Index  Topics 
arc.strength {bnlearn}  R Documentation 
Measure arc strength
Description
Measure the strength of the probabilistic relationships expressed by the arcs of a Bayesian network, and use model averaging to build a network containing only the significant arcs.
Usage
# strength of the arcs present in x.
arc.strength(x, data, criterion = NULL, ..., debug = FALSE)
# strength of all possible arcs, as learned from bootstrapped data.
boot.strength(data, cluster, R = 200, m = nrow(data),
algorithm, algorithm.args = list(), cpdag = TRUE, shuffle = TRUE,
debug = FALSE)
# strength of all possible arcs, from a list of custom networks.
custom.strength(networks, nodes, weights = NULL, cpdag = TRUE, debug = FALSE)
# strength of all possible arcs, computed using Bayes factors.
bf.strength(x, data, score, ..., debug = FALSE)
# average arc strengths.
## S3 method for class 'bn.strength'
mean(x, ..., weights = NULL)
# averaged network structure.
averaged.network(strength, threshold)
# strength threshold for inclusion in the averaged network structure.
inclusion.threshold(strength)
Arguments
x 
an object of class 
networks 
a list, containing either object of class 
data 
a data frame containing the data the Bayesian network was learned from (for

cluster 
an optional cluster object from package parallel. 
strength 
an object of class 
threshold 
a numeric value, the minimum strength required for an arc to be included in the averaged network.
The default value is the 
nodes 
a vector of character strings, the labels of the nodes in the network. 
criterion,score 
a character string. For 
For bf.strength()
, the label of the score used to compute the Bayes factors; see
BF
for details.
R 
a positive integer, the number of bootstrap replicates. 
m 
a positive integer, the size of each bootstrap replicate. 
weights 
a vector of nonnegative numbers, to be used as weights when averaging arc strengths (in

cpdag 
a boolean value. If 
shuffle 
a boolean value. If 
algorithm 
a character string, the structure learning algorithm to be applied to the bootstrap replicates. See

algorithm.args 
a list of extra arguments to be passed to the learning algorithm. 
... 
in 
debug 
a boolean value. If 
Details
arc.strength()
computes a measure of confidence or strength for each arc, while keeping fixed
the rest of the network structure.
If criterion
is a conditional independence test, the strength is a pvalue (so the lower the
value, the stronger the relationship). The conditional independence test would be that to drop the arc from
the network. The only two possible additional arguments are alpha
, which sets the significance
threshold that is used in strength.plot()
; and B
, the number of permutations to be
generated for each permutation test.
If criterion
is the label of a score function, the strength is measured by the score
gain/loss which would be caused by the arc's removal. In other words, it is the difference between the score
of the network in which the arc is not present and the score of the network in which the arc is present.
Negative values correspond to decreases in the network score and positive values correspond to increases in
the network score (the stronger the relationship, the more negative the difference). There may be additional
arguments depending on the choice of the score, see score
for
details. The significance threshold is set to 0
.
boot.strength()
estimates the strength of each arc as its empirical frequency over a set of
networks learned from bootstrap samples. It computes the probability of each arc (modulo its direction) and
the probabilities of each arc's directions conditional on the arc being present in the graph (in either
direction). The significance threshold is computed automatically from the strength estimates.
bf.strength()
estimates the strength of each arc using Bayes factors to overcome the fact
that Bayesian posterior scores are not normalised, and uses the latter to estimate the probabilities of all
possible states of an arc given the rest of the network. The significance threshold is set to
1
.
custom.strength()
takes a list of networks and estimates arc strength in the same way
as
boot.strength()
.
Model averaging is supported for objects of class bn.strength
returned by boot.strength
, custom.strength
and bf.strength
. The returned network contains the arcs whose strength is greater
than the threshold
attribute of the bn.strength
object passed to
averaged.network()
.
Value
arc.strength()
, boot.strength()
, custom.strength()
,
bf.strength()
and mean()
return an object of class bn.strength
;
boot.strength()
and custom.strength()
also include information about the relative
probabilities of arc directions.
averaged.network()
returns an object of class bn
.
See bn.strength class
and bnclass
for details.
Note
averaged.network()
typically returns a completely directed graph; an arc can be undirected if
and only if the probability of each of its directions is exactly 0.5. This may happen, for example, if the
arc is undirected in all the networks being averaged.
Author(s)
Marco Scutari
References
for model averaging and boostrap strength (confidence):
Friedman N, Goldszmidt M, Wyner A (1999). "Data Analysis with Bayesian Networks: A Bootstrap Approach". Proceedings of the 15th Annual Conference on Uncertainty in Artificial Intelligence, 196–201.
for the computation of the bootstrap strength (confidence) significance threshold:
Scutari M, Nagarajan R (2013). "On Identifying Significant Edges in Graphical Models of Molecular Networks". Artificial Intelligence in Medicine, 57(3):207–217.
See Also
strength.plot
, score
, ci.test
.
Examples
data(learning.test)
dag = hc(learning.test)
arc.strength(dag, learning.test)
## Not run:
arcs = boot.strength(learning.test, algorithm = "hc")
arcs[(arcs$strength > 0.85) & (arcs$direction >= 0.5), ]
averaged.network(arcs)
start = random.graph(nodes = names(learning.test), num = 50)
netlist = lapply(start, function(net) {
hc(learning.test, score = "bde", iss = 10, start = net) })
arcs = custom.strength(netlist, nodes = names(learning.test),
cpdag = FALSE)
arcs[(arcs$strength > 0.85) & (arcs$direction >= 0.5), ]
modelstring(averaged.network(arcs))
## End(Not run)
bf.strength(dag, learning.test, score = "bds", prior = "marginal")
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