Package 'deal' reference manual

Title:	Learning Bayesian Networks with Mixed Variables
Description:	Bayesian networks with continuous and/or discrete variables can be learned and compared from data. The method is described in Boettcher and Dethlefsen (2003), <doi:10.18637/jss.v008.i20>.
Authors:	Susanne Gammelgaard Bottcher, Claus Dethlefsen.
Maintainer:	Claus Dethlefsen <[email protected]>
License:	GPL (>= 2)
Version:	1.2-42
Built:	2024-12-15 07:30:22 UTC
Source:	CRAN

Greedy search

Description

From initial network, does local perturbations to increase network score.

Usage

autosearch(initnw,data,prior=jointprior(network(data)),maxiter=50,
           trylist= vector("list",size(initnw)),trace=TRUE,
           timetrace=TRUE,showban=FALSE,removecycles=FALSE) 

heuristic(initnw,data,prior=jointprior(network(data)),
          maxiter=100,restart=10,degree=size(initnw),
          trylist= vector("list",size(initnw)),trace=TRUE,
          timetrace=TRUE,removecycles=FALSE)
gettable(x)
autosearch(initnw,data,prior=jointprior(network(data)),maxiter=50,
           trylist= vector("list",size(initnw)),trace=TRUE,
           timetrace=TRUE,showban=FALSE,removecycles=FALSE) 

heuristic(initnw,data,prior=jointprior(network(data)),
          maxiter=100,restart=10,degree=size(initnw),
          trylist= vector("list",size(initnw)),trace=TRUE,
          timetrace=TRUE,removecycles=FALSE)
gettable(x)

Arguments

`initnw`	an object of class `network`, from which the search is started.
`data`	a data frame used for learning the network, see `network`.
`prior`	a list containing parameter priors, generated by `jointprior`.
`maxiter`	an integer, which gives the maximum number of steps in the search algorithm.
`restart`	an integer, which gives the number of times to perturb `initnw` and rerun the search.
`degree`	an integer, which gives the degree of perturbation, see `perturb`.
`trylist`	a list used internally for reusing learning of nodes, see `maketrylist`.
`trace`	a logical. If `TRUE`, plots the accepted networks during search.
`timetrace`	a logical. If `TRUE`, prints some timing information on the screen.
`showban`	a logical passed to the plot method for network objects. If `FALSE`, the banned arrows are not shown in the plots (if `trace` is `TRUE`).
`removecycles`	a logical. If `TRUE`, all networks explored in the search is returned, except for networks containing a cycle. If `FALSE`, all networks are returned, including cyclic networks.
`x`	an output object from a search.

Details

In autosearch, a list of networks is in each step created with either one arrow added, one arrow deleted or one arrow turned (if a cycle is not generated). The network scores of all the proposal networks are calculated and the network with the highest score is chosen for the next step in the search. If no proposed network has a higher network score than the previous network, the search is terminated. The network with the highest network score is returned, along with a list containing all tried networks (depending on the value of removecycles).

heuristic restarts by perturbing initnw degree times and calling autosearch again. The number of restarts is given by the option restart.

Value

autosearch and heuristic returns a list with three elements, that may be accessed using getnetwork, gettable and gettrylist. The elements are

`nw`	an object of class `network`, which gives the network with the highest score.
`table`	a table with all tried networks. If removecycles is `FALSE`, the networks may contain cycles. The table contains two columns: `model` with a string representation of the model and `score` with the corresponding log network score. The table can be translated to a `networkfamily` using `makenw`.
`trylist`	an updated list used internally for reusing learning of nodes, see `maketrylist`.

Author(s)

Susanne Gammelgaard Bottcher,
Claus Dethlefsen [email protected].

Examples

data(rats)
fit       <- network(rats)
fit.prior <- jointprior(fit,12)
fit       <- getnetwork(learn(fit,rats,fit.prior))
fit       <- getnetwork(insert(fit,2,1,rats,fit.prior))
fit       <- getnetwork(insert(fit,1,3,rats,fit.prior))
hisc      <- autosearch(fit,rats,fit.prior,trace=FALSE)
hisc      <- autosearch(fit,rats,fit.prior,trace=FALSE,removecycles=TRUE) # slower
plot(getnetwork(hisc))

hisc2     <- heuristic(fit,rats,fit.prior,restart=10,trace=FALSE)
plot(getnetwork(hisc2))
print(modelstring(getnetwork(hisc2)))
plot(makenw(gettable(hisc2),fit))
data(rats)
fit       <- network(rats)
fit.prior <- jointprior(fit,12)
fit       <- getnetwork(learn(fit,rats,fit.prior))
fit       <- getnetwork(insert(fit,2,1,rats,fit.prior))
fit       <- getnetwork(insert(fit,1,3,rats,fit.prior))
hisc      <- autosearch(fit,rats,fit.prior,trace=FALSE)
hisc      <- autosearch(fit,rats,fit.prior,trace=FALSE,removecycles=TRUE) # slower
plot(getnetwork(hisc))

hisc2     <- heuristic(fit,rats,fit.prior,restart=10,trace=FALSE)
plot(getnetwork(hisc2))
print(modelstring(getnetwork(hisc2)))
plot(makenw(gettable(hisc2),fit))

Graphical interface for editing networks

Description

drawnetwork allows the user to specify a Bayesian network through a point and click interface.

Usage

drawnetwork(nw,df,prior,trylist=vector("list",size(nw)),
            unitscale=20,cexscale=8,
            arrowlength=.25,nocalc=FALSE,
            yr=c(0,350),xr=yr,...)


drawnetwork(nw,df,prior,trylist=vector("list",size(nw)),
            unitscale=20,cexscale=8,
            arrowlength=.25,nocalc=FALSE,
            yr=c(0,350),xr=yr,...)

Arguments

`nw`	an object of class `network` to be edited.
`df`	a data frame used for learning the network, see `network`.
`prior`	a list containing parameter priors, generated by `jointprior`.
`trylist`	a list used internally for reusing learning of nodes, see `maketrylist`.
`cexscale`	a numeric passed to the plot method for network objects. Measures the scaled size of text and symbols.
`arrowlength`	a numeric passed to the plot method for network objects. Measures the length of the edges of the arrowheads.
`nocalc`	a logical. If `TRUE`, no learning procedure is called, see eg. `rnetwork`.
`unitscale`	a numeric passed to the plot method for network objects. Scale parameter for chopping off arrow heads.
`xr`	a numeric vector with two components containing the range on x-axis.
`yr`	a numeric vector with two components containing the range on y-axis.
`...`	additional plot arguments, passed to the plot method for network objects.

