Fit the parameters of a Bayesian network
Fit, assign or replace the parameters of a Bayesian network conditional on its structure.
bn.fit(x, data, cluster = NULL, method = "mle", ..., keep.fitted = TRUE, debug = FALSE) custom.fit(x, dist, ordinal, debug = FALSE) bn.net(x, debug = FALSE)
x |
an object of class |
data |
a data frame containing the variables in the model. |
cluster |
an optional cluster object from package parallel. |
dist |
a named list, with element for each node of |
method |
a character string, either |
... |
additional arguments for the parameter estimation procedure, see below. |
ordinal |
a vector of character strings, the labels of the discrete
nodes which should be saved as ordinal random variables
( |
keep.fitted |
a boolean value. If |
debug |
a boolean value. If |
bn.fit() fits the parameters of a Bayesian network given its structure
and a data set; bn.net returns the structure underlying a fitted
Bayesian network.
Additional arguments for the bn.fit() function:
iss: a numeric value, the imaginary sample size used by the
bayes method to estimate the conditional probability tables
associated with discrete nodes (see score for details).
replace.unidentifiable: a boolean value. If TRUE and
method is mle, unidentifiable parameters are replaced by
zeroes (in the case of regression coefficients and standard errors in
Gaussian and conditional Gaussian nodes) or by uniform conditional
probabilities (in discrete nodes).
If FALSE (the default), the conditional probabilities in the local
distributions of discrete nodes have a mximum likelihood estimate of
NaN for all parents configurations that are not observed in
data. Similarly, regression coefficients are set to NA
if the linear regressions correspoding to the local distributions of
continuous nodes are singular. Such missing values propagate to the
results of functions such as predict().
An in-place replacement method is available to change the parameters of each
node in a bn.fit object; see the examples for discrete, continuous and
hybrid networks below. For a discrete node (class bn.fit.dnode or
bn.fit.onode), the new parameters must be in a table object.
For a Gaussian node (class bn.fit.gnode), the new parameters can be
defined either by an lm, glm or pensim object (the
latter is from the penalized package) or in a list with elements named
coef, sd and optionally fitted and resid. For
a conditional Gaussian node (class bn.fit.cgnode), the new parameters
can be defined by a list with elements named coef, sd and
optionally fitted, resid and configs. In both cases
coef should contain the new regression coefficients, sd the
standard deviation of the residuals, fitted the fitted values and
resid the residuals. configs should contain the configurations
if the discrete parents of the conditional Gaussian node, stored as a factor.
custom.fit() takes a set of user-specified distributions and their
parameters and uses them to build a bn.fit object. Its purpose is to
specify a Bayesian network (complete with the parameters, not only the
structure) using knowledge from experts in the field instead of learning it
from a data set. The distributions must be passed to the function in a list,
with elements named after the nodes of the network structure x. Each
element of the list must be in one of the formats described above for
in-place replacement.
bn.fit() and custom.fit()returns an object of class
bn.fit, bn.net() an object of class bn. See
bn class and bn.fit class for details.
The bayes and mle methods in bn.fit() handle missing
values in data by estimating the parameters of each local distribution
using the observations that are complete for the variables involved (the node
and its parents).
When method is set to mle, bn.fit() produces NA
parameter estimates for discrete and conditional Gaussian nodes when there
are (discrete) parents configurations that are not observed in data.
To avoid this either set replace.unidentifiable to TRUE or, in
the case of discrete networks, use method = "bayes".
Marco Scutari
data(learning.test)
# learn the network structure.
res = gs(learning.test)
# set the direction of the only undirected arc, A - B.
res = set.arc(res, "A", "B")
# estimate the parameters of the Bayesian network.
fitted = bn.fit(res, learning.test)
# replace the parameters of the node B.
new.cpt = matrix(c(0.1, 0.2, 0.3, 0.2, 0.5, 0.6, 0.7, 0.3, 0.1),
byrow = TRUE, ncol = 3,
dimnames = list(B = c("a", "b", "c"), A = c("a", "b", "c")))
fitted$B = as.table(new.cpt)
# the network structure is still the same.
all.equal(res, bn.net(fitted))
# learn the network structure.
res = hc(gaussian.test)
# estimate the parameters of the Bayesian network.
fitted = bn.fit(res, gaussian.test)
# replace the parameters of the node F.
fitted$F = list(coef = c(1, 2, 3, 4, 5), sd = 3)
# set again the original parameters
fitted$F = lm(F ~ A + D + E + G, data = gaussian.test)
# discrete Bayesian network from expert knowledge.
net = model2network("[A][B][C|A:B]")
cptA = matrix(c(0.4, 0.6), ncol = 2, dimnames = list(NULL, c("LOW", "HIGH")))
cptB = matrix(c(0.8, 0.2), ncol = 2, dimnames = list(NULL, c("GOOD", "BAD")))
cptC = c(0.5, 0.5, 0.4, 0.6, 0.3, 0.7, 0.2, 0.8)
dim(cptC) = c(2, 2, 2)
dimnames(cptC) = list("C" = c("TRUE", "FALSE"), "A" = c("LOW", "HIGH"),
"B" = c("GOOD", "BAD"))
cfit = custom.fit(net, dist = list(A = cptA, B = cptB, C = cptC))
# for ordinal nodes it is nearly the same.
cfit = custom.fit(net, dist = list(A = cptA, B = cptB, C = cptC),
ordinal = c("A", "B"))
# Gaussian Bayesian network from expert knowledge.
distA = list(coef = c("(Intercept)" = 2), sd = 1)
distB = list(coef = c("(Intercept)" = 1), sd = 1.5)
distC = list(coef = c("(Intercept)" = 0.5, "A" = 0.75, "B" = 1.32), sd = 0.4)
cfit = custom.fit(net, dist = list(A = distA, B = distB, C = distC))
# conditional Gaussian Bayesian network from expert knowledge.
cptA = matrix(c(0.4, 0.6), ncol = 2, dimnames = list(NULL, c("LOW", "HIGH")))
distB = list(coef = c("(Intercept)" = 1), sd = 1.5)
distC = list(coef = matrix(c(1.2, 2.3, 3.4, 4.5), ncol = 2,
dimnames = list(c("(Intercept)", "B"), NULL)),
sd = c(0.3, 0.6))
cgfit = custom.fit(net, dist = list(A = cptA, B = distB, C = distC))Please choose more modern alternatives, such as Google Chrome or Mozilla Firefox.