Bayesian Belief Network

A Bayesian belief network (also known as a BayesianNetwork, a BeliefNetwork or a BayesNet) is a representation of dependence (and so also independence) of random variables. It is named after ThomasBayes.

A belief network can be described in terms of

• structure: a directed acyclic graph where the nodes are random variables and a domain for each random variable
• function: how each variable depends on its parents, such as using a table, a decision tree, a "noisy or", or some parametrized form
• number: the actual numbers needed to specify a conditional probability of each variable given its parents

History

Algorithms for Inference in Belief networks

Exact Algorithms

The main exact algorithms are

• VariableElimination^? which exploits the sparseness of the graph to answer single queries
• CliqueTreePropagation^? which creates a secondary structure to give the posterior on each variable and allow for the incorporation of new evidence.
• RecursiveConditioning^? that allows for the tradeoff between time and space

Approximate Algorithms

• StochasticSimulation^?
• VariationalMethods^?
• Search-basedAlgorithms^?

Learning Belief networks

Causality

Alternative Related Representations

• A DecisionNetwork^? adds decision varibles and utility variables for making sequential decisions
• A CausalNetwork makes predictions of interventions

Industrial Applications

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