PnetAdjoin: Merges (or separates) two Pnets with common variables

In ralmond/PNetica: Parameterized Bayesian Networks Netica Interface

Merges (or separates) two Pnets with common variables

Description

In the hub-and-spoke Bayes net construction method, number of spoke models (evidence models in educational applications) are connected to a central hub model (proficiency models in educational applications). The PnetAdjoin operation combines a hub and spoke model to make a motif, replacing references to hub variables in the spoke model with the actual hub nodes. The PnetDetach operation reverses this.

Usage

## S4 method for signature 'NeticaBN'
PnetAdjoin(hub, spoke)
## S4 method for signature 'NeticaBN'
PnetDetach(motif, spoke) 

Arguments

hub	A complete Pnet to which new variables will be added.
spoke	An incomplete Pnet which may contain stub nodes, references to nodes in the hub

.

motif

The combined Pnet which is formed by joining a hub and spoke together.

Details

The hub-and-spoke model for Bayes net construction (Almond and Mislevy, 1999; Almond, 2017) divides a Bayes net into a central hub model and a collection of spoke models. The motivation is that the hub model represents the status of a system—in educational applications, the proficiency of the student—and the spoke models are related to collections of evidence that can be collected about the system state. In the educational application, the spoke models correspond to a collection of observable outcomes from a test item or task. A motif is a hub plus a collection of spoke model corresponding to a single task.

While the hub model is a complete Bayesian network, the spoke models are fragments. In particular, several hub model variables are parents of variables in the spoke model. These variables are not defined in spoke model, but are rather replaced with stub nodes, nodes which reference, but do not define the spoke model.

The PnetAdjoin operation copies the Pnodes from the spoke model into the hub model, and connects the stub nodes to the nodes with the same name in the spoke model. The result is a motif consisting of the hub and the spoke. (If this operation is repeated many times it can be used to build an arbitrarily complex motif.)

The PnetDetach operation reverses the adjoin operation. It removes the nodes associated with the spoke model only, leaving the joint probability distribution of the hub model (along with any evidence absorbed by setting values of observable variables in the spoke) intact.

Value

The function PnetAdjoin returns a list of the newly created nodes corresponding to the spoke model nodes. Note that the names may have changed to avoid duplicate names. The names of the list are the spoke node names, so that any name changes can be discovered.

In both cases, the first argument is destructively modified, for PnetAdjoin the hub model becomes the motif. For PnetDetach the motif becomes the hub again.

Known Bugs

Netica version 5.04 has a bug that when nodes with no graphical information (e.g., position) are absorbed in a net in which some of the nodes have graphical information, it will generate an error. This was found and fixed in version 6.07 (beta) of the API. However, the function PnetDetach may generate internal Netica errors in this condition.

Right now they are logged, but nothing is done. Hopefully, they are harmless.

Note

Node names must be unique within a Bayes net. If several spokes are attached to a hub and those spokes have common names for observable variables, then the names will need to be modified to make them unique. The function PnetAdjoin always returns the new nodes so that any name changes can be noted by the calling program.

I anticipate that there will be considerable varation in how these functions are implemented depending on the underlying implementation of the Bayes net package. In particular, there is no particular need for the PnetDetach function to do anything. While removing variables corresponding to an unneeded spoke model make the network smaller, they are harmless as far as calculations of the posterior distribution.

Author(s)

Russell Almond

References

Almond, R. G. & Mislevy, R. J. (1999) Graphical models and computerized adaptive testing. Applied Psychological Measurement, 23, 223–238.

Almond, R., Herskovits, E., Mislevy, R. J., & Steinberg, L. S. (1999). Transfer of information between system and evidence models. In Artificial Intelligence and Statistics 99, Proceedings (pp. 181–186). Morgan-Kaufman

Almond, R. G. (presented 2017, August). Tabular views of Bayesian networks. In John-Mark Agosta and Tomas Singlair (Chair), Bayeisan Modeling Application Workshop 2017. Symposium conducted at the meeting of Association for Uncertainty in Artificial Intelligence, Sydney, Australia. (International) Retrieved from http://bmaw2017.azurewebsites.net/

See Also

Pnet, PnetHub, Qmat2Pnet, PnetMakeStubNodes

Examples

sess <- NeticaSession()
startSession(sess)

PM <- ReadNetworks(system.file("testnets", "miniPP-CM.dne",
                               package="PNetica"), session=sess)
EM1 <- ReadNetworks(system.file("testnets", "PPcompEM.dne",
                               package="PNetica"), session=sess)

Phys <- PnetFindNode(PM,"Physics")

## Prior probability for high level node
PnetCompile(PM)
bel1 <- PnodeMargin(PM, Phys)

## Adjoin the networks.
EM1.obs <- PnetAdjoin(PM,EM1)
PnetCompile(PM)

## Enter a finding
PnodeEvidence(EM1.obs[[1]]) <- "Right"
## Posterior probability for high level node

bel2 <- PnodeMargin(PM,Phys)

PnetDetach(PM,EM1)
PnetCompile(PM)

## Findings are unchanged
bel2a <- PnodeMargin(PM,Phys)
stopifnot(all.equal(bel2,bel2a,tol=1e-6))

DeleteNetwork(list(PM,EM1))
stopSession(sess)

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