gRapHD (version 0.2.2)

minForest: Minimum forest

Description

Returns the forest that minimises the -2*log-likelihood, AIC, or BIC using Chow-Liu lgorithm.

Usage

minForest(dataset,homog=TRUE,forbEdges=NULL,stat="BIC",
          cond=NULL,...)

Arguments

dataset

matrix or data frame (nrow(dataset) observations and ncol(dataset) variables).

homog

TRUE for homogeneous covariance structure, FALSE for heterogeneous. This is only meaningful with mixed models. Default is homogeneous (TRUE).

forbEdges

matrix specifying edges that should not be considered. Matrix with 2 columns, each row representing one edge, and each column one of the vertices in the edge. Default is NULL.

stat

measure to be minimized: LR (-2*log-likelihood), AIC, or BIC. Default is LR. It can also be a user defined function with format: FUN(newEdge, numCat, dataset); where

cond

list with complete sets of vertices, to specify mandatory edges.

...

arguments to be passed to the user function in stat.

Value

• A list containing:
• edges
  matrix with 2 columns, each row representing one edge, and each column one of the vertices in the edge. Column 1 contains the vertex with lower index.
• p
  number of variables (vertices) in the model.
• stat.minForest
  measure used (LR, AIC, or BIC).
• statSeq
  vector with value of stat.minForest for each edge.
• vertNames
  vector with the original vertices' names. If there are no names in dataset then the vertices will be named according to the original column indexes in dataset.
• numCat
  vector with number of levels for each variable (0 if continuous).
• homog
  TRUE if the covariance is homogeneous.
• numP
  vector with number of estimated parameters for each edge.
• minForest
  first and last edges found with minForest.

Details

Returns for the tree or forest that minimizes the -2*log-likelihood, AIC, or BIC. If the log-likelihood is used, the result is a tree, if AIC or BIC is used, the result is a tree or forest. The dataset contains variables (vertices) in the columns, and observations in the rows. The result has vertices numbered according to the column indexes in vertNames. All discrete variables must be factors. All factor levels must be represented in the data. Missing values are not allowed.

References

Chow, C.K. and Liu, C.N. (1968) Approximating discrete probability distributions with dependence trees. IEEE Transactions on Information Theory, Vol. IT-14, 3:462-7. Edwards, D., de Abreu, G.C.G. and Labouriau, R. (2010). Selecting high- dimensional mixed graphical models using minimal AIC or BIC forests. BMC Bioinformatics, 11:18.

Examples

set.seed(7,kind="Mersenne-Twister")
dataset <- matrix(rnorm(1000),nrow=100,ncol=10)
m <- minForest(dataset,stat="BIC")

#######################################################################
# Example with continuous variables
data(dsCont)
# m1 <- minForest(dataset,homog=TRUE,forbEdges=NULL,stat="LR")
#          1. in this case, there is no use for homog
#          2. no forbidden edges
#          3. the measure used is the LR (the result is a tree)
m1 <- minForest(dsCont,homog=TRUE,forbEdges=NULL,stat="LR")
plot(m1,numIter=1000)

#######################################################################
# Example with discrete variables
data(dsDiscr)
# m1 <- minForest(dataset,homog=TRUE,forbEdges=NULL,stat="LR")
#          1. in this case, there is no use for homog
#          2. no forbidden edges
#          3. the measure used is the LR (the result is a tree)
m1 <- minForest(dsDiscr,homog=TRUE,forbEdges=NULL,stat="LR")
plot(m1,numIter=1000)

#######################################################################
# Example with mixed variables
data(dsMixed)
# m1 <- minForest(dataset,homog=TRUE,forbEdges=NULL,stat="LR")
#          1. it is to be considered homogeneous
#          2. no forbidden edges
#          3. the measure used is the LR (the result is a tree)
m1 <- minForest(dsMixed,homog=TRUE,forbEdges=NULL,stat="LR")
plot(m1,numIter=1000)

#######################################################################
# Example using a user defined function
#   The function userFun calculates the same edges weigths as the 
# option stat="LR". It means that the final result, using either 
# option, is the same.
userFun <- function(newEdge,numCat,dataset)
{
  sigma <- var(dataset[,newEdge])
  v <- nrow(dataset)*log(prod(diag(sigma))/det(sigma))
  return(c(v,1))
}

data(dsCont)
m <- minForest(dsCont,stat="LR")
m1 <- minForest(dsCont,stat=userFun)
identical(m@edges,m1@edges)

#######################################################################
# Example with mandatory edges (the so-called conditional Chow-Liu 
# algorithm).  The edges (1,2), (1,3) and (2,3) are specified as 
# mandatory. The algorithm returns the optimal graph containing the 
# mandatory edges such that only cycles with mandatory edges are 
# allowed.
data(dsCont)
m1 <- minForest(dsCont,cond=list(1:3))
plot(m1)