Details

To insert an arrow from node 'A' to node 'B', first click node 'A' and then click node 'B'. When the graph is finished, click 'stop'.

To specify that an arrow must not be present, press 'ban' (a toggle) and draw the arrow. This is shown as a red dashed arrow. It is possible to ban both directions between nodes. The ban list is stored with the network in the property banlist. It is a matrix with two columns. Each row is the 'from' node index and the 'to' node index, where the indices are the column number in the data frame.

Note that the network score changes as the network is re-learned whenever a change is made (unless nocalc is TRUE).

Value

A list with two elements that may be accessed using getnetwork and gettrylist. The elements are

`nw`	an object of class `network` with the final network.
`trylist`	an updated list used internally for reusing learning of nodes, see `maketrylist`.

Author(s)

Susanne Gammelgaard Bottcher,
Claus Dethlefsen [email protected].

Examples

data(rats)
rats.nw    <- network(rats)
rats.prior <- jointprior(rats.nw,12)
rats.nw    <- getnetwork(learn(rats.nw,rats,rats.prior))

## Not run: newrat  <- getnetwork(drawnetwork(rats.nw,rats,rats.prior))
data(rats)
rats.nw    <- network(rats)
rats.prior <- jointprior(rats.nw,12)
rats.nw    <- getnetwork(learn(rats.nw,rats,rats.prior))

## Not run: newrat  <- getnetwork(drawnetwork(rats.nw,rats,rats.prior))

From a network family, generate LaTeX output

Description

The networks in a network family is arranged as pictex-graphs in a LaTeX-table.

Usage

genlatex(nwl,outdir="pic/",prefix="scoretable",picdir="",picpre="pic",
         ncol=5,nrow=7,width=12/ncol,vadjust=-1.8)
genpicfile (nwl,outdir="pic/",prefix="pic",w=1.6,h=1.6,bigscale=3) 
genlatex(nwl,outdir="pic/",prefix="scoretable",picdir="",picpre="pic",
         ncol=5,nrow=7,width=12/ncol,vadjust=-1.8)
genpicfile (nwl,outdir="pic/",prefix="pic",w=1.6,h=1.6,bigscale=3)

Arguments

`nwl`	object of class `networkfamily` containing a list of objects of class `network`.
`outdir`	character string, the directory for storing output.
`prefix`	character string, the filename (without extension) of the LaTeX file. The filenames of the picfiles begin with the given prefix.
`picdir`	character string, the directory where pic-files are stored.
`picpre`	character string, prefix for pic-files.
`ncol`	integer, the number of columns in LaTeX table.
`nrow`	integer, the number of rows in LaTeX table.
`width`	numeric, the width of each cell in the LaTeX table.
`vadjust`	numeric, the vertical adjustment in LaTeX table.
`w`	numeric, the width of pictex objects
`h`	numeric, the height of pictex objects
`bigscale`	numeric, the scaling of the best network, which is output in 'nice.tex'

Value

Files:

`{outdir}{picpre}xx.tex`	one pictex file for each network in the network family, indexed by xx.
`{outdir}{prefix}.tex`	LaTeX file with table including all pictex files.
`{outdir}{picpre}nice.tex`	pictex file with the best network.

Author(s)

Susanne Gammelgaard Bottcher,
Claus Dethlefsen [email protected].

Examples

data(rats)
allrats <- getnetwork(networkfamily(rats,network(rats)))
allrats <- nwfsort(allrats)

## Not run: dir.create("c:/temp")
## Not run: genpicfile(allrats,outdir="c:/temp/pic/")
## Not run: genlatex(allrats,outdir="c:/temp/pic/",picdir="c:/temp/pic/")

## LATEX FILE:
#\documentclass{article}
#\usepackage{array,pictex}
#\begin{document}
#\input{scoretable}
#\input{picnice}
#\end{document}

#data(ksl)
#ksl.nw  <- network(ksl)
#ksl.prior <- jointprior(ksl.nw,64)
#mybanlist <- matrix(c(5,5,6,6,7,7,9,
#                    8,9,8,9,8,9,8),ncol=2)
#banlist(ksl.nw) <- mybanlist                  
#ksl.nw <- getnetwork(learn(ksl.nw,ksl,ksl.prior))
#ksl.search <- autosearch(ksl.nw,ksl,ksl.prior,
#                      trace=TRUE)
#ksl.searchlist <- makenw(ksl.search$table,ksl.search$nw)
#ksl.searchlist <- nwfsort(ksl.searchlist)
## Not run: genpicfile(ksl.searchlist)
## Not run: genlatex(ksl.searchlist)

data(rats)
allrats <- getnetwork(networkfamily(rats,network(rats)))
allrats <- nwfsort(allrats)

## Not run: dir.create("c:/temp")
## Not run: genpicfile(allrats,outdir="c:/temp/pic/")
## Not run: genlatex(allrats,outdir="c:/temp/pic/",picdir="c:/temp/pic/")

## LATEX FILE:
#\documentclass{article}
#\usepackage{array,pictex}
#\begin{document}
#\input{scoretable}
#\input{picnice}
#\end{document}

#data(ksl)
#ksl.nw  <- network(ksl)
#ksl.prior <- jointprior(ksl.nw,64)
#mybanlist <- matrix(c(5,5,6,6,7,7,9,
#                    8,9,8,9,8,9,8),ncol=2)
#banlist(ksl.nw) <- mybanlist                  
#ksl.nw <- getnetwork(learn(ksl.nw,ksl,ksl.prior))
#ksl.search <- autosearch(ksl.nw,ksl,ksl.prior,
#                      trace=TRUE)
#ksl.searchlist <- makenw(ksl.search$table,ksl.search$nw)
#ksl.searchlist <- nwfsort(ksl.searchlist)
## Not run: genpicfile(ksl.searchlist)
## Not run: genlatex(ksl.searchlist)

Insert/remove an arrow in network

Description

Inserts/removes one arrow in a network (if legal)

Usage

insert (nw,j,i,df,prior,nocalc=FALSE,trylist=vector("list",size(nw))) 
remover(nw,j,i,df,prior,nocalc=FALSE,trylist=vector("list",size(nw))) 
insert (nw,j,i,df,prior,nocalc=FALSE,trylist=vector("list",size(nw))) 
remover(nw,j,i,df,prior,nocalc=FALSE,trylist=vector("list",size(nw)))

Arguments

`nw`	an object of class `network`.
`j`	integer, giving the index of the 'from' node.
`i`	integer, giving the index of the 'to' node.
`df`	a data frame used for learning the network, see `network`.
`prior`	a list describing parameter priors, generated by `jointprior`.
`nocalc`	a logical. If `TRUE`, learning is not called.
`trylist`	a list, used internally for reusing learning of nodes, see `maketrylist`.

