PnodePostWeight: Fetches the posterior weight associated with a node

In ralmond/Peanut: Parameterized Bayesian Networks, Abstract Classes

Fetches the posterior weight associated with a node

Description

Before running GEMfit, nodes are given a prior weight (PnodePriorWeight) indicating how much weight should be given to the prior distribution. After running the calcExpTables step, there will be a posterior weight giving the total weight of the prior plus data.

Usage

PnodePostWeight(node)

Arguments

node	A Pnode object.

Details

Let s be a configuration of the parent variables, which corresponds to a row of the CPT of node (PnodeProbs(node)). Let \bold{p}_s = (p_{s,1}, \ldots, p_{s,K}) be the corresponding row of the conditional probability table and let n_s be the corresponding prior weight (an element of codePnodePriorWeight(node)). The corresponding row of the effective Dirichlet prior for that row is \alpha_s = (\alpha_{s,1}, \ldots, \alpha_{s,K}), where \alpha_{s,1}=p_{s,1}n_s. Note that the matrix \bold{P} and the vector \bold{n} (stacking the conditional probability vectors and the prior weights) are sufficient statistics for the conditional probability distribution of node.

The function calcExpTables does the E-step (and some of the M-step) of the GEMfit algorithm. Its output is new values for the sufficient statistics, \tilde{\bold{P}} and \tilde{\bold{n}}. At this point, the function PnodeProbs should return \tilde{\bold{P}} (although possibly as an array rather than a matrix) and PnodePostWeight(node) returns \tilde{\bold{n}}.

Although the PnodePostWeight(node) is used in the next step, maxAllTableParams, it is not retained for the next round of the GEMfit algorithm, instead the PnodePriorWeight(node) is used for the next time calcExpTables is run.

Often, PnodePriorWeight(node) is set to a scalar, indicating that every row should be given the same weight, e.g., 10. In this case, PnodePostWeight(node) will usually be vector valued as different numbers of data points correspond to each row of the CPT. Furthermore, unless the parent variables are fully observed, the PnodePostWeight(node) are unlikely to be integer valued even if the prior weights are integers. However, the posterior weights should always be at least as large as the prior weights.

Value

A vector of numeric values corresponding to the rows of the CPT of node. An error may be produced if calcExpTables has not yet been run.

Author(s)

Russell Almond

References

Almond, R. G. (2015) An IRT-based parameterization for conditional probability tables. In Agosta, J. M. and Carvalho, R. N. (Eds.) Proceedings of the Twelfth UAI Bayesian Modeling Application Workshop (BMAW 2015). CEUR Workshop Proceedings, 1565, 14–23. http://ceur-ws.org/Vol-1565/bmaw2015_paper4.pdf.

See Also

PnodePriorWeight, GEMfit, calcExpTables, 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="PNetica"),
                           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.