kpcalg (version 1.0.1)

hsic.gamma: Hilber Schmidt Independence Criterion gamma test

Description

Test to check the independence between two variables x and y using HSIC. The hsic.gamma() function, uses Hilbert-Schmidt independence criterion to test for independence between random variables.

Usage

hsic.gamma(x, y, sig = 1, numCol = 100)

Arguments

x

data of first sample

y

data of second sample

sig

Gaussian kernel width for HSIC tests. Default is 1

numCol

maximum number of columns that we use for the incomplete Cholesky decomposition

Value

hsic.gamma() returns a list with class htest containing hsic.gamma() returns a list with class htest containing

Details

Let x and y be two samples of length n. Gram matrices K and L are defined as: $K_{i,j} =exp((x_i-x_j)^2/sig^2)$ and $L_{i,j} =exp((y_i-y_j)^2/sig^2)$. $H_{i,j} = delta_{i,j} - 1/n$. Let $A=HKH$ and $B=HLH$, then $HSIC(x,y)=Tr(AB)/n^2$. Gamma test compares HSIC(x,y) with the $alpha$ quantile of the gamma distribution with mean and variance such as HSIC under independence hypothesis.

References

A. Gretton et al. (2005). Kernel Methods for Measuring Independence. JMLR 6 (2005) 2075-2129.

See Also

hsic.perm, hsic.clust, kernelCItest

Examples

library(energy)
set.seed(10)
#independence
x <- runif(300)
y <- runif(300)

hsic.gamma(x,y)
hsic.perm(x,y)
dcov.gamma(x,y)
dcov.test(x,y)

#uncorelated but not dependent
z <- 10*(runif(300)-0.5)
w <- z^2 + 10*runif(300)

cor(z,w)
hsic.gamma(z,w)
hsic.perm(z,w)
dcov.gamma(z,w)
dcov.test(z,w)