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score {bnlearn}  R Documentation 
Score of the Bayesian network
Description
Compute the score of the Bayesian network.
Usage
## S4 method for signature 'bn'
score(x, data, type = NULL, ..., by.node = FALSE, debug = FALSE)
## S4 method for signature 'bn.naive'
score(x, data, type = NULL, ..., by.node = FALSE, debug = FALSE)
## S4 method for signature 'bn.tan'
score(x, data, type = NULL, ..., by.node = FALSE, 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 
data 
a data frame containing the data the Bayesian network that will be used to compute the score. 
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

by.node 
a boolean value. If 
debug 
a boolean value. If 
... 
extra arguments from the generic method (for the 
k 
a numeric value, the penalty coefficient to be used; the default 
Details
Additional arguments of the score()
function:

iss
: the imaginary sample size used by the Bayesian Dirichlet scores (bde
,mbde
,bds
,bdj
). It is also known as “equivalent sample size”. The default value is equal to1
. 
iss.mu
: the imaginary sample size for the normal component of the normalWishart prior in the Bayesian Gaussian score (bge
). The default value is1
. 
iss.w
: the imaginary sample size for the Wishart component of the normalWishart prior in the Bayesian Gaussian score (bge
). The default value isncol(data) + 2
. 
nu
: the mean vector of the normal component of the normalWishart prior in the Bayesian Gaussian score (bge
). The default value is equal tocolMeans(data)
. 
l
: the number of scores to average in the locally averaged Bayesian Dirichlet score (bdla
). The default value is5
. 
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, BIC and penalized nodeaverage loglikelihood scores. The default value is1
for AIC,log(nrow(data)) / 2
for BIC and1 / nnnodes(x) * nrow(data) ^ 0.25
for the nodeaverage loglikelihood scores. 
gamma
: the additional penalty in the extended BIC scores. The default value is0.5
. 
prior
: the prior distribution to be used with the various Bayesian Dirichlet scores (bde
,mbde
,bds
,bdj
,bdla
) 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. 
marginal
: an independent marginal uniform for each arc. 
cs
: the Castelo & Siebes prior, which puts an independent prior probability on each arc and direction).


beta
: the parameter associated withprior
.
If
prior
isuniform
,beta
is ignored. 
If
prior
isvsp
,beta
is the probability of inclusion of an additional parent. The default is1/ncol(data)
. 
If
prior
ismarginal
,beta
is the probability of inclusion of an arc. Each direction has a probability of inclusion ofbeta / 2
and the probability that the arc is not included is therefore1  beta
. The default value is0.5
, so that arc inclusion and arc exclusion have the same probability. 
If
prior
iscs
,beta
is a data frame with columnsfrom
,to
andprob
specifying the prior probability for a set of arcs. A uniform probability distribution is assumed for the remaining arcs.


newdata
: the test set whose predictive likelihood will be computed bypredloglik
,predloglikg
orpredloglikcg
. It should be a data frame with the same variables asdata
. 
fun
: the function that computes the score component for a single node in thecustom
score.fun
must have argumentsnode
,parents
,data
andargs
, in this order; in other words, it must have signaturefunction(node, parents, data, args)
.node
will contain the label of the node to be scored (a character string);parents
will contain the labels of its parents (a character vector);data
will contain the complete data set, with all the variables (a data frame); andargs
will be a list containing any additional arguments to the score. 
args
: a list containing the optional arguments tofun
, for tuningcustom
score functions.
Value
For score()
with 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.
Note
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 probabilities 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 scorebased and hybrid
structure learning.
Author(s)
Marco Scutari
See Also
network scores
, arc.strength
, alpha.star
.
Examples
data(learning.test)
dag = hc(learning.test)
score(dag, learning.test, type = "bde")
## let's see score equivalence in action!
dag2 = set.arc(dag, "B", "A")
score(dag2, learning.test, type = "bde")
## K2 score on the other hand is not score equivalent.
score(dag, learning.test, type = "k2")
score(dag2, 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(dag, learning.test, type = "bde", prior = "cs", beta = beta)
## equivalent to logLik(dag, learning.test)
score(dag, learning.test, type = "loglik")
## equivalent to AIC(dag, learning.test)
score(dag, learning.test, type = "aic")
## custom score, computing BIC manually.
my.bic = function(node, parents, data, args) {
n = nrow(data)
if (length(parents) == 0) {
counts = table(data[, node])
nparams = dim(counts)  1
sum(counts * log(counts / n))  nparams * log(n) / 2
}#THEN
else {
counts = table(data[, node], configs(data[, parents, drop = FALSE]))
nparams = ncol(counts) * (nrow(counts)  1)
sum(counts * log(prop.table(counts, 2)))  nparams * log(n) / 2
}#ELSE
}#MY.BIC
score(dag, learning.test, type = "customscore", fun = my.bic, by.node = TRUE)
score(dag, learning.test, type = "bic", by.node = TRUE)
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