score: Score of the Bayesian network

In vspinu/bnlearn: Bayesian network structure learning, parameter learning and inference

Description

Compute the score of the Bayesian network.

Usage

score(x, data, type = NULL, ..., debug = FALSE)

## S3 method for class 'bn'
logLik(object, data, ...)
## S3 method for class 'bn'
AIC(object, data, ..., k = 1)
## S3 method for class 'bn'
BIC(object, data, ...)

Arguments

x, object	an object of class bn.
data	a data frame containing the data the Bayesian network was learned from.
type	a character string, the label of a network score. If none is specified, the default score is the Bayesian Information Criterion for both discrete and continuous data sets. See bnlearn-package for details.
debug	a boolean value. If TRUE a lot of debugging output is printed; otherwise the function is completely silent.
...	extra arguments from the generic method (for the AIC and logLik functions, currently ignored) or additional tuning parameters (for the score function).
k	a numeric value, the penalty per parameter to be used; the default k = 1 gives the expression used to compute the AIC in the context of scoring Bayesian networks.

Details

Additional parameters of the score function:

• iss: the imaginary sample size, used by the Bayesian Dirichlet equivalent score (both the bde and mbde) and the Bayesian Gaussian score (bge). It is also known as “equivalent sample size”. The default value is equal to 10 for both the bde/mbde scores and bge.

• exp: a list of indexes of experimental observations (those that have been artificially manipulated). Each element of the list must be named after one of the nodes, and must contain a numeric vector with indexes of the observations whose value has been manipulated for that node.

• k: the penalty per parameter to be used by the AIC and BIC scores. The default value is 1 for AIC and log(nrow(data))/2 for BIC.

• phi: the prior phi matrix formula to use in the Bayesian Gaussian equivalent (bge) score. Possible values are heckerman (default) and bottcher (the one used by default in the deal package.)

• prior: the prior distribution to be used with the Bayesian Dirichlet equivalent score (bde) and the Bayesian Gaussian score (bge). Possible values are uniform (the default), vsp (the Bayesian variable selection prior, which puts a probability of inclusion on parents) and cs (the Castelo & Siebes prior, which puts an independent prior probability on each arc and direction).

• beta: the parameter associated with prior. If prior is uniform, beta is ignored. If prior is vsp, beta is the probability of inclusion of an additional parent (the default is 1/ncol(data)). If prior is cs, beta is a data frame with columns from, to and prob specifying the prior probability for a set of arcs. A uniform probability distribution is assumed for the remaining arcs.

Value

A numeric value, the score of the Bayesian network.

Author(s)

Marco Scutari

References

Castelo R, Siebes A (2000). "Priors on Network Structures. Biasing the Search for Bayesian Networks". International Journal of Approximate Reasoning, 24(1), 39-57.

Chickering DM (1995). "A Transformational Characterization of Equivalent Bayesian Network Structures". In "UAI '95: Proceedings of the Eleventh Annual Conference on Uncertainty in Artificial Intelligence", pp. 87-98. Morgan Kaufmann.

Cooper GF, Yoo C (1999). "Causal Discovery from a Mixture of Experimental and Observational Data". In "UAI '99: Proceedings of the Fifteenth Annual Conference on Uncertainty in Artificial Intelligence", pp. 116-125. Morgann Kaufmann.

Geiger D, Heckerman D (1994). "Learning Gaussian Networks". Technical report, Microsoft Research. Available as Technical Report MSR-TR-94-10.

Heckerman D, Geiger D, Chickering DM (1995). "Learning Bayesian Networks: The Combination of Knowledge and Statistical Data". Machine Learning, 20(3), 197-243. Available as Technical Report MSR-TR-94-09.

See Also

choose.direction, arc.strength.

Examples

data(learning.test)
res = set.arc(gs(learning.test), "A", "B")
score(res, learning.test, type = "bde")

## let's see score equivalence in action!
res2 = set.arc(gs(learning.test), "B", "A")
score(res2, learning.test, type = "bde")

## BDe with a prior.
beta = data.frame(from = c("A", "D"), to = c("B", "F"), 
         prob = c(0.2, 0.5), stringsAsFactors = FALSE)
score(res, learning.test, type = "bde", prior = "cs", beta = beta)

## k2 score on the other hand is not score equivalent.
score(res, learning.test, type = "k2")
score(res2, learning.test, type = "k2")

## equivalent to logLik(res, learning.test)
score(res, learning.test, type = "loglik")

## equivalent to AIC(res, learning.test)
score(res, learning.test, type = "aic")

vspinu/bnlearn documentation built on May 3, 2019, 7:08 p.m.