calcExpTables: Calculate expected tables for a parameterized network

In ralmond/Peanut: Parameterized Bayesian Networks, Abstract Classes

Calculate expected tables for a parameterized network

Description

The performs the E-step of the GEM algorithm by running the internal EM algorithm of the host Bayes net package on the cases. After this is run, the posterior parameters for each conditional probability distribution should be the expected cell counts, that is the expected value of the sufficient statistic, for each Pnode in the net.

Usage

calcExpTables(net, cases, Estepit = 1, tol = sqrt(.Machine$double.eps))

Arguments

net	A Pnet object
cases	An object representing a set of cases. Note the type of object is implementation dependent. It could be either a data frame providing cases or a filename for a case file.
Estepit	An integer scalar describing the number of steps the Bayes net package should take in the internal EM algorithm.
tol	A numeric scalar giving the stopping tolerance for the Bayes net package internal EM algorithm.

Details

The GEMfit algorithm uses a generalized EM algorithm to fit the parameterized network to the given data. This loops over the following steps:

E-step

Run the internal EM algorithm of the Bayes net package to calculate expected tables for all of the tables being learned. The function calcExpTables carries out this step.

M-step

Find a set of table parameters which maximize the fit to the expected counts by calling mapDPC for each table. The function maxAllTableParams does this step.

Update CPTs

Set all the conditional probability tables in the network to the new parameter values. The function BuildAllTables does this.

Convergence Test

Calculate the log likelihood of the cases under the new parameters and stop if no change. The function calcPnetLLike calculates the log likelihood.

The function calcExpTables performs the E-step. It assumes that the native Bayes net class which net represents has a function which does EM learning with hyper-Dirichlet priors. After this internal EM algorithm is run, then the posterior should contain the expected cell counts that are the expected value of the sufficient statistics, i.e., the output of the E-step. Note that the function maxAllTableParams is responsible for reading these from the network.

The internal EM algorithm should be set to use the current value of the conditional probability tables (as calculated by BuildTable(node) for each node) as a starting point. This starting value is given a prior weight of GetPriorWeight(node). Note that some Bayes net implementations allow a different weight to be given to each row of the table. The prior weight counts as a number of cases, and should be scaled appropriately for the number of cases in cases.

The parameters Estepit and tol are passed to the internal EM algorithm of the Bayes net. Note that the outer EM algorithm assumes that the expected table counts given the current values of the parameters, so the default value of one is sufficient. (It is possible that a higher value will speed up convergence, the parameter is left open for experimentation.) The tolerance is largely irrelevant as the outer EM algorithm does the tolerance test.

Value

The net argument is returned invisibly.

As a side effect, the internal conditional probability tables in the network are updated as are the internal weights given to each row of the conditional probability tables.

Note

The function calcExpTables is an abstract generic functions, and it needs specific implementations. See the PNetica-package for an example.

This function assumes that the host Bayes net implementation (e.g., RNetica-package): (1) net has an EM learning function, (2) the EM learning supports hyper-Dirichlet priors, (3) it is possible to recover the hyper-Dirichlet posteriors after running the internal EM algorithm.

Author(s)

Russell Almond

References

Almond, R. G. (2015) An IRT-based Parameterization for Conditional Probability Tables. Paper presented at the 2015 Bayesian Application Workshop at the Uncertainty in Artificial Intelligence Conference.

See Also

Pnet, GEMfit, calcPnetLLike, maxAllTableParams

Examples

## Not run: 

library(PNetica) ## Need a specific implementation
sess <- NeticaSession()
startSession(sess)

irt10.base <- ReadNetworks(system.file("testnets","IRT10.2PL.base.dne",
                                       package="Peanut"),
                           session=sess)
irt10.base <- as.Pnet(irt10.base)  ## Flag as Pnet, fields already set.
irt10.theta <- PnetFindNode(irt10.base,"theta")
irt10.items <- PnetPnodes(irt10.base)
## Flag items as Pnodes
for (i in 1:length(irt10.items)) {
  irt10.items[[i]] <- as.Pnode(irt10.items[[i]])
  ## Add node to list of observed nodes
  PnodeLabels(irt10.items[[1]]) <-
     union(PnodeLabels(irt10.items[[1]]),"onodes")
}
PnetCompile(irt10.base) ## Netica requirement

casepath <- system.file("testdat","IRT10.2PL.200.items.cas", package="PNetica")


item1 <- irt10.items[[1]]

priorcounts <- sweep(PnodeProbs(item1),1,GetPriorWeight(item1),"*")

calcExpTables(irt10.base,casepath)

postcounts <- sweep(PnodeProbs(item1),1,PnodePostWeight(item1),"*")

## Posterior row sums should always be larger.
stopifnot(
  all(apply(postcounts,1,sum) >= apply(priorcounts,1,sum))
)

DeleteNetwork(irt10.base)
stopSession(sess)

## End(Not run)

ralmond/Peanut documentation built on Sept. 19, 2023, 8:27 a.m.