Details

Examines if the arrow from j to i is legal according to the following criteria

Arrows from/to the same node are not legal.

Arrows from continous nodes to discrete nodes are not legal.

Arrows banned in ban list are not legal, see drawnetwork.

Arrows already existing in the network are not legal.

If the arrow is not legal, a NULL network is returned. Otherwise, the arrow is inserted/removed, the network is re-learned (if nocalc is FALSE). The trylist is updated.

Value

A list with two elements

`nw`	an object of class `network` with the arrow added/removed if this is possible. If not, `NULL` is returned.
`trylist`	an updated list, used internally for reusing learning of nodes, see `maketrylist`.

Author(s)

Susanne Gammelgaard Bottcher,
Claus Dethlefsen [email protected].

Examples

data(rats)
rats.nw    <- network(rats)
rats.nw    <- getnetwork(insert(rats.nw,2,1,nocalc=TRUE))
rats.prior <- jointprior(rats.nw,12)

rats.nw2   <- network(rats)
rats.nw2   <- getnetwork(learn(rats.nw2,rats,rats.prior))
rats.nw2   <- getnetwork(insert(rats.nw2,1,2,rats,rats.prior))

rats.nw3   <- getnetwork(remover(rats.nw2,1,2,rats,rats.prior))
data(rats)
rats.nw    <- network(rats)
rats.nw    <- getnetwork(insert(rats.nw,2,1,nocalc=TRUE))
rats.prior <- jointprior(rats.nw,12)

rats.nw2   <- network(rats)
rats.nw2   <- getnetwork(learn(rats.nw2,rats,rats.prior))
rats.nw2   <- getnetwork(insert(rats.nw2,1,2,rats,rats.prior))

rats.nw3   <- getnetwork(remover(rats.nw2,1,2,rats,rats.prior))

Calculates the joint prior distribution

Description

Given a network with a prob property for each node, derives the joint probability distribution. Then the quantities needed in the local master procedure for finding the local parameter priors are deduced.

Usage

jointprior(nw,N=NA,phiprior="bottcher",timetrace=FALSE) 
jointprior(nw,N=NA,phiprior="bottcher",timetrace=FALSE)

Arguments

`nw`	an object of class `network`. Each node must have a `prob` property to describe the local probability distribution. The `prob` property is created using `prob` method for network objects, which is called by the `network` function.
`N`	an integer, which gives the size of the imaginary data base. If this is too small, `NA`'s may be created in the output, resulting in errors in `learn`. If no `N` is given, the procedure tries to set a value as low as possible.
`phiprior`	a string, which specifies how the prior for phi is calculated. Either `phiprior="bottcher"` or `phiprior="heckerman"` can be used.
`timetrace`	a logical. If `TRUE`, prints some timing information on the screen.

Details

For the discrete part of the network, the joint probability distribution is calculated by multiplying together the local probability distributions. Then, jointalpha is determined by multiplying each entry in the joint probability distribution by the size of the imaginary data base N.

For the mixed part of the network, for each configuration of the discrete variables, the joint Gaussian distribution of the continuous variables is constructed and represented by jointmu (one row for each configuration of the discrete parents) and jointsigma (a list of matrices – one for each configuration of the discrete parents). The configurations of the discrete parents are ordered according to findex. The algorithm for constructing the joint distribution of the continuous variables is described in Shachter and Kenley (1989).

Then, jointalpha, jointnu, jointrho, mu and jointphi are deduced. These quantities are later used for deriving local parameter priors.

For each configuration i of the discrete variables,

$\nu_i=\rho_i=\alpha_i$

and

$\phi_i = (\nu_i -1)\Sigma_i$

if phiprior="bottcher", see Bottcher(2001) and

$\phi_i = \nu_i(\rho_i -2)\Sigma_i/(\nu_i+1)$

if phiprior="heckerman", see Heckerman, Geiger and Chickering (1995).

Value

A list with the following elements,

`jointalpha`	a table used in the local master procedure for discrete variables.
`jointnu`	a table used in the local master procedure for continuous variables.
`jointrho`	a table used in the local master procedure for continuous variables.
`jointmu`	a numeric matrix used in the local master procedure for continuous variables.
`jointsigma`	a list of numeric matrices (not used in further calculations).
`jointphi`	a list of numeric matrices used in the local master procedure for continuous variables.

Author(s)

Susanne Gammelgaard Bottcher,
Claus Dethlefsen [email protected].

References

Bottcher, S.G. (2001). Learning Bayesian Networks with Mixed Variables, Artificial Intelligence and Statistics 2001, Morgan Kaufmann, San Francisco, CA, USA, 149-156.

Heckerman, D., Geiger, D. and Chickering, D. (1995). Learning Bayesian networks: The combination of knowledge and statistical data. Machine Learning, 20: 197-243.

Shachter, R.D. and Kenley, C.R. (1989), Gaussian influence diagrams. Management Science, 35:527-550.

Examples

data(rats)
rats.nw    <- network(rats)
rats.prior <- jointprior(rats.nw,12)

## Not run: savenet(rats.nw,file("rats.net"))
## Not run: rats.nw <- readnet(file("rats.net"))
## Not run: rats.nw <- prob(rats.nw,rats)
## Not run: rats.prior <- jointprior(rats.nw,12)

data(rats)
rats.nw    <- network(rats)
rats.prior <- jointprior(rats.nw,12)

## Not run: savenet(rats.nw,file("rats.net"))
## Not run: rats.nw <- readnet(file("rats.net"))
## Not run: rats.nw <- prob(rats.nw,rats)
## Not run: rats.prior <- jointprior(rats.nw,12)

Health and social characteristics

Description

Data from a study measuring health and social characteristics of representative samples of Danish 70 year olds, taken in 1967 and 1984.

Format

A data frame with variables of both discrete and continuous types.

FEV: Forced ejection volume
Kol: Cholesterol
Hyp: Hypertension (no/yes)
logBMI: Logarithm of Body Mass Index
Smok: Smoking (no/yes)
Alc: Alcohol consumption (seldom/frequently)
Work: Working (yes/no)
Sex: male/female
Year: Survey year (1967/1984)

Estimation of parameters in the local probability distributions

Description

Updates the distributions of the parameters in the network, based on a prior network and data. Also, the network score is calculated.

