Strong Limit Theorems for the Bayesian Scoring Criterion in Bayesian Networks

@article{Slobodianik2009StrongLT,
  title={Strong Limit Theorems for the Bayesian Scoring Criterion in Bayesian Networks},
  author={Nikolai Slobodianik and Dmitry Yu. Zaporozhets and Neal Madras},
  journal={Journal of Machine Learning Research},
  year={2009},
  volume={10},
  pages={1511-1526}
}
In the machine learning community, the Bayesian scoring cri terion is widely used for model selection problems. One of the fundamental theoretical properti es justifying the usage of the Bayesian scoring criterion is its consistency. In this paper we refine this property for the case of binomial Bayesian network models. As a by-product of our derivations we establish strong consistency and obtain the law of iterated logarithm for the Bayesian scorin g criterion.