Predict or impute missing data from a Bayesian network

Description

Impute missing values in a data set or predict a variable from a Bayesian network.

Usage

## S3 method for class 'bn.fit'
predict(object, node, data, cluster, method = "parents", ...,
  prob = FALSE, debug = FALSE)

impute(object, data, cluster, method, ..., strict = TRUE, debug = FALSE)

Arguments

Details

predict() returns the predicted values for node given the data specified by data and the fitted network. Depending on the value of method, the predicted values are computed as follows.

• parents: the predicted values are computed by plugging in the new values for the parents of node in the local probability distribution of node extracted from fitted.

• bayes-lw: the predicted values are computed by averaging likelihood weighting simulations performed using all the available nodes as evidence (obviously, with the exception of the node whose values we are predicting). The number of random samples which are averaged for each new observation is controlled by the n optional argument; the default is 500. If the variable being predicted is discrete, the predicted level is that with the highest conditional probability. If the variable is continuous, the predicted value is the expected value of the conditional distribution. The variables that are used to compute the predicted values can be specified with the from optional argument; the default is to use all the relevant variables from the data. Note that the predicted values will differ in each call to predict() since this method is based on a stochastic simulation.

• exact: the predicted values are computed using exact inference. They are maximum a posteriori estimates obtained using junction trees and belief propagation in the case of discrete networks, or posterior expectations computed using closed-form results for the multivariate normal distribution for Gaussian networks. Conditional Gaussian networks are not supported. The variables that are used to compute the predicted values can be specified with the from optional argument; the default is to use those in the Markov blanket of node.

impute() is based on predict(), and can impute missing values with the same methods (parents, bayes-lw and exact). The method bayes-lw can take an additional argument n with the number of random samples which are averaged for each observation. As in predict(), imputed values will differ in each call to impute() when method is set to bayes-lw.

If object contains NA parameter estimates (because of unobserved discrete parents configurations in the data the parameters were learned from), predict will predict NAs when those parents configurations appear in data. See bn.fit for details on how to make sure bn.fit objects contain no NA parameter estimates.

Value

predict() returns a numeric vector (for Gaussian and conditional Gaussian nodes), a factor (for categorical nodes) or an ordered factor (for ordinal nodes). If prob = TRUE and the network is discrete, the probabilities used for prediction are attached to the predicted values as an attribute called prob.

impute() returns a data frame with the same structure as data.

Note

Ties in prediction are broken using Bayesian tie breaking, i.e. sampling at random from the tied values. Therefore, setting the random seed is required to get reproducible results.

Classifiers have a separate predict() method, see naive.bayes.

Author(s)

Marco Scutari

Examples

# missing data imputation.
with.missing.data = gaussian.test
with.missing.data[sample(nrow(with.missing.data), 500), "F"] = NA
fitted = bn.fit(model2network("[A][B][E][G][C|A:B][D|B][F|A:D:E:G]"),
           gaussian.test)
imputed = impute(fitted, with.missing.data)

# predicting a variable in the test set.
training = bn.fit(model2network("[A][B][E][G][C|A:B][D|B][F|A:D:E:G]"),
           gaussian.test[1:2000, ])
test = gaussian.test[2001:nrow(gaussian.test), ]
predicted = predict(training, node = "F", data = test)

# obtain the conditional probabilities for the values of a single variable
# given a subset of the rest, they are computed to determine the predicted
# values.
fitted = bn.fit(model2network("[A][C][F][B|A][D|A:C][E|B:F]"), learning.test)
evidence = data.frame(A = factor("a", levels = levels(learning.test$A)),
                      F = factor("b", levels = levels(learning.test$F)))
predicted = predict(fitted, "C", evidence,
              method = "bayes-lw", prob = TRUE)
attr(predicted, "prob")