Usage

learn (nw, df, prior=jointprior(nw),
               nodelist=1:size(nw),
               trylist=vector("list",size(nw)),
               timetrace=FALSE) 

learn (nw, df, prior=jointprior(nw),
               nodelist=1:size(nw),
               trylist=vector("list",size(nw)),
               timetrace=FALSE)

Arguments

`nw`	an object of class `network`.
`df`	a data frame used for learning the network, see `network`.
`prior`	a list containing parameter priors, generated by `jointprior`.
`nodelist`	a numeric vector of indices of nodes to be learned.
`trylist`	a list used internally for reusing learning of nodes, see `maketrylist`.
`timetrace`	a logical. If `TRUE`, prints some timing information on the screen.

Details

The procedure learn determines the master prior, local parameter priors and local parameter posteriors, see Bottcher (2001). It may be called on all nodes (default) or just a single node.

From the joint prior distribution, the marginal distribution of all parameters in the family consisting of the node and its parents can be determined. This is the master prior, see localmaster.

The local parameter priors are now determined by conditioning in the master prior distribution, see conditional. The hyperparameters associated with the local parameter prior distribution is attached to each node in the property condprior.

Finally, the local parameter posterior distributions are calculated (see post) and attached to each node in the property condposterior.

A so-called trylist is maintained to speedup the learning process. The trylist consists of a list of matrices for each node. The matrix for a given node holds previously evaluated parent configurations and the corresponding log-likelihood contribution. If a node with a certain parent configuration needs to be learned, it is checked, whether the node has already been learned. The previously learned nodes are given as input in the trylist parameter and is updated in the learning procedure.

When one or more nodes in a network have been learned, the network score is updated and attached to the network in the property score.

The learning procedure is called from various functions using the principle, that networks should always be updated with their score. Thus, e.g.\ drawnetwork keeps the network updated when the graph is altered.

Value

A list with two elements that may be accessed using getnetwork and gettrylist. The elements are

`nw`	an object of class `network`, with the `condposterior` properties updated for the nodes. Also, the property `score` is updated and contains the network score. The contribution to the network score for each node is contained in the property `loglik` for each node.
`trylist`	an updated list used internally for reusing learning of nodes, see `maketrylist`.

Author(s)

Susanne Gammelgaard Bottcher,
Claus Dethlefsen [email protected].

References

Bottcher, S.G. (2001). Learning Bayesian Networks with Mixed Variables, Artificial Intelligence and Statistics 2001, Morgan Kaufmann, San Francisco, CA, USA, 149-156.

Examples

data(rats)
fit       <- network(rats)
fit.prior <- jointprior(fit,12)
fit.learn <- learn(fit,rats,fit.prior,timetrace=TRUE)
fit.nw    <- getnetwork(fit.learn)
fit.learn2<- learn(fit,rats,fit.prior,trylist=gettrylist(fit.learn),timetrace=TRUE)
data(rats)
fit       <- network(rats)
fit.prior <- jointprior(fit,12)
fit.learn <- learn(fit,rats,fit.prior,timetrace=TRUE)
fit.nw    <- getnetwork(fit.learn)
fit.learn2<- learn(fit,rats,fit.prior,trylist=gettrylist(fit.learn),timetrace=TRUE)

Make a suggestion for simulation probabilities

Description

Creates local probability distributions reflecting the graph of the network. These are attached as a simprob property to each node in the network and can be edited and used for rnetwork.

Usage

makesimprob(nw,
                        s2=function(idx,cf) {
                          cf <- as.vector(cf)
                          xs <- (1:length(cf))
                          log(xs%*%cf+1)
                        },
                        m0=function(idx,cf) {
                          cf <- as.vector(cf)
                          xs <- (1:length(cf))^2
                          .69*(xs%*%cf)
                          },
                        m1=function(idx,cf) {
                          cf <- as.vector(cf)
                          xs <- (1:length(cf))*10
                          idx*(cf%*%xs)
                          })
makesimprob(nw,
                        s2=function(idx,cf) {
                          cf <- as.vector(cf)
                          xs <- (1:length(cf))
                          log(xs%*%cf+1)
                        },
                        m0=function(idx,cf) {
                          cf <- as.vector(cf)
                          xs <- (1:length(cf))^2
                          .69*(xs%*%cf)
                          },
                        m1=function(idx,cf) {
                          cf <- as.vector(cf)
                          xs <- (1:length(cf))*10
                          idx*(cf%*%xs)
                          })

Arguments

`nw`	an object of class `network`.
`s2`	function that returns the variance as a function of the node index and the configuration of the discrete variables.
`m0`	function that returns the intercept as a function of the node index and the configuration of the discrete variables.
`m1`	function that returns the regression coefficients as a function of the node index and the configuration of the discrete variables.

Details

For each node, the local simprob is determined. If the node is discrete, the probability distribution is uniform (and thus not reflecting the dependence in the graph, as it should). If the node is continuous, one mean and variance is attached per configuration of the discrete parents. The mean depends on the continuos parents and is the regression coefficients determined by the functions m0 (intercept) and m1 (regression coefficients). The variance is determined by the function s2.

Value

The network object nw, where each node has attached the property simprob.

Author(s)

Susanne Gammelgaard Bottcher,
Claus Dethlefsen [email protected].

Creates the full trylist

Description

For faster learning, a trylist is maintained as a lookup table for a given parent configuration of a node.

Usage

maketrylist(initnw,data,prior=jointprior(network(data)),timetrace=FALSE) 
maketrylist(initnw,data,prior=jointprior(network(data)),timetrace=FALSE)

Arguments

`initnw`	an object of class `network`, from which the search is started.
`data`	a data frame used for learning the network, see `network`.
`prior`	a list containing parameter priors, generated by `jointprior`.
`timetrace`	a logical. If `TRUE`, prints some timing information on the screen.

Details

This procedure is included for illustrative purposes. For each node in the network, all possible parent configurations are created and learned. The result is called a trylist. To create the full trylist is very time-consuming, and a better choice is to maintain a trylist while searching and indeed this is automatically done. The trylist is given as output to all functions that call the learning procedure and can be given as an argument.

Value

A list with one element per node in the network. In the list, element i is a matrix with two columns: a string with the indices of the parent nodes, separated by ":", and a numeric with the log-likelihood contribution of the node given the parent configuration. Whenever learning is performed of a node given a parent configuration, the trylist is consulted to yield faster learning, especially useful when using autosearch or heuristic.

Author(s)

Susanne Gammelgaard Bottcher,
Claus Dethlefsen [email protected].

