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If I understand it right, both use Bayes Theorem to generate an acyclic graph and calculate percentages based on functions applied at every node.

What is the difference?

iceburn
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  • Here is a [pdf](http://www.researchgate.net/publication/26803642_Comparison_of_Bayesian_network_and_decision_tree_methods_for_predicting_access_to_the_renal_transplant_waiting_list/file/79e4150b7b248e0384.pdf) to a paper: 'Comparison of Bayesian network and decision tree methods for predicting access to the renal transplant waiting list', comparing decision trees and Bayesian networks. –  Apr 04 '13 at 23:22

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One simple and fundamental difference is Acyclic Graph != Tree

For example, a->b<-c is not a tree (it has two roots), but it is an acyclic graph.

I am not well versed in decision trees, but I am well versed in Bayesian Networks. Here are some things that you can do with Bayesian Networks that I am not sure if you can do with a decision tree. Researching how to do these things with a decision tree may reveal interesting differences.

  • Compute the joint probability table between the variables
  • Determine if two variables are conditionally independent
  • Given some evidence, determine the distribution of the non-evidence variables given the evidence
Carlos Rendon
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  • Can the Acyclic Graph generated by a Bayesian Network be a Forest then? Because otherwise they both generate Trees since a connected Acyclic Graph is a Tree. – iceburn Aug 11 '10 at 23:01
  • Yes. It is possible for two variables to be independent. In which case they are not connected. Also a Bayesian Network does not "generate" a graph, it is a graphical representation of conditional independence relationships between the variables of a probability distribution. – Carlos Rendon Aug 11 '10 at 23:33