| Title: | Weighted Generalised Covariance Measure Conditional Independence Test |
|---|---|
| Description: | A conditional independence test that can be applied both to univariate and multivariate random variables. The test is based on a weighted form of the sample covariance of the residuals after a nonlinear regression on the conditioning variables. Details are described in Scheidegger, Hoerrmann and Buehlmann (2021) "The Weighted Generalised Covariance Measure" <arXiv:2111.04361>. The test is a generalisation of the Generalised Covariance Measure (GCM) implemented in the R package 'GeneralisedCovarianceMeasure' by Jonas Peters and Rajen D. Shah based on Shah and Peters (2020) "The Hardness of Conditional Independence Testing and the Generalised Covariance Measure" <arXiv:1804.07203>. |
| Authors: | Cyrill Scheidegger [aut, cre], Julia Hoerrmann [ths], Peter Buehlmann [ths], Jonas Peters [ctb, cph] (The code in 'trainFunctions.R' is copied (with small modifications) from the R package 'GeneralisedCovarianceMeasure' by Jonas Peters and Rajen D. Shah), Rajen D. Shah [ctb, cph] (The code in 'trainFunctions.R' is copied (with small modifications) from the R package 'GeneralisedCovarianceMeasure' by Jonas Peters and Rajen D. Shah) |
| Maintainer: | Cyrill Scheidegger <[email protected]> |
| License: | GPL-2 |
| Version: | 0.1.0 |
| Built: | 2025-02-15 03:39:18 UTC |
| Source: | https://github.com/cran/weightedGCM |
The Weighted Generalised Covariance Measure (WGCM) with Estimated Weight Function is a test for conditional independence. It is a generalisation of the Generalised Covariance Measure implemented in the R package GeneralisedCovarianceMeasure.
wgcm.est(X, Y, Z, beta = 0.3, regr.meth, regr.pars = list(), nsim = 499)wgcm.est(X, Y, Z, beta = 0.3, regr.meth, regr.pars = list(), nsim = 499)
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. |
beta |
A real number between 0 and 1 indicating the fraction of the sample used to estimate the weight function. |
regr.meth |
One of "gam" and "xgboost" indicating the regression method used to estimate the conditional expectations E[X|Z] and E[Y|Z] and the weight function sign(E[(X-E[X|Z])(Y-E[Y|Z])|Z]). |
regr.pars |
Optional additional regression parameters according to GeneralisedCovarianceMeasure::comp.resids() |
nsim |
Number of samples used to calculate the p-value using simulation. Only used if max(d_X, d_Y) > 1. |
A p-value for the null hypothesis of conditional independence of X and Y given Z.
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
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.est(X, Y1, Z, beta = 0.3, regr.meth = "gam") wgcm.est(X, Y2, Z, beta = 0.3, regr.meth = "gam") wgcm.est(X, Y3, Z, beta = 0.3, regr.meth = "gam")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.est(X, Y1, Z, beta = 0.3, regr.meth = "gam") wgcm.est(X, Y2, Z, beta = 0.3, regr.meth = "gam") wgcm.est(X, Y3, Z, beta = 0.3, regr.meth = "gam")
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.
wgcm.fix( X, Y, Z, regr.meth, regr.pars = list(), weight.num, weight.meth = "sign", nsim = 499 )wgcm.fix( X, Y, Z, regr.meth, regr.pars = list(), weight.num, weight.meth = "sign", nsim = 499 )
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. |
A p-value for the null hypothesis of conditional independence of X and Y given Z.
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
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")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")