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Main.BayesianBeliefNetworkr1.2 - 23 Mar 2006 - 00:52 - MarkCrowleytopic end

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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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