Examples

data(rats)
rats.nw <- network(rats)
rats.pr <- jointprior(rats.nw,12)
rats.nw <- getnetwork(learn(rats.nw,rats,rats.pr))
rats.tr <- maketrylist(rats.nw,rats,rats.pr)

rats.hi <- getnetwork(heuristic(rats.nw,rats,rats.pr,trylist=rats.tr))
data(rats)
rats.nw <- network(rats)
rats.pr <- jointprior(rats.nw,12)
rats.nw <- getnetwork(learn(rats.nw,rats,rats.pr))
rats.tr <- maketrylist(rats.nw,rats,rats.pr)

rats.hi <- getnetwork(heuristic(rats.nw,rats,rats.pr,trylist=rats.tr))

Bayesian network data structure

Description

A Bayesian network is represented as an object of class network. Methods for printing and plotting are defined.

Usage

network(df,specifygraph=FALSE,inspectprob=FALSE,
        doprob=TRUE,yr=c(0,350),xr=yr) 
## S3 method for class 'network'
print(x,filename=NA,condposterior=FALSE,
                          condprior=FALSE,...) 
## S3 method for class 'network'
 plot(x,arrowlength=.25,
                        notext=FALSE,
                        sscale=7,showban=TRUE,yr=c(0,350),xr=yr,
                        unitscale=20,cexscale=8,...)


network(df,specifygraph=FALSE,inspectprob=FALSE,
        doprob=TRUE,yr=c(0,350),xr=yr) 
## S3 method for class 'network'
print(x,filename=NA,condposterior=FALSE,
                          condprior=FALSE,...) 
## S3 method for class 'network'
 plot(x,arrowlength=.25,
                        notext=FALSE,
                        sscale=7,showban=TRUE,yr=c(0,350),xr=yr,
                        unitscale=20,cexscale=8,...)

Arguments

`df`	a data frame, where the columns define the variables. A continuous variable should have type `numeric` and discrete varibles should have type `factor`.
`specifygraph`	a logical. If `TRUE`, provides a call to `drawnetwork` to interactively specify a directed acyclic graph and possibly a ban list (see below).
`inspectprob`	a logical. If `TRUE`, provides a plot of the graph and possibility to inspect the calculated probability distribution by clicking on the nodes.
`doprob`	a logical. If `TRUE`, do not calculate a probability distribution. Used for example in `rnetwork`.
`x`	an object of class `network`.
`filename`	a string or `NA`. If not `NA`, output is printed to a file.
`condprior`	a logical. If `TRUE`, the conditional prior is printed, see `conditional`.
`condposterior`	a logical. If `TRUE`, the conditional posterior is printed, see `learn`.
`sscale`	a numeric. The nodes are initially placed on a circle with radius `sscale`.
`unitscale`	a numeric. Scale parameter for chopping off arrow heads.
`cexscale`	a numeric. Scale parameter to set the size of the nodes.
`arrowlength`	a numeric containing the length of the arrow heads.
`xr`	a numeric vector with two components containing the range on x-axis.
`yr`	a numeric vector with two components containing the range on y-axis.
`notext`	a logical. If `TRUE`, no text is displayed in the nodes on the plot.
`showban`	a logical. If `TRUE`, banned arrows are shown in red.
`...`	additional plot arguments, passed to `plot.node`.

Value

The netork creator function returns an object of class network, which is a list with the following elements (properties),

`nodes`	a list of objects of class `node`. If `doprob` is `TRUE`, the nodes are given the property `prob` which is the initial probability distribution used by `jointprior`.
`n`	an integer containing the number of nodes in the network.
`discrete`	a numeric vector of indices of discrete nodes.
`continuous`	a numeric vector of indices of continuous nodes.
`banlist`	a numeric matrix with two columns. Each row contains the indices `i -> j` of arrows that may not be allowed in the directed acyclic graph.
`score`	a numeric added by `learn` and is the log network score.
`relscore`	a numeric added by `nwfsort` and is the relative network score – compared with the best network in a network family.

Author(s)

Susanne Gammelgaard Bottcher,
Claus Dethlefsen [email protected].

Examples

A <- factor(rep(c("A1","A2"),50))
B <- factor(rep(rep(c("B1","B2"),25),2))
thisnet <- network( data.frame(A,B) )

set.seed(109)
sex     <- gl(2,4,label=c("male","female"))
age     <- gl(2,2,8)
yield   <- rnorm(length(sex))
weight  <- rnorm(length(sex))
mydata  <- data.frame(sex,age,yield,weight)
mynw    <- network(mydata)

# adjust prior probability distribution
localprob(mynw,"sex")   <- c(0.4,0.6)
localprob(mynw,"age")   <- c(0.6,0.4)
localprob(mynw,"yield") <- c(2,0)
localprob(mynw,"weight")<- c(1,0)

print(mynw)
plot(mynw)

prior <- jointprior(mynw)
mynw  <- getnetwork(learn(mynw,mydata,prior))
thebest <- getnetwork(autosearch(mynw,mydata,prior))

print(mynw,condposterior=TRUE)

## Not run: savenet(mynw,file("yield.net"))
A <- factor(rep(c("A1","A2"),50))
B <- factor(rep(rep(c("B1","B2"),25),2))
thisnet <- network( data.frame(A,B) )

set.seed(109)
sex     <- gl(2,4,label=c("male","female"))
age     <- gl(2,2,8)
yield   <- rnorm(length(sex))
weight  <- rnorm(length(sex))
mydata  <- data.frame(sex,age,yield,weight)
mynw    <- network(mydata)

# adjust prior probability distribution
localprob(mynw,"sex")   <- c(0.4,0.6)
localprob(mynw,"age")   <- c(0.6,0.4)
localprob(mynw,"yield") <- c(2,0)
localprob(mynw,"weight")<- c(1,0)

print(mynw)
plot(mynw)

prior <- jointprior(mynw)
mynw  <- getnetwork(learn(mynw,mydata,prior))
thebest <- getnetwork(autosearch(mynw,mydata,prior))

print(mynw,condposterior=TRUE)

## Not run: savenet(mynw,file("yield.net"))

Tools for manipulating networks

Description

Various extraction/replacement functions for networks

Usage

modelstring(x)
makenw(tb,template)
as.network(nwstring,template)
size(x)
banlist(x)
banlist(x) <- value
getnetwork(x)
gettrylist(x)
modelstring(x)
makenw(tb,template)
as.network(nwstring,template)
size(x)
banlist(x)
banlist(x) <- value
getnetwork(x)
gettrylist(x)

Arguments

`x`	an object of class `network`.
`tb`	a table output from `autosearch` or `heuristic` in the list property `table`. Can be translated into a `networkfamily`.
`template`	an object of class `network` with the same nodes as the networks described in the table `tb`.
`nwstring`	a string representing the network.
`value`	a numeric matrix with two columns. Each row contains the indices `i -> j` of arrows that may not be allowed in the directed acyclic graph.

