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Bayesian network
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Bayesian network
A Bayesian network is a form of probabilistic graphical model, also known as Bayesian belief network or just belief network.
A Bayesian network can be represented by a graph (as in graph theory) with probabilities attached. Thus, a Bayesian network represents a set of variables together with a joint probability distribution with explicit independence assumptions.
- 1 Definition
- 2 Example
- 3 Causal Bayesian networks
- 4 Structure learning
In the simplest case, a Bayesian network is specified by an expert and is then used to perform inference. In other applications the task of defining the network is too complex for humans. In this case the network structure and the parameters of the local distributions must be learned from data.
Learning the structure of a Bayesian network (i.e., the graph) is a very important part of machine learning. Assuming that the data is generated from a Bayesian network and that all the variables are visible in every iteration, optimization based search method can be used to find the structure of the network. It requires a scoring function and a search strategy. A common scoring function is posterior probability of the structure given the training data. The time requirement of an exhaustive search returning back a structure that maximizes the score is superexponential in the number of variables. A local search strategy makes incremental changes aimed at improving the score of the structure. A global search algorithm like Markov chain Monte Carlo can avoid getting trapped in local minima. Friedman et al.[citation needed] talk about using mutual information between variables and finding a structure that maximizes this. They do this by restricting the parent candidate set to k nodes and exhaustively searching therein.
- 5 Parameter learning
- 6 Inference
- 7 Applications
- 8 See also
- 9 Links and software
- 10 References
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