R/rags2ridgesVariants.r
support4ridgeP.RdConvert the support of an undirected, chordal graph into a lists of cliques
and separators. When the graph is not chordal, it is triangulated to make it
so. The undirected graph may be specified as an adjacency matrix, or by the
complement of its support as a matrix with the indices of the adjancency
matrix corresponding to absent edges. The function thus caters for the two
different types of output from the
sparsify-function. The function is meant
to preceede the ridgePchordal, as it its output directly feeds
into the latter.
support4ridgeP(adjMat = NULL, nNodes = NULL, zeros = NULL, verbose = FALSE)Adjacency matrix of an undirected graph.
Positive integer of length one: number nodes of the
network.
A matrix with indices of entries of the adjacency matrix
that are zero. The matrix comprises two columns, each row corresponding to
an entry of the adjacency matrix.
A logical indicator: should intermediate output be
printed on the screen?
A list-object comprising three slots: 'zeros', 'cliques,
'separators' and 'addedEdges'. The 'zeros'-slot: a matrix with
indices of entries of the adjacency matrix that are zero. The matrix
comprises two columns, each row corresponding to an entry of the adjacency
matrix. The first column contains the row indices and the second the column
indices. The specified graph should be undirected and decomposable. If not,
it is symmetrized and triangulated. Hence, it may differ from the input
'zeros'. The 'cliques'-slot: a list-object containing the node
indices per clique as obtained from the rip-function. The
'separators'-slot: a list-object containing the node indices per
clique as obtained from the rip-function. The 'addedEdges'-slot: a
matrix with indices of edges that have been added in the
triangulation.
Essentially, it is a wrapper for the rip-function from the
gRbase-package, which takes different input and yields slightly
different output. Its main purpose is to mold the input such that it is
convenient for the ridgePchordal-function, which provides ridge
maximum likelihood estimation of the precision matrix with known support.
Lauritzen, S.L. (2004). Graphical Models. Oxford University Press.
# obtain some (high-dimensional) data
p <- 8
n <- 100
set.seed(333)
Y <- matrix(rnorm(n*p), nrow = n, ncol = p)
# create sparse precision
P <- covML(Y)
P[1:3, 6:8] <- 0
P[6:8, 1:3] <- 0
# draw some data
S <- covML(matrix(rnorm(n*p), nrow = n, ncol = p))
# obtain (triangulated) support info
zeros <- which(P==0, arr.ind=TRUE)
supportP <- support4ridgeP(adjMat=adjacentMat(P))
# alternative specification of the support
zeros <- which(P==0, arr.ind=TRUE)
supportP <- support4ridgeP(nNodes=p, zeros=zeros)
# estimate precision matrix with known (triangulated) support
Phat <- ridgePchordal(S, 0.1, zeros=supportP$zeros,
cliques=supportP$cliques, separators=supportP$separators)
#>
#> Progress report ....
#> -> ----------------------------------------------------------------------
#> -> optimization over : 27 out of 36 unique
#> -> parameters (75%)
#> -> cond. number of initial estimate : 1.93 (if >> 100, consider
#> -> larger values of lambda)
#> -> # graph components : 1 (optimization per component)
#> -> optimization per component :
#>
|
| | 0%
|
|......................................................................| 100%
#>
#> -> estimation done ...
#> -> formatting output ...
#> -> overall summary ....
#> -> initial pen. log-likelihood : -7.62070127
#> -> optimized pen. log-likelihood : -7.62070123
#> -> optimization : converged (most likely)
#> -> for all components
#> -> ----------------------------------------------------------------------