Details

The string representation of a network is a minimal size representation to speed up calculations. The functions modelstring, as.network and makenw converts between the string represention and network objects.

size extracts the number of nodes in a network object.

banlist extracts the banlist from a network object.

getnetwork and gettrylist are accessor function that extracts a network object or trylist from the result from autosearch, heuristic, learn, perturb, networkfamily, drawnetwork.

Generates and learns all networks for a set of variables.

Description

Method for generating and learning all networks that are possible for a given set of variables. These may be plotted or printed. Also, functions for sorting according to the network score (see nwfsort) and for making a network family unique (see the unique method for networkfamily objects) are available.

Usage

networkfamily(data,nw=network(data), prior=jointprior(nw),
              trylist=vector("list",size(nw)), timetrace=TRUE) 

## S3 method for class 'networkfamily'
print(x,...)
## S3 method for class 'networkfamily'
plot(x,layout=,
        cexscale=5,arrowlength=0.1,sscale=7,...) 
networkfamily(data,nw=network(data), prior=jointprior(nw),
              trylist=vector("list",size(nw)), timetrace=TRUE) 

## S3 method for class 'networkfamily'
print(x,...)
## S3 method for class 'networkfamily'
plot(x,layout=,
        cexscale=5,arrowlength=0.1,sscale=7,...)

Arguments

`nw`	an object of class `network`. This should be the empty network for the set of variables.
`data`	a data frame used for learning the network, see `network`.
`prior`	a list containing parameter priors, generated by `jointprior`.
`trylist`	a list used internally for reusing learning of nodes, see `maketrylist`.
`timetrace`	a logical. If `TRUE`, prints some timing information on the screen.
`x`	an object of class `networkfamily`.
`layout`	a numeric two dimensional vector with the number of plots in the rows and columns of each plotting page. Default set to `rep(min(1+floor(sqrt(length(x))),5),2)`.
`cexscale`	a numeric. A scaling parameter to set the size of the nodes.
`arrowlength`	a numeric, which gives the length of the arrow heads.
`sscale`	a numeric. The nodes are initially placed on a circle with radius `sscale`.
`...`	additional plot arguments passed to the plot method for network objects.

Details

networkfamily generates and learns all possible networks with the nodes given as in the initial network nw. This is done by successively trying to generate the networks with all possible arrows to/from each node (see addarrows). If there is a ban list present in nw (see network), then this is respected, as are the restrictions described in insert.

After generation of all possible networks, a test for cycles (see cycletest) is performed and only networks with directed acyclic graphs are returned.

Value

The function networkfamily returns a list with two components,

`nw`	an object of class `networkfamily`.
`trylist`	an updated list used internally for reusing learning of nodes, see `maketrylist`.

Note

Generating all possible networks can be very time consuming!

Author(s)

Susanne Gammelgaard Bottcher,
Claus Dethlefsen [email protected].

Examples

data(rats)
allrats <- getnetwork(networkfamily(rats))
plot(allrats)
print(allrats)
data(rats)
allrats <- getnetwork(networkfamily(rats))
plot(allrats)
print(allrats)

Representation of nodes

Description

An important part of a network is the list of nodes. The nodes summarize the local properties of a node, given the parents of the node.

Usage

node (idx,parents,type="discrete",name=paste(idx),
                 levels=2,levelnames=paste(1:levels),position=c(0,0)) 
## S3 method for class 'node'
 print(x,filename=NA,condposterior=TRUE,condprior=TRUE,...) 
## S3 method for class 'node'
 plot(x,cexscale=10,notext=FALSE,...)
nodes(nw)
nodes(nw) <- value
node (idx,parents,type="discrete",name=paste(idx),
                 levels=2,levelnames=paste(1:levels),position=c(0,0)) 
## S3 method for class 'node'
 print(x,filename=NA,condposterior=TRUE,condprior=TRUE,...) 
## S3 method for class 'node'
 plot(x,cexscale=10,notext=FALSE,...)
nodes(nw)
nodes(nw) <- value

Arguments

`x`	an object of class `node`.
`parents`	a numeric vector with indices of the parents of the node.
`idx`	an integer, which gives the index of the node (the column number of the corresponding data frame).
`type`	a string, which gives the type of the node. Either `"discrete"` (for factors) or `"continuous"` (for numeric).
`name`	a string, which gives the name used when plotting and printing. Defaults to the column name in the data frame.
`levels`	an integer. If `type` is `"discrete"`, this is the number of levels for the discrete variable.
`levelnames`	if `type` is `"discrete"`, this is a vector of strings (same length as `levels`) with the names of the levels. If `type` is `"continuous"`, the argument is ignored.
`position`	a numeric vector with coordinates where the node should appear in the plot. Usually set by `network` and `drawnetwork`.
`nw`	an object of class `network`.
`value`	a list of elements of class `node`.
`filename`	a string or `NA`. If not `NA`, output is printed to a file.
`condprior`	a logical. If `TRUE`, the conditional prior is printed, see `conditional`.
`condposterior`	a logical. If `TRUE`, the conditional posterior is printed, see `learn`.
`cexscale`	a numeric. Scale parameter to set the size of the nodes.
`notext`	a logical. If `TRUE`, no text is displayed in the nodes on the plot.
`...`	additional plot arguments.

Details

The operations on a node are typically done when operating on a network, so these functions are not to be called directly.

When a network is created with network, the nodes in the nodelist are created using the node procedure.

Local probability distributions are added as the property prob to each node using prob.node. If the node is continuous, this is a numeric vector with the conditional variance and the conditional regression coefficients arising from a regression on the continuous parents, using data. If the node has discrete parents, prob is a matrix with a row for each configuration of the discrete parents. If the node is discrete, prob is a multiway array which gives the conditional probability distribution for each configuration of the discrete parents. The generated prob can be replaced to match the prior information available.

nodes gives the list of nodes of a network. localprob gives the probability distribution for each node in the network.

