# Kernel Conditional Independence test Test to check the (conditional) dependence between two variables x and y given a set of variables S, using independence criteria. The kernelCItest() function, uses Distance Covariance or Hilbert-Schmidt Independence Criterion to test for the (conditional) independence between random variables, with an interface that can easily by used in `skeleton`, `pc` or `kpc`. ```r kernelCItest(x, y, S = NULL, suffStat, verbose = FALSE, data, ic.method = NULL, p = NULL, index = NULL, sig = NULL, numCol = NULL, numCluster = NULL, eps = NULL, paral = NULL) ``` ## Arguments - `x, y, S`: It is tested, whether x and y are conditionally independent given the subset S of the remaining nodes. x, y, S all are integers, corresponding to variable or node numbers. - `suffStat`: a list of parameters consisting of data, ic.method, p, index, sig, numCol, numCluster, eps, paral - `verbose`: a logical parameter, if TRUE, detailed output is provided. - `data`: numeric matrix witch collumns representing variables and rows representing samples - `ic.method`: Method for the (conditional) independence test: Distance Covariance (permutation or gamma test), HSIC (permutation or gamma test) or HSIC cluster - `p`: Number of permutations for Distance Covariance, HSIC permutation and HSIC cluster tests. Default is Distance Covariance - `index`: Number in (0,2] the power of the distance in the Distance Covariance - `sig`: Gaussian kernel width for HSIC tests. Default is 1 - `numCol`: Number of columns used in the incomplete Cholesky decomposition. Default is 50 - `numCluster`: Number of clusters for kPC clust algorithm - `eps`: Normalization parameter for kPC clust. Default is 0.1 - `paral`: Number of cores to use for parallel calculations. ## Returns kernelCItest() returns the p-value of the test. ## Examples ```r set.seed(10) library(pcalg) z <- 10*runif(300) w <- 10*runif(300) x <- sin(z) + runif(300) y <- cos(z) + runif(300) data <- cbind(x,y,z,w) #conditionally independent test1a <- kernelCItest(x=1,y=2,S=c(3),suffStat = list(data=data,ic.method="dcc.gamma")) test2a <- kernelCItest(x=1,y=2,S=c(3),suffStat = list(data=data,ic.method="dcc.perm")) test3a <- kernelCItest(x=1,y=2,S=c(3),suffStat = list(data=data,ic.method="hsic.gamma")) test4a <- kernelCItest(x=1,y=2,S=c(3),suffStat = list(data=data,ic.method="hsic.perm")) test5a <- kernelCItest(x=1,y=2,S=c(3),suffStat = list(data=data,ic.method="hsic.clust")) test6a <- gaussCItest( x=1,y=2,S=c(3),suffStat = list(C=cor(data),n=4)) test1a test2a test3a test4a test5a test6a #dependent test1b <- kernelCItest(x=1,y=2,S=c(4),suffStat = list(data=data,ic.method="dcc.gamma")) test2b <- kernelCItest(x=1,y=2,S=c(4),suffStat = list(data=data,ic.method="dcc.perm")) test3b <- kernelCItest(x=1,y=2,S=c(4),suffStat = list(data=data,ic.method="hsic.gamma")) test4b <- kernelCItest(x=1,y=2,S=c(4),suffStat = list(data=data,ic.method="hsic.perm")) test5b <- kernelCItest(x=1,y=2,S=c(4),suffStat = list(data=data,ic.method="hsic.clust")) test6b <- gaussCItest( x=1,y=2,S=c(4),suffStat = list(C=cor(data),n=4)) test1b test2b test3b test4b test5b test6b ``` ## Author(s) Petras Verbyla (petras.verbyla@mrc-bsu.cam.ac.uk ) and Nina Ines Bertille Desgranges ## References G. Szekely, M. Rizzo and N. Bakirov (2007). Measuring and Testing Dependence by Correlation of Distances. The Annals of Statistics 2007, Vol. 35, No. 6, 2769-2794. A. Gretton et al. (2005). Kernel Methods for Measuring Independence. JMLR 6 (2005) 2075-2129. R. Tillman, A. Gretton and P. Spirtes (2009). Nonlinear directed acyclic structure learning with weakly additive noise model. NIPS 22, Vancouver.

kernelCItest function