of a subset of variables by integrating over all other variables in the model.
Hugin Algorithm
Specific implementation of exact inference in junction trees, using bidirectional message propagation for optimal marginal computation.
Shafer-Shenoy Algorithm
Variant of exact inference in junction trees explicitly separating collection and distribution phases, avoiding division by potential zeros.
Cliques
Subsets of nodes forming complete subgraphs in a graph, playing a central role in constructing junction trees and organizing computations.
Exponential time complexity
Intrinsic property of exact inference in general graphical models, where computation time grows exponentially with the size of cliques or the treewidth of the graph.
Treewidth
Structural complexity measure of a graph that determines the efficiency of exact inference, defined as the maximum size of cliques minus one in an optimal tree decomposition.
Factorization
Decomposition of a complex joint probability distribution into a product of simpler factors, exploiting the conditional independence properties of the graphical model.