Value

The node creator function returns an object of class node, which is a list with the following elements (properties),

`idx`	an integer. A unique index for this node. It MUST correspond to the column index of the variable in the data frame.
`name`	a string. The printed name of the node.
`type`	a string. Either `"continuous"` or `"discrete"`.
`levels`	an integer. If the node is of type `"discrete"`, this integer is the number of levels of the node.
`levelnames`	if `type` is `"discrete"`, this is a vector of strings (same length as `levels`) with the names of the levels. If `type` is `"continuous"`, the node does not have this property.
`parents`	a vector of indices of the parents to this node. It is best to manage this vector using the `insert` function.
`prob`	a numeric vector, matrix or multiway array, giving the initial probability distribution. If the node is discrete, `prob` is a multiway array. If the node is continuous, `prob` is a matrix with one row for each configuration of the discrete parents, reducing to a vector if the node has no discrete parents.
`condprior`	a list, generated by `conditional` giving the parameter priors deduced from `jointprior` using the master prior procedure (see `localmaster`).
`condposterior`	a list, which gives the parameter posteriors obtained from `learnnode`.
`loglik`	a numeric giving the log likelihood contribution for this node, calculated in `learnnode`.
`simprob`	a numeric vector, matrix or multiway array similar to `prob`, added by `makesimprob` and used by `rnetwork`.

Author(s)

Susanne Gammelgaard Bottcher,
Claus Dethlefsen [email protected].

The number of possible networks

Description

Calculates the number of different directed acyclic graphs for a set of discrete and continuous nodes.

Usage

numbermixed(nd,nc)
numbermixed(nd,nc)

Arguments

`nd`	an integer, which gives the number of discrete nodes.
`nc`	an integer, which gives the number of continuous nodes.

Details

No arrows are allowed from continuous nodes to discrete nodes. Cycles are not allowed. The number of networks is given by Bottcher (2003), using the result in Robinson (1977).

When nd+nc>15, the procedure is quite slow.

Value

A numeric containing the number of directed acyclic graphs with the given node configuration.

Author(s)

Susanne Gammelgaard Bottcher,
Claus Dethlefsen [email protected].

References

Bottcher, S.G. (2003). Learning Conditional Gaussian Networks. Aalborg University, 2003.

Robinson, R.W. (1977). Counting unlabeled acyclic digraphs, Lecture Notes in Mathematics, 622: Combinatorial Mathematics.

Examples

numbermixed(2,2)
## Not run: numbermixed(5,10)
numbermixed(2,2)
## Not run: numbermixed(5,10)

Sorts a list of networks

Description

According to the score property of the networks in a network family, the networks are sorted and the relative score, i.e.\ the score of a network relative to the highest score, is attached to each network as the relscore property.

Usage

nwfsort(nwf)
nwfsort(nwf)

Arguments

nwf

an object of class networkfamily.

Author(s)

Susanne Gammelgaard Bottcher,
Claus Dethlefsen [email protected].

Perturbs a network

Description

Randomly insert/delete/turn arrows to obtain another network.

Usage

perturb(nw,data,prior,degree=size(nw),trylist=vector("list",size(nw)),
        nocalc=FALSE,timetrace=TRUE) 
perturb(nw,data,prior,degree=size(nw),trylist=vector("list",size(nw)),
        nocalc=FALSE,timetrace=TRUE)

Arguments

`nw`	an object of class `network`, from which arrows are added/removed/turned.
`data`	a data frame used for learning the network, see `network`.
`prior`	a list containing parameter priors, generated by `jointprior`.
`degree`	an integer, which gives the number of attempts to randomly insert/remove/turn an arrow.
`trylist`	a list used internally for reusing learning of nodes, see `maketrylist`.
`nocalc`	a logical. If `TRUE` no learning procedure is called, see eg. `rnetwork`.
`timetrace`	a logical. If `TRUE`, prints some timing information on the screen.

Details

Given the initial network, a new network is constructed by randomly choosing an action: remove, turn, add. After the action is chosen, we choose randomly among all possibilities of that action. If there are no possibilites, the unchanged network is returned.

Value

A list with two elements that may be accessed using getnetwork and gettrylist. The elements are

`nw`	an object of class `network` with the generated network.
`trylist`	an updated list used internally for reusing learning of nodes, see `maketrylist`.

Author(s)

Susanne Gammelgaard Bottcher,
Claus Dethlefsen [email protected].

Examples

set.seed(200)
data(rats)
fit       <- network(rats)
fit.prior <- jointprior(fit)
fit       <- getnetwork(learn(fit,rats,fit.prior))
fit.new   <- getnetwork(perturb(fit,rats,fit.prior,degree=10))

data(ksl)
ksl.nw    <- network(ksl)
ksl.rand  <- getnetwork(perturb(ksl.nw,nocalc=TRUE,degree=10))
plot(ksl.rand)
set.seed(200)
data(rats)
fit       <- network(rats)
fit.prior <- jointprior(fit)
fit       <- getnetwork(learn(fit,rats,fit.prior))
fit.new   <- getnetwork(perturb(fit,rats,fit.prior,degree=10))

data(ksl)
ksl.nw    <- network(ksl)
ksl.rand  <- getnetwork(perturb(ksl.nw,nocalc=TRUE,degree=10))
plot(ksl.rand)

Local probability distributions

Description

Methods for accessing or changing the local probability distributions and for accessing the local prior and posterior distributions

Usage

prob(x,df,...)

## S3 method for class 'node'
 prob(x,df,nw,...)
## S3 method for class 'network'
 prob(x,df,...)

localprob(nw)
localprob(nw,name) <- value

localprior(node)
localposterior(node)

prob(x,df,...)

## S3 method for class 'node'
 prob(x,df,nw,...)
## S3 method for class 'network'
 prob(x,df,...)

localprob(nw)
localprob(nw,name) <- value

localprior(node)
localposterior(node)

Arguments

`x`	an object of class `node` or `network`.
`df`	a data frame, where the columns define the variables. A continuous variable should have type `numeric` and discrete varibles should have type `factor`.
`nw`	an object of class `network`.
`node`	an object of class `node`.
`name`	a string, which gives the node name.
`...`	additional arguments for specific methods.
`value`	If the node is continuous, this is a numeric vector with the conditional variance and the conditional regression coefficients arising from a regression on the continuous parents, using data. If the node has discrete parents, it is a matrix with a row for each configuration of the discrete parents. If the node is discrete, it is a multiway array which gives the conditional probability distribution for each configuration of the discrete parents.

Details

The prob methods add local probability distributions to each node. If the node is continuous, this is a numeric vector with the conditional variance and the conditional regression coefficients arising from a regression on the continuous parents, using data. If the node has discrete parents, prob is a matrix with a row for each configuration of the discrete parents. If the node is discrete, prob is a multiway array which gives the conditional probability distribution for each configuration of the discrete parents. The generated prob can be replaced to match the prior information available.

localprob returns the probability distribution for each node in the network.

In a learned network, the local prior and posterior can be accessed for each node using localprior and localposterior.

Author(s)

Susanne Gammelgaard Bottcher,
Claus Dethlefsen [email protected].

Weightloss of rats

Description

An artificial data set. 24 rats (12 female, 12 male) have been randomized to use one of three drugs (products for loosing weight). The weightloss for each rat is noted after one and two weeks.

Format

A data frame with 4 variables.

Sex: a factor with two levels: "M" (male), "F" (female)
Drug: a factor with three levels: "D1", "D2", "D3" (three types)
W1: a numeric: weightloss, week one.
W2: a numeric: weightloss, week 2.

References

Morrison, D.F. (1976). Multivariate Statistical Methods. McGraw-Hill, USA.

Edwards, D. (1995). Introduction to Graphical Modelling, Springer-Verlag. New York.

Reads/saves .net file

Description

Reads/saves a Bayesian network specification in the .net language used by Hugin.

Usage

readnet(con=file("default.net"))
savenet(nw, con=file("default.net"))
readnet(con=file("default.net"))
savenet(nw, con=file("default.net"))

Arguments

`con`	a connection.
`nw`	an object of class `network`.

Details

readnet reads only the structure of a network, i.e.\ the directed acyclic graph.

savenet exports the prob property for each node in the network object along with the network structure defined by the parents of each node.

Value

readnet creates an object of class network with the nodes specified as in the .net connection. The network has not been learned and the nodes do not have prob properties (see prob.network).

savenet writes the object to the connection.

Note

The call to readnet(savenet(network)) is not the identity function as information is thrown away in both savenet and readnet.

Author(s)

Susanne Gammelgaard Bottcher,
Claus Dethlefsen [email protected].

Examples

data(rats)
nw <- network(rats)
## Not run: savenet(nw,file("default.net"))
## Not run: nw2 <- readnet(file("default.net"))
## Not run: nw2 <- prob(nw2,rats)

data(rats)
nw <- network(rats)
## Not run: savenet(nw,file("default.net"))
## Not run: nw2 <- readnet(file("default.net"))
## Not run: nw2 <- prob(nw2,rats)

Simulation of data sets with a given dependency structure

Description

Given a network with nodes having the simprob property, rnetwork simulates a data set.

Usage

rnetwork(nw, n=24, file="") 
rnetwork(nw, n=24, file="")

Arguments

`nw`	an object of class `network`, where each node has the property `simprob` (see `makesimprob`).
`n`	an integer, which gives the number of cases to simulate.
`file`	a string. If non-empty, the data set is stored there.

Details

The variables are simulated one at a time in an order that ensures that the parents of the node have already been simulated. For discrete variables a multinomial distribution is used and for continuous variables, a Gaussian distribution is used, according to the simprob property in each node.

Value

A data frame with one row per case. If a file name is given, a file is created with the data set.

Author(s)

Susanne Gammelgaard Bottcher,
Claus Dethlefsen [email protected].

Examples

A  <- factor(NA,levels=paste("A",1:2,sep=""))
B  <- factor(NA,levels=paste("B",1:3,sep=""))
c1 <- NA
c2 <- NA
df <- data.frame(A,B,c1,c2)

nw <- network(df,doprob=FALSE) # doprob must be FALSE
nw <- makesimprob(nw)          # create simprob properties

set.seed(944) 
sim <- rnetwork(nw,n=100)    # create simulated data frame
A  <- factor(NA,levels=paste("A",1:2,sep=""))
B  <- factor(NA,levels=paste("B",1:3,sep=""))
c1 <- NA
c2 <- NA
df <- data.frame(A,B,c1,c2)

nw <- network(df,doprob=FALSE) # doprob must be FALSE
nw <- makesimprob(nw)          # create simprob properties

set.seed(944) 
sim <- rnetwork(nw,n=100)    # create simulated data frame

Network score

Description

Accessor for the score from a node or network

Usage

score(x,...)

## S3 method for class 'node'
    score(x,...)
## S3 method for class 'network'
 score(x,...)

score(x,...)

## S3 method for class 'node'
    score(x,...)
## S3 method for class 'network'
 score(x,...)

Arguments

`x`	an object of class `node` or `network`.
`...`	additional arguments for specific methods.

Value

For networks, the log network score is returned. For nodes, the contribution to the log network score is returned.

Author(s)

Susanne Gammelgaard Bottcher,
Claus Dethlefsen [email protected].

Makes a network family unique.

Description

Removes networks that are equal or equivalent to networks already in the network family.

Usage

## S3 method for class 'networkfamily'
unique(x,incomparables=FALSE,equi=FALSE,timetrace=FALSE,epsilon=1e-12,...)
## S3 method for class 'networkfamily'
unique(x,incomparables=FALSE,equi=FALSE,timetrace=FALSE,epsilon=1e-12,...)

Arguments

`x`	an object of class `networkfamily`.
`incomparables`	a logical, but has no effect.
`equi`	a logical. If `TRUE`, also equivalent networks are thrown out (i.e. if their score is within `epsilon` from another network).
`timetrace`	a logical. If `TRUE`, prints some timing information on the screen.
`epsilon`	a numeric, which measures how close network scores are allowed to be from each other to be 'equivalent'.
`...`	further arguments (no effect)

Author(s)

Susanne Gammelgaard Bottcher,
Claus Dethlefsen [email protected].

Examples

data(rats)
rats.nwf <- networkfamily(rats)
rats.nwf2<- unique(getnetwork(rats.nwf),equi=TRUE)
data(rats)
rats.nwf <- networkfamily(rats)
rats.nwf2<- unique(getnetwork(rats.nwf),equi=TRUE)

Package 'deal'

Help Index

Greedy search

Description

Usage

Arguments

Details

Value

Author(s)

See Also

Examples

Graphical interface for editing networks

Description

Usage

Arguments

Details

Value

Author(s)

See Also

Examples

From a network family, generate LaTeX output

Description

Usage

Arguments

Value

Author(s)

See Also

Examples

Insert/remove an arrow in network

Description

Usage

Arguments

Details

Value

Author(s)

Examples

Calculates the joint prior distribution

Description

Usage

Arguments

Details

Value

Author(s)

References

See Also

Examples

Health and social characteristics

Description

Format

Estimation of parameters in the local probability distributions

Description

Usage

Arguments

Details

Value

Author(s)

References

See Also

Examples

Make a suggestion for simulation probabilities

Description

Usage

Arguments

Details

Value

Author(s)

See Also

Creates the full trylist

Description

Usage

Arguments

Details

Value

Author(s)

See Also

Examples

Bayesian network data structure

Description

Usage

Arguments