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Which are the widely used scoring functions for structural learning? More, specifically I am interested in scoring function that favours the random variables which have binary possible states.

For an example like:

A) Bayesian scoring function: - BD
- BDe
- BDeu
- K2

B) Information theoretic function:
- LL
- MDL/BIC
- AIC
- NML
- MIT

Or SparsityBoost scoring function

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  • $\begingroup$ You mean like the Ising model? $\endgroup$
    – Emre
    Jun 17, 2015 at 17:33
  • $\begingroup$ I am newbie in BN so I dont know how to apply the Ising model or how would it help in computing scoring functions for a possible BN structure $\endgroup$ Jun 17, 2015 at 17:43

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This paper answers your question.

In summary there are two subgroups: i. Bayesian functions and ii. Information theoretic functions (Log-likelihood based, which apply to any generative model, not just BN's).

Bear in mind that some of the scoring functions they list under i. are theoretical, and cannot be used (in practice) without simplifying assumptions. I think it will be clear when you read the paper.

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  • $\begingroup$ Yes, thanks for the input. I was also looking for more inputs as how one would leverage the case that random variables are binary while evaluating the scoring functions $\endgroup$ Jun 17, 2015 at 17:41
  • $\begingroup$ @skn, Sorry, I am not clear on this. Can you explain a bit more: more inputs as how one would leverage the case that random variables are binary. None of the scores should have a problem with binary (or in general categorical) variables. A binary variable in your BN would follow a binomial distribution and for each structure, the routines learn the parameters (as well as the structures). Learning the parameters refers to learning the Conditional Probability Tables (CPTs). $\endgroup$
    – Zhubarb
    Jun 18, 2015 at 7:16

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