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Perform conditional probability queries (CPQs).
cpquery(fitted, event, evidence, cluster = NULL, method = "ls", ...,
debug = FALSE)
cpdist(fitted, nodes, evidence, cluster = NULL, method = "ls", ...,
debug = FALSE)mutilated(x, evidence)
an object of class bn.fit.
an object of class bn or bn.fit.
see below.
a vector of character strings, the labels of the nodes whose conditional distribution we are interested in.
an optional cluster object from package parallel.
a character string, the method used to perform the conditional
probability query. Currently only logic sampling (ls, the
default) and likelihood weighting (lw) are implemented.
additional tuning parameters.
a boolean value. If TRUE a lot of debugging output is
printed; otherwise the function is completely silent.
cpquery() returns a numeric value, the conditional probability of
event() conditional on evidence.
cpdist() returns a data frame containing the observations generated from
the conditional distribution of the nodes conditional on
evidence(). The data frame has class c("bn.cpdist", "data.frame"),
and a meth, -8od attribute storing the value of the method
gument. In the case of likelihood weighting, the weights are also attached as an
attribute called weights.
mutilated returns a bn or bn.fit object, depending on the
class of x.
The event and evidence arguments must be two expressions
describing the event of interest and the conditioning evidence in a format
such that, if we denote with data the data set the network was learned
from, data[evidence, ] and data[event, ] return the correct
observations. If either event or evidence is set to TRUE
an unconditional probability query is performed with respect to that argument.
Three tuning parameters are available:
n: a positive integer number, the number of random observations
to generate from fitted. The default value is
5000 * log10(nparams.fitted(fitted)) for discrete and coditional
Gaussian networks and 500 * nparams.fitted(fitted) for Gaussian
networks.
batch: a positive integer number, the size of each batch of
random observations. Defaults to 10^4.
query.nodes: a a vector of character strings, the labels of
the nodes involved in event and evidence. Simple queries do
not require to generate observations from all the nodes in the network,
so cpquery and cpdist try to identify which nodes are used
in event and evidence and reduce the network to their upper
closure. query.nodes may be used to manually specify these nodes
when automatic identification fails; there is no reason to use it
otherwise.
Note that the number of observations returned by cpdist() is always
smaller than n, because logic sampling is a form of rejection sampling.
Therefore, only the obervations matching evidence (out of the n
that are generated) are returned, and their number depends on the probability
of evidence.
The event argument must be an expression describing the event of
interest, as in logic sampling. The evidence argument must be a named
list:
Each element corresponds to one node in the network and must contain the value that node will be set to when sampling.
In the case of a continuous node, two values can also be provided. In that case, the value for that node will be sampled from a uniform distribution on the interval delimited by the specified values.
In the case of a discrete or ordinal node, two or more values can also be provided. In that case, the value for that node will be sampled with uniform probability from the set of specified values.
If either event or evidence is set to TRUE an
unconditional probability query is performed with respect to that argument.
Tuning parameters are the same as for logic sampling: n, batch
and query.nodes.
Note that the observations returned by cpdist() are generated from the
mutilated network, and need to be weighted appropriately when computing
summary statistics (for more details, see the references below).
cpquery does that automatically when computing the final conditional
probability. Also note that the batch argument is ignored in cpdist
for speed and memory efficiency.
cpquery estimates the conditional probability of event given
evidence using the method specified in the method argument.
cpdist generates random observations conditional on the
evidence using the method specified in the method argument.
mutilated constructs the mutilated network arising from an ideal
intervention setting the nodes involved to the values specified by
evidence. In this case evidence must be provided as a list
in the same format as for likelihood weighting (see below).
Note that both cpquery and cpdist are based on Monte Carlo
particle filters, and therefore they may return slightly different values
on different runs.
Koller D, Friedman N (2009). Probabilistic Graphical Models: Principles and Techniques. MIT Press.
Korb K, Nicholson AE (2010). Bayesian Artificial Intelligence. Chapman & Hall/CRC, 2nd edition.
# NOT RUN {
## discrete Bayesian network (it is the same with ordinal nodes).
data(learning.test)
fitted = bn.fit(hc(learning.test), learning.test)
# the result should be around 0.025.
cpquery(fitted, (B == "b"), (A == "a"))
# programmatically build a conditional probability query...
var = names(learning.test)
obs = 2
str = paste("(", names(learning.test)[-3], " == '",
sapply(learning.test[obs, -3], as.character), "')",
sep = "", collapse = " & ")
str
str2 = paste("(", names(learning.test)[3], " == '",
as.character(learning.test[obs, 3]), "')", sep = "")
str2
cmd = paste("cpquery(fitted, ", str2, ", ", str, ")", sep = "")
eval(parse(text = cmd))
# ... but note that predict works better in this particular case.
attr(predict(fitted, "C", learning.test[obs, -3], prob = TRUE), "prob")
# do the same with likelihood weighting.
cpquery(fitted, event = eval(parse(text = str2)),
evidence = as.list(learning.test[2, -3]), method = "lw")
attr(predict(fitted, "C", learning.test[obs, -3],
method = "bayes-lw", prob = TRUE), "prob")
# conditional distribution of A given C == "c".
table(cpdist(fitted, "A", (C == "c")))
## Gaussian Bayesian network.
data(gaussian.test)
fitted = bn.fit(hc(gaussian.test), gaussian.test)
# the result should be around 0.04.
cpquery(fitted,
event = ((A >= 0) & (A <= 1)) & ((B >= 0) & (B <= 3)),
evidence = (C + D < 10))
## ideal interventions and mutilated networks.
mutilated(fitted, evidence = list(F = 42))
# }
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