mdm {EDMeasure}

Mutual Dependence Measures

Description

mdm measures mutual dependence of all components in X, where each component contains one variable (univariate) or more variables (multivariate).

Usage

mdm(X, dim_comp = NULL, dist_comp = FALSE, type = "comp_simp")

Arguments

X

A matrix or data frame, where rows represent samples, and columns represent variables.

dim_comp

The numbers of variables contained by all components in X. If omitted, each component is assumed to contain exactly one variable.

dist_comp

Logical. If TRUE, the distances between all components from all samples in X will be returned.

type

The type of mutual dependence measures, including

• asym_dcov: asymmetric measure \mathcal{R}_n based on distance covariance \mathcal{V}_n;

• sym_dcov: symmetric measure \mathcal{S}_n based on distance covariance \mathcal{V}_n;

• comp: complete measure \mathcal{Q}_n based on complete V-statistics;

• comp_simp: simplified complete measure \mathcal{Q}_n^\star based on incomplete V-statistics;

• asym_comp: asymmetric measure \mathcal{J}_n based on complete measure \mathcal{Q}_n;

• asym_comp_simp: simplified asymmetric measure \mathcal{J}_n^\star based on simplified complete measure \mathcal{Q}_n^\star;

• sym_comp: symmetric measure \mathcal{I}_n based on complete measure \mathcal{Q}_n;

• sym_comp_simp: simplified symmetric measure \mathcal{I}_n^\star based on simplified complete measure \mathcal{Q}_n^\star.

From experiments, asym_dcov, sym_dcov, comp_simp are recommended.

Value

mdm returns a list including the following components:

stat

The value of the mutual dependence measure.

dist

The distances between all components from all samples.

References

Jin, Z., and Matteson, D. S. (2017). Generalizing Distance Covariance to Measure and Test Multivariate Mutual Dependence. arXiv preprint arXiv:1709.02532. https://arxiv.org/abs/1709.02532.

Examples

# X is a 10 x 3 matrix with 10 samples and 3 variables
X <- matrix(rnorm(10 * 3), 10, 3)

# assume X = (X1, X2) where X1 is 1-dim, X2 is 2-dim
mdm(X, dim_comp = c(1, 2), type = "asym_dcov")

# assume X = (X1, X2) where X1 is 2-dim, X2 is 1-dim
mdm(X, dim_comp = c(2, 1), type = "sym_dcov")

# assume X = (X1, X2, X3) where X1 is 1-dim, X2 is 1-dim, X3 is 1-dim
mdm(X, dim_comp = c(1, 1, 1), type = "comp_simp")