EDMeasure: A package for energy-based dependence measures
Measuring mutual dependence
The mutual dependence measures include:
asymmetric measure \(\mathcal{R}_n\) based on distance covariance \(\mathcal{V}_n\)
symmetric measure \(\mathcal{S}_n\) based on distance covariance \(\mathcal{V}_n\)
complete measure \(\mathcal{Q}_n\) based on complete V-statistics
simplified complete measure \(\mathcal{Q}_n^\star\) based on incomplete V-statistics
asymmetric measure \(\mathcal{J}_n\) based on complete measure \(\mathcal{Q}_n\)
simplified asymmetric measure \(\mathcal{J}_n^\star\) based on simplified complete measure \(\mathcal{Q}_n^\star\)
symmetric measure \(\mathcal{I}_n\) based on complete measure \(\mathcal{Q}_n\)
simplified symmetric measure \(\mathcal{I}_n^\star\) based on simplified complete measure \(\mathcal{Q}_n^\star\)
Testing mutual independence
The mutual independence tests based on the mutual dependence measures are implemented as permutation tests.
Applying mutual dependence measures
The mutual dependence measures include:
distance-based energy statistics
asymmetric measure \(\mathcal{R}_n\) