Perform a k-fold or hold-out cross-validation for a learning algorithm or a fixed network structure.
bn.cv(data, bn, loss = NULL, ..., algorithm.args = list(),
loss.args = list(), fit = "mle", fit.args = list(), method = "k-fold",
cluster, debug = FALSE)# S3 method for bn.kcv
plot(x, ..., main, xlab, ylab, connect = FALSE)
# S3 method for bn.kcv.list
plot(x, ..., main, xlab, ylab, connect = FALSE)
loss(x)
bn.cv() returns an object of class bn.kcv.list if runs
is at least 2, an object of class bn.kcv if runs is equal to 1.
loss() returns a numeric vector with a length equal to runs.
a data frame containing the variables in the model.
either a character string (the label of the learning algorithm to
be applied to the training data in each iteration) or an object of class
bn (a fixed network structure).
a character string, the label of a loss function. If none is specified, the default loss function is the Classification Error for Bayesian networks classifiers; otherwise, the Log-Likelihood Loss for both discrete and continuous data sets. See below for additional details.
a list of extra arguments to be passed to the learning algorithm.
a list of extra arguments to be passed to the loss function
specified by loss.
a character string, the label of the method used to fit the
parameters of the network. See bn.fit for details.
additional arguments for the parameter estimation procedure,
see again bn.fit for details.
a character string, either k-fold, custom-folds
or hold-out. See below for details.
an optional cluster object from package parallel.
a boolean value. If TRUE a lot of debugging output is
printed; otherwise the function is completely silent.
an object of class bn.kcv or bn.kcv.list returned by
bn.cv().
additional objects of class bn.kcv or bn.kcv.list
to plot alongside the first.
the title of the plot, an array of labels for the boxplot, the label for the y axis.
a logical value. If TRUE, the medians points in the
boxplots will be connected by a segmented line.
The following cross-validation methods are implemented:
k-fold: the data are split in k subsets of equal
size. For each subset in turn, bn is fitted (and possibly learned
as well) on the other k - 1 subsets and the loss function is then
computed using that subset. Loss estimates for each of the k
subsets are then combined to give an overall loss for data.
custom-folds: the data are manually partitioned by the user into subsets, which are then used as in k-fold cross-validation. Subsets are not constrained to have the same size, and every observation must be assigned to one subset.
hold-out: k subsamples of size m are sampled
independently without replacement from the data. For each subsample,
bn is fitted (and possibly learned) on the remaining
m - nrow(data) samples and the loss function is computed on the
m observations in the subsample. The overall loss estimate is the
average of the k loss estimates from the subsamples.
If cross-validation is used with multiple runs, the overall loss is the
averge of the loss estimates from the different runs.
To clarify, cross-validation methods accept the following optional arguments:
k: a positive integer number, the number of groups into which the
data will be split (in k-fold cross-validation) or the number of times
the data will be split in training and test samples (in hold-out
cross-validation).
m: a positive integer number, the size of the test set in
hold-out cross-validation.
runs: a positive integer number, the number of times
k-fold or hold-out cross-validation will be run.
folds: a list in which element corresponds to one fold and
contains the indices for the observations that are included to that fold;
or a list with an element for each run, in which each element is itself a
list of the folds to be used for that run.
The following loss functions are implemented:
Log-Likelihood Loss (logl): also known as negative
entropy or negentropy, it is the negated expected log-likelihood
of the test set for the Bayesian network fitted from the training set.
Lower valuer are better.
Gaussian Log-Likelihood Loss (logl-g): the negated
expected log-likelihood for Gaussian Bayesian networks. Lower values are
better.
Classification Error (pred): the prediction error
for a single node in a discrete network. Frequentist predictions are used,
so the values of the target node are predicted using only the information
present in its local distribution (from its parents). Lower values are
better.
Posterior Classification Error (pred-lw and
pred-lw-cg): similar to the above, but predictions are computed
from an arbitrary set of nodes using likelihood weighting to obtain
Bayesian posterior estimates. pred-lw applies to discrete Bayesian
networks, pred-lw-cg to (discrete nodes in) hybrid networks. Lower
values are better.
Exact Classification Error (pred-exact): closed-form
exact posterior predictions are available for Bayesian network
classifiers. Lower values are better.
Predictive Correlation (cor): the correlation
between the observed and the predicted values for a single node in a
Gaussian Bayesian network. Higher values are better.
Posterior Predictive Correlation (cor-lw and
cor-lw-cg): similar to the above, but predictions are computed from
an arbitrary set of nodes using likelihood weighting to obtain Bayesian
posterior estimates. cor-lw applies to Gaussian networks and
cor-lw-cg to (continuous nodes in) hybrid networks. Higher values
are better.
Mean Squared Error (mse): the mean squared error
between the observed and the predicted values for a single node in a
Gaussian Bayesian network. Lower values are better.
Posterior Mean Squared Error (mse-lw and
mse-lw-cg): similar to the above, but predictions are computed from
an arbitrary set of nodes using likelihood weighting to obtain Bayesian
posterior estimates. mse-lw applies to Gaussian networks and
mse-lw-cg to (continuous nodes in) hybrid networks. Lower values
are better.
Optional arguments that can be specified in loss.args are:
target: a character string, the label of target node for
prediction in all loss functions but logl, logl-g and
logl-cg.
from: a vector of character strings, the labels of the nodes
used to predict the target node in pred-lw, pred-lw-cg,
cor-lw, cor-lw-cg, mse-lw and mse-lw-cg. The
default is to use all the other nodes in the network. Loss functions
pred, cor and mse implicitly predict only from the
parents of the target node.
n: a positive integer, the number of particles used by
likelihood weighting for pred-lw, pred-lw-cg, cor-lw,
cor-lw-cg, mse-lw and mse-lw-cg.
The default value is 500.
Note that if bn is a Bayesian network classifier, pred and
pred-lw both give exact posterior predictions computed using the
closed-form formulas for naive Bayes and TAN.
Both plot methods accept any combination of objects of class bn.kcv or
bn.kcv.list (the first as the x argument, the remaining as the
... argument) and plot the respected expected loss values side by side.
For a bn.kcv object, this mean a single point; for a bn.kcv.list
object this means a boxplot.
Marco Scutari
Koller D, Friedman N (2009). Probabilistic Graphical Models: Principles and Techniques. MIT Press.
bn.boot, rbn, bn.kcv-class.
bn.cv(learning.test, 'hc', loss = "pred", loss.args = list(target = "F"))
folds = list(1:2000, 2001:3000, 3001:5000)
bn.cv(learning.test, 'hc', loss = "logl", method = "custom-folds",
folds = folds)
xval = bn.cv(gaussian.test, 'mmhc', method = "hold-out",
k = 5, m = 50, runs = 2)
xval
loss(xval)
if (FALSE) {
# comparing algorithms with multiple runs of cross-validation.
gaussian.subset = gaussian.test[1:50, ]
cv.gs = bn.cv(gaussian.subset, 'gs', runs = 10)
cv.iamb = bn.cv(gaussian.subset, 'iamb', runs = 10)
cv.inter = bn.cv(gaussian.subset, 'inter.iamb', runs = 10)
plot(cv.gs, cv.iamb, cv.inter,
xlab = c("Grow-Shrink", "IAMB", "Inter-IAMB"), connect = TRUE)
# use custom folds.
folds = split(sample(nrow(gaussian.subset)), seq(5))
bn.cv(gaussian.subset, "hc", method = "custom-folds", folds = folds)
# multiple runs, with custom folds.
folds = replicate(5, split(sample(nrow(gaussian.subset)), seq(5)),
simplify = FALSE)
bn.cv(gaussian.subset, "hc", method = "custom-folds", folds = folds)
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