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**A scoring function for learning Bayesian networks based on mutual information and conditional independence tests.**
*(English)*
Zbl 1222.62036

Summary: We propose a new scoring function for learning Bayesian networks from data using score+search algorithms. This is based on the concept of mutual information and exploits some well-known properties of this measure in a novel way. Essentially, a statistical independence test based on the chi-square distribution, associated with the mutual information measure, together with a property of additive decomposition of this measure, are combined in order to measure the degree of interaction between each variable and its parent variables in the network. The result is a non-Bayesian scoring function called MIT (mutual information tests) which belongs to the family of scores based on information theory. The MIT score also represents a penalization of the Kullback-Leibler divergence between the joint probability distributions associated with a candidate network and with the available data set. Detailed results of a complete experimental evaluation of the proposed scoring function and its comparison with the well-known K2, BDeu and BIC/MDL scores are also presented.

### MSC:

62F15 | Bayesian inference |

62B10 | Statistical aspects of information-theoretic topics |

68T99 | Artificial intelligence |

62G10 | Nonparametric hypothesis testing |