R: Fit the parameters of a Bayesian network

bn.fit {bnlearn} | R Documentation

## Fit the parameters of a Bayesian network

### Description

Fit the parameters of a Bayesian network conditional on its structure.

### Usage

    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)

### Arguments

`x` | an object of class `bn` (for `bn.fit()` and `custom.fit()`) or an object of class `bn.fit` (for `bn.net`).
`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 `x`. See below.
`method` | a character string, either `mle` for Maximum Likelihood parameter estimation or `bayes` for Bayesian parameter estimation (currently implemented only for discrete data).
`...` | 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 (`bn.fit.onode`) instead of unordered factors (`bn.fit.dnode`).
`keep.fitted` | a boolean value. If `TRUE`, the object returned by `bn.fit` will contain fitted values and residuals for all Gaussian and conditional Gaussian nodes, and the configurations of the discrete parents for conditional Gaussian nodes.
`debug` | a boolean value. If `TRUE` a lot of debugging output is printed; otherwise the function is completely silent.

### 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.

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.

### 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 `pdag2dag` for two ways of manually setting the direction of one or more arcs.

The `bayes` and `mle` methods handle missing values by estimating the parameters of each distribution using the observations that are complete for the variables involved in that local distribution.

### Author(s)

Marco Scutari

### See Also

`bn.fit utilities`, `bn.fit plots`.

### Examples

    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))

[Package bnlearn version 4.4.1 Index]