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cpquery {bnlearn}  R Documentation 
Perform conditional probability queries
Description
Perform conditional probability queries (CPQs).
Usage
cpquery(fitted, event, evidence, cluster = NULL, method = "ls", ..., debug = FALSE) cpdist(fitted, nodes, evidence, cluster = NULL, method = "ls", ..., debug = FALSE) mutilated(x, evidence)
Arguments
fitted 
an object of class 
x 
an object of class 
event, evidence 
see below. 
nodes 
a vector of character strings, the labels of the nodes whose conditional distribution we are interested in. 
cluster 
an optional cluster object from package parallel. 
method 
a character string, the method used to perform the conditional probability query. Currently only
logic sampling ( 
... 
additional tuning parameters. 
debug 
a boolean value. If 
Details
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 used for sampling in likelihood
weighting.
Note that both cpquery
and cpdist
are based on Monte Carlo particle filters, and
therefore they may return slightly different values on different runs.
Value
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 method
attribute storing the value of the
method
argument. 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
.
Logic Sampling
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 fromfitted
. The default value is5000 * log10(nparams.fitted(fitted))
for discrete and coditional Gaussian networks and500 * nparams.fitted(fitted)
for Gaussian networks. 
batch
: a positive integer number, the size of each batch of random observations. Defaults to10^4
. 
query.nodes
: a a vector of character strings, the labels of the nodes involved inevent
andevidence
. Simple queries do not require to generate observations from all the nodes in the network, socpquery
andcpdist
try to identify which nodes are used inevent
andevidence
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
.
Likelihood Weighting
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.
Author(s)
Marco Scutari
References
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.
Examples
## 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 = "bayeslw", 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))
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