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bn.fit {bnlearn}  R Documentation 
Fit the parameters of a Bayesian network
Description
Fit, assign or replace the parameters of a Bayesian network conditional on its structure.
Usage
bn.fit(x, data, cluster, method, ..., keep.fitted = TRUE,
debug = FALSE)
custom.fit(x, dist, ordinal, debug = FALSE)
bn.net(x)
Arguments
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, see below for details. 
... 
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 
Details
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.
bn.fit()
accepts data with missing values encoded as NA
. If the parameter
estimation method was not specifically designed to deal with incomplete data, bn.fit()
uses
locally complete observations to fit the parameters of each local distribution.
Available methods for discrete Bayesian networks are:

mle
: the maximum likelihood estimator for conditional probabilities. 
bayes
: the classic Bayesian posterior estimator with a uniform prior matching that in the Bayesian Dirichlet equivalent (bde
) score. 
hdir
: the hierarchical Dirichlet posterior estimator for related data sets from Azzimonti, Corani and Zaffalon (2019). 
hardem
: the ExpectationMaximization implementation of the estimators above.
Available methods for hybrid Bayesian networks are:

mleg
: the maximum likelihood estimator for least squares regression models. 
hardemg
: the ExpectationMaximization implementation of the estimators above.
Available methods for discrete Bayesian networks are:

mlecg
: a combination of the maximum likelihood estimatorsmle
andmleg
. 
hardemcg
: the ExpectationMaximization implementation of the estimators above.
Additional arguments for the bn.fit()
function:

iss
: a numeric value, the imaginary sample size used by thebayes
method to estimate the conditional probability tables associated with discrete nodes (seescore
for details). 
replace.unidentifiable
: a boolean value. IfTRUE
andmethod
one ofmle
,mleg
ormlecg
, 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 ofNaN
for all parents configurations that are not observed indata
. Similarly, regression coefficients are set toNA
if the linear regressions correspoding to the local distributions of continuous nodes are singular. Such missing values propagate to the results of functions such aspredict()
. 
alpha0
: a positive number, the amount of information pooling between the related data sets in thehdir
estimator. 
group
: a character string, the label of the node with the grouping of the observations into the related data sets in thehdir
estimator. 
impute
andimpute.args
: a character string, the label of the imputation method (and its arguments) used byhardem
,hardemg
andhardemcg
to complete the data in the expectation step. The default method is the same as forimpute()
. 
fit
andfit.args
: a character string, the label of the parameter estimation method used byhardem
,hardemg
andhardemcg
to estimate the parameters in the maximization step. The default method is the same as forbn.fit()
. 
loglik.threshold
: a nonnegative numeric value, the minimum improvement threshold to continue iterating inhardem
,hardemg
andhardemcg
. The threshold is defined as the relative likelihood improvement divided by the sample size ofdata
, and defaults to1e3
. Setting it to zero means that iterations only stop in case of negative improvement, which can happen due to stochastic noise if the imputation of the missing data uses approximate inference. 
params.threshold
: a nonnegative numeric value, the minimum maximum elative change in the parameter values to continue iterating inhardem
,hardemg
andhardemcg
. The threshold is defined as the maximum of the differences between parameter values divided scaled by the parameter value in the lastest iteration. The default value is1e3
. 
max.iter
: a positive integer value, the maximum number of iterations inhardem
,hardemg
andhardemcg
. The default value is5
. 
start
: abn.fit
object, the fitted network used to initialize thehardem
,hardemg
andhardemcg
estimators. The default is to use thebn.fit
object obtained fromx
with the default parameter estimator for the data, which will use locally complete data to fit the local distributions. 
newdata
: a data frame, a separate set of data used to assess the convergence of thehardem
,hardemg
andhardemcg
estimators. The data indata
are used by default for this purpose.
An inplace 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 userspecified 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 inplace replacement.
Value
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.
Note
Due to the way Bayesian networks are defined it is possible to estimate their parameters only if the
network structure is completely directed (i.e. there are no undirected arcs). See set.arc
and cextend
for two ways of
manually setting the direction of one or more arcs.
In the case of maximum likelihood estimators, 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"
.
Author(s)
Marco Scutari
References
Azzimonti L, Corani G, Zaffalon M (2019). "Hierarchical Estimation of Parameters in Bayesian Networks". Computational Statistics & Data Analysis, 137:67–91.
See Also
bn.fit utilities
, bn.fit plots
.
Examples
data(learning.test)
# learn the network structure.
cpdag = pc.stable(learning.test)
# set the direction of the only undirected arc, A  B.
dag = set.arc(cpdag, "A", "B")
# estimate the parameters of the Bayesian network.
fitted = bn.fit(dag, 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$B = as.table(new.cpt)
# the network structure is still the same.
all.equal(dag, bn.net(fitted))
# learn the network structure.
dag = hc(gaussian.test)
# estimate the parameters of the Bayesian network.
fitted = bn.fit(dag, gaussian.test)
# replace the parameters of the node F.
fitted$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.
dag = model2network("[A][B][CA: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(dag, dist = list(A = cptA, B = cptB, C = cptC))
# for ordinal nodes it is nearly the same.
cfit = custom.fit(dag, 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(dag, 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(dag, dist = list(A = cptA, B = distB, C = distC))
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