bn.fit | R Documentation |
Fit, assign or replace the parameters of a Bayesian network conditional on its structure.
bn.fit(x, data, cluster, method, ..., keep.fitted = TRUE,
debug = FALSE)
custom.fit(x, dist, ordinal, debug = FALSE)
bn.net(x)
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 |
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).
hard-em
: the Expectation-Maximization implementation of the
estimators above.
Available methods for hybrid Bayesian networks are:
mle-g
: the maximum likelihood estimator for least squares
regression models.
hard-em-g
: the Expectation-Maximization implementation of the
estimators above.
Available methods for discrete Bayesian networks are:
mle-cg
: a combination of the maximum likelihood estimators
mle
and mle-g
.
hard-em-cg
: the Expectation-Maximization implementation of the
estimators above.
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
one of mle
, mle-g
or mle-cg
,
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()
.
alpha0
: a positive number, the amount of information pooling
between the related data sets in the hdir
estimator.
group
: a character string, the label of the node with the
grouping of the observations into the related data sets in the hdir
estimator.
impute
and impute.args
: a character string, the label of
the imputation method (and its arguments) used by hard-em
,
hard-em-g
and hard-em-cg
to complete the data in the
expectation step. The default method is the same as for
impute()
.
fit
and fit.args
: a character string, the label of the
parameter estimation method used by hard-em
, hard-em-g
and
hard-em-cg
to estimate the parameters in the maximization
step. The default method is the same as for bn.fit()
.
threshold
: a positive numeric value, the minimum improvement
threshold used to step iterating in hard-em
, hard-em-g
and
hard-em-cg
. The threshold is defined as the relative likelihood
improvement divided by the sample size of data
, and defaults to
1e-3
.
max.iter
: a positive integer value, the maximum number of
iterations in hard-em
, hard-em-g
and hard-em-cg
. The
default value is 5
.
start
: a bn.fit
object, the fitted network used to
initialize the hard-em
, hard-em-g
and hard-em-cg
estimators. The default is to use the bn.fit
object obtained from
x
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 the hard-em
, hard-em-g
and
hard-em-cg
estimators. The data in data
are used by default
for this purpose.
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.
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"
.
Marco Scutari
Azzimonti L, Corani G, Zaffalon M (2019). "Hierarchical Estimation of Parameters in Bayesian Networks". Computational Statistics & Data Analysis, 137:67–91.
bn.fit utilities
, bn.fit plots
.
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][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(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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