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Bayesian network structure learning (1)

Problem: have all data but does not know the structure of the Bayesian Netowrk


determining whether there is an edge between two nodes (A,B): measure the likelihood p(B|A).

What’s the problem of using likelihood in structure learning?


likelihood cannot do better than completely connected network structure.

one way to avoid overfitting is to have a good estimation of the prior probability.

uniform prior is not good because MAP will be Maximum likelihood given uniform prior on hypothesis.

penalty of how many edges in the network.

put your knowledge into initial bayessian network. staring from there, do estimation on adding, adjusting, removing edges.

In all, how to learn unknow structure for Bayesian Network:

1. initial state: empty network  or prior network

2. operators: add arc, deletec arc, reverse arc

3. Evaluation: Posterior Probability