kpc {kpcalg}

Estimate the WAN-PDAG using the kPC Algorithm

Description

Estimates the weakly additive noise partially directed acyclic graph (WAN-PDAG) from observational data, using the kPC algorithm. This is a version of pc from pcalg package, that uses HSIC (hsic.gamma, hsic.perm or hsic.clust) or distance covariance (dcov.test or dcov.gamma) independence tests and udag2wanpdag instead of udag2pdag in the last step.

Usage

kpc(suffStat, indepTest, alpha, labels, p, fixedGaps = NULL,
  fixedEdges = NULL, NAdelete = TRUE, m.max = Inf, u2pd = c("relaxed",
  "rand", "retry"), skel.method = c("stable", "original", "stable.fast"),
  conservative = FALSE, maj.rule = FALSE, solve.confl = FALSE,
  verbose = FALSE)

Arguments

suffStat

a list of sufficient statistics, containing all necessary elements for the conditional independence decisions in the function indepTest

indepTest

A function for testing conditional independence. It is internally called as indepTest(x,y,S,suffStat), and tests conditional independence of x and y given S. Here, x and y are variables, and S is a (possibly empty) vector of variables (all variables are denoted by their column numbers in the adjacency matrix). suffStat is a list, see the argument above. The return value of indepTest is the p-value of the test for conditional independence. Default is kernelCItest.

alpha

significance level (number in (0,1) for the individual conditional independence tests.

labels

(optional) character vector of variable (or "node") names. Typically preferred to specifying p.

p

(optional) number of variables (or nodes). May be specified if labels are not, in which case labels is set to 1:p.

fixedGaps

A logical matrix of dimension p*p. If entry [i,j] or [j,i] (or both) are TRUE, the edge i-j is removed before starting the algorithm. Therefore, this edge is guaranteed to be absent in the resulting graph.

fixedEdges

A logical matrix of dimension p*p. If entry [i,j] or [j,i] (or both) are TRUE, the edge i-j is never considered for removal. Therefore, this edge is guaranteed to be present in the resulting graph.

NAdelete

If indepTest returns NA and this option is TRUE, the corresponding edge is deleted. If this option is FALSE, the edge is not deleted.

m.max

Maximal size of the conditioning sets that are considered in the conditional independence tests.

u2pd

String specifying the method for dealing with conflicting information when trying to orient edges (see details below).

skel.method

Character string specifying method; the default, "stable" provides an order-independent skeleton, see skeleton.

conservative

Logical indicating if the conservative PC is used. In this case, only option u2pd = "relaxed" is supported. Note that therefore the resulting object might not be extendable to a DAG. See details for more information.

maj.rule

Logical indicating that the triples shall be checked for ambiguity using a majority rule idea, which is less strict than the conservative PC algorithm. For more information, see details.

solve.confl

If TRUE, the orientation of the v-structures and the orientation rules work with lists for candidate sets and allow bi-directed edges to resolve conflicting edge orientations. In this case, only option u2pd = relaxed is supported. Note, that therefore the resulting object might not be a CPDAG because bi-directed edges might be present. See details for more information.

verbose

If TRUE, detailed output is provided.

Details

For more information: pc.

Value

An object of class "pcAlgo" (see pcAlgo) containing an estimate of the equivalence class of the underlying DAG.

Author(s)

Petras Verbyla ([e-mail])

References

Tillman, R. E., Gretton, A. and Spirtes, P. (2009). Nonlinear directed acyclic structure learning with weakly additive noise model. NIPS 22, Vancouver.

Examples

## Not run: 
library(pcalg)
set.seed(4)
n <- 300
data <- NULL
x1 <- 2*(runif(n)-0.5)
x2 <- x1 + runif(n)-0.5
x3 <- x1^2 + 0.6*runif(n)
x4 <- rnorm(n)
x5 <- x3 + x4^2 + 2*runif(n)
x6 <- 10*(runif(n)-0.5)
x7 <- x6^2 + 5*runif(n)
x8 <- 2*x7^2 + 1.5*rnorm(n)
x9 <- x7 + 4*runif(n)
data <- cbind(x1,x2,x3,x4,x5,x6,x7,x8,x9)
true <- matrix(0,9,9)
true[c(1),c(2,3)]<-true[c(3,4),5]<-true[c(6),c(7)]<-true[c(7),c(8)]<-true[7,9]<-1

pc <- pc(suffStat = list(C = cor(data), n = 9),
         indepTest = gaussCItest,
         alpha = 0.9,
         labels = colnames(data),
         u2pd = "relaxed",
         skel.method = "stable",
         verbose = TRUE)
kpc1 <- kpc(suffStat = list(data=data, ic.method="dcc.perm"),
            indepTest = kernelCItest,
            alpha = 0.1,
            labels = colnames(data),
            u2pd = "relaxed",
            skel.method = "stable",
            verbose = TRUE)
kpc2 <- kpc(suffStat = list(data=data, ic.method="hsic.gamma"),
            indepTest = kernelCItest,
            alpha = 0.1,
            labels = colnames(data),
            u2pd = "relaxed",
            skel.method = "stable",
            verbose = TRUE)
kpc3 <- kpc(suffStat = list(data=data, ic.method="hsic.perm"),
            indepTest = kernelCItest,
            alpha = 0.1,
            labels = colnames(data),
            u2pd = "relaxed",
            skel.method = "stable",
            verbose = TRUE)
kpc4 <- kpc(suffStat = list(data=data, ic.method="hsic.clust"),
            indepTest = kernelCItest,
            alpha = 0.1,
            labels = colnames(data),
            u2pd = "relaxed",
            skel.method = "stable",
            verbose = TRUE)

if (require(Rgraphviz)) {
 par(mfrow=c(2,3))
 plot(pc,main="pc")
 plot(kpc1,main="dpc.perm")
 plot(kpc2,main="kpc.gamma")
 plot(kpc3,main="kpc.perm")
 plot(kpc4,main="kpc.clust")
 plot(as(true,"graphNEL"),main="True DAG")
}

## End(Not run)