Compute the score of the Bayesian network.
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an object of class
a data frame containing the data the Bayesian network that will be used to compute the score.
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
a boolean value. If
a boolean value. If
extra arguments from the generic method (for the
a numeric value, the penalty coefficient to be used; the default
Additional arguments of the
iss: the imaginary sample size, used by the Bayesian Dirichlet
bdj) and the Bayesian
Gaussian score (
bge). It is also known as “equivalent sample
size”. The default value is equal to
1 for the Dirichlet scores and
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 coefficient to be used by the AIC and BIC
scores. The default value is
1 for AIC and
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 various
Bayesian Dirichlet scores (
bds) and the
Bayesian Gaussian score (
bge). Possible values are
vsp (the Bayesian variable selection prior, which
puts a probability of inclusion on parents),
independent marginal uniform for each arc) and
cs (the Castelo &
Siebes prior, which puts an independent prior probability on each arc
beta: the parameter associated with
beta is ignored.
beta is the probability of
inclusion of an additional parent. The default is
beta is the probability
of inclusion of an arc. Each direction has a probability of inclusion
beta / 2 and the probability that the arc is not included is
1 - beta. The default value is
0.5, so that
arc inclusion and arc exclusion have the same probability.
beta is a data frame with
prob specifying the prior
probability for a set of arcs. A uniform probability distribution is
assumed for the remaining arcs.
by.node = TRUE, a vector of numeric values, the
individual node contributions to the score of the Bayesian network.
Otherwise, a single numeric value, the score of the Bayesian network.
AIC and BIC are computed as
logLik(x) - k * nparams(x), that is, the
classic definition rescaled by -2. Therefore higher values are better, and
for large sample sizes BIC converges to log(BDe).
When using the Castelo & Siebes prior in structure learning, the prior
probabilties associated with an arc are bound away from zero and one by
shrinking them towards the uniform distribution as per Hausser and Strimmer
(2009) with a lambda equal to
3 * sqrt(.Machine$double.eps). This
dramatically improves structure learning, which is less likely to get stuck
when starting from an empty graph. As an alternative to prior probabilities,
a blacklist can be used to prevent arcs from being included in the network,
and a whitelist can be used to force the inclusion of particular arcs.
beta is not modified when the prior is used from functions other than
those implementing score-based and hybrid structure learning.
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". In "UAI '94: Proceedings of the Tenth Annual Conference on Uncertainty in Artificial Intelligence", pp. 235-243. Morgann Kaufmann. Available as Technical Report MSR-TR-94-10.
Hausser J, Strimmer K (2009). "Entropy inference and the James-Stein estimator, with application to nonlinear gene association networks". Statistical Applications in Genetics and Molecular Biology, 10, 1469-1484.
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.
Suzuki J (2016). "A Theoretical Analysis of the BDeu Scores in Bayesian Network Structure Learning". Behaviormetrika, 44(1), 97-116.
Scutari M (2016). "An Empirical-Bayes Score for Discrete Bayesian Networks". Journal of Machine Learning Research, 52, 438-448.
Cano A and Gomez-Olmedo M and Masegosa AR and Moral S (2013). "Locally Averaged Bayesian Dirichlet Metrics for Learning the Structure and the Parameters of Bayesian Networks". International Journal of Approximate Reasoning, 54, 526-540.
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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") ## K2 score on the other hand is not score equivalent. score(res, learning.test, type = "k2") score(res2, learning.test, type = "k2") ## 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) ## equivalent to logLik(res, learning.test) score(res, learning.test, type = "loglik") ## equivalent to AIC(res, learning.test) score(res, learning.test, type = "aic")
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