wgcm.fix {weightedGCM}

Weighted Generalised Covariance Measure (WGCM) With Fixed Weight Functions Conditional Independence Test

Description

The Weighted Generalised Covariance Measure (WGCM) with Fixed Weight Functions is a test for conditional independence. It is a generalisation of the Generalised Covariance Measure implemented in the R package GeneralisedCovarianceMeasure.

Usage

wgcm.fix(
  X,
  Y,
  Z,
  regr.meth,
  regr.pars = list(),
  weight.num,
  weight.meth = "sign",
  nsim = 499
)

Arguments

X

A (n x d_X) numeric matrix with n observations of d_X variables.

Y

A (n x d_Y) numeric matrix with n observations of d_Y variables.

Z

A (n x d_Z) numeric matrix with n observations of d_Z variables.

regr.meth

One of "gam" and "xgboost" indicating the regression method used to estimate the conditional expectations E[X|Z] and E[Y|Z].

regr.pars

Optional additional regression parameters according to GeneralisedCovarianceMeasure::comp.resids().

weight.num

Number k_0 of weight functions per dimension of Z to be used additionally to the constant weight function w(z) = 1. The total number of weight functions will be 1 + k_0 * d_Z. In case of max(d_X, d_Y) > 1, the same 1 + k_0 * d_Z weight functions are used for every combination of the components of X and Y.

weight.meth

String indicating the method to choose the weight functions. Currently, only "sign" is implemented.

nsim

Number of samples used to calculate the p-value using simulation.

Value

A p-value for the null hypothesis of conditional independence of X and Y given Z.

References

Please cite the following papers. Cyrill Scheidegger, Julia Hoerrmann, Peter Buehlmann: "The Weighted Generalised Covariance Measure" https://arxiv.org/abs/2111.04361

Rajen D. Shah, Jonas Peters: "The Hardness of Conditional Independence Testing and the Generalised Covariance Measure" https://arxiv.org/abs/1804.07203

Examples

set.seed(1)
n <- 200
Z <- rnorm(n)
X <- Z + 0.3*rnorm(n)
Y1 <- Z + 0.3*rnorm(n)
Y2 <- Z + 0.3*rnorm(n) + 0.3*X
Y3 <- Z + 0.3*rnorm(n) + 0.15*X^2
wgcm.fix(X, Y1, Z, regr.meth = "gam", weight.num = 7, weight.meth = "sign")
wgcm.fix(X, Y2, Z, regr.meth = "gam", weight.num = 7, weight.meth = "sign")
wgcm.fix(X, Y3, Z, regr.meth = "gam", weight.num = 7, weight.meth = "sign")