# Estimate the WAN-PDAG using the kPC Algorithm 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. ```r 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. ## Returns An object of class "pcAlgo" (see `pcAlgo`) containing an estimate of the equivalence class of the underlying DAG. ## Details For more information: `pc`. ## Examples ```r ## 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) ``` ## Author(s) Petras Verbyla (petras.verbyla@mrc-bsu.cam.ac.uk ) ## References Tillman, R. E., Gretton, A. and Spirtes, P. (2009). Nonlinear directed acyclic structure learning with weakly additive noise model. NIPS 22, Vancouver.

kpc function