PnetPriorWeight: Gets the weight to be associated with the prior table during...

In ralmond/Peanut: Parameterized Bayesian Networks, Abstract Classes

Gets the weight to be associated with the prior table during EM learning

Description

The EM learning algorithm GEMfit uses the built-in EM learning of the Bayes net to build expected count tables for each Pnode. The expected count tables are a weighted average of the case data and the prior from the parameterized table. This gives the weight, in number of cases, given to the prior.

Usage

PnetPriorWeight(net)
PnetPriorWeight(net) <- value
PnodePriorWeight(node)
PnodePriorWeight(node) <- value
GetPriorWeight(node)

Arguments

net	A Pnet object whose prior weight is to be accessed.
node	A Pnode object whose prior weight is to be accessed.
value	A nonnegative numeric vector giving the prior weight. This should either be a scalar or a vector with length equal to the number of rows of the conditional probability table. In the case of PnetPriorWeight using a non-scalar value will produce unpredictable results.

Details

Suppose that value of the node and all of its parents are fully observed, and let X_{1i},\ldots,X_{ki} be the observed counts for row i, and let p_{1i},\ldots,p_{ki} be the conditional probabilities for row i. Then the posterior probabilities for row i can be found by normalizing X_{1i}+w_ip_{1i},\ldots,X_{ki}+w_ip_{ki}. In the EM algorithm, the table is not fully observed but the expected value of X_{1i},\ldots,X_{ki} is used instead.

This function gets or sets the vector w_1,\ldots,w_I (where I is the number of rows in the conditional probability table). If value is a scalar this is the same as giving all w_i the same value.

The function PnodePriorWeight gets or sets the prior weight for a given node. The function PnetPriorWeight gets or sets the default weight for all nodes (a property of the network). Unless all nodes have the name number of parents with the same number of states, this should be a scalar. The expression GetPriorWeight(node) gets the prior weight for the node or if that is null, it gets the default prior weight from the net (using the function PnodeNet.

Value

A numeric vector or scalar giving the weight or NULL if the default network weight is to be used.

Note

The GEMfit algorithm will update the prior weight for each node based on how much information is available for each row. Thus, even if the values are initially the same for each row, after calling GEMfit they usually will be different for each row.

The functions PnetPriorWeight and PnodePriorWeight are abstract generic functions, and they needs specific implementations. See the PNetica-package for an example.

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, Pnode, PnodeNet, BuildTable, GEMfit

Examples

 ## Not run: 

library(PNetica)  ## Implementation of Peanut protocol
sess <- NeticaSession()
startSession(sess)
## Create network structure using RNetica calls
IRT10.2PL <- CreateNetwork("IRT10_2PL",session=sess)

theta <- NewDiscreteNode(IRT10.2PL,"theta",
                         c("VH","High","Mid","Low","VL"))
PnodeStateValues(theta) <- effectiveThetas(PnodeNumStates(theta))
PnodeProbs(theta) <- rep(1/PnodeNumStates(theta),PnodeNumStates(theta))

J <- 10 ## Number of items
items <- NewDiscreteNode(IRT10.2PL,paste("item",1:J,sep=""),
                         c("Correct","Incorrect"))
for (j in 1:J) {
  PnodeParents(items[[j]]) <- list(theta)
  PnodeStateValues(items[[j]]) <- c(1,0)
  PnodeLabels(items[[j]]) <- c("observables")
}

## Convert into a Pnet
IRT10.2PL <- as.Pnet(IRT10.2PL)
PnetPriorWeight(IRT10.2PL) <- 10


## Convert nodes to Pnodes
for (j in 1:J) {
  items[[j]] <- Pnode(items[[j]])
}

PnodePriorWeight(items[[2]]) <- 5
## 5 states in parent, so 5 rows
PnodePriorWeight(items[[3]]) <- c(10,7,5,7,10)

stopifnot(
  abs(PnetPriorWeight(IRT10.2PL)-10) < .0001, 
  is.null(PnodePriorWeight(items[[1]])),
  abs(GetPriorWeight(items[[1]])-10) < .0001,
  abs(GetPriorWeight(items[[2]])-5) < .0001,
  any(abs(GetPriorWeight(items[[3]])-c(10,7,5,7,10)) < .0001)
)

PnetPriorWeight(IRT10.2PL) <- 15

stopifnot(
  abs(PnetPriorWeight(IRT10.2PL)-15) < .0001, 
  is.null(PnodePriorWeight(items[[1]])),
  abs(GetPriorWeight(items[[1]])-15) < .0001,
  abs(GetPriorWeight(items[[2]])-5) < .0001,
  any(abs(GetPriorWeight(items[[3]])-c(10,7,5,7,10)) < .0001)
)

DeleteNetwork(IRT10.2PL)
stopSession(sess)

## End(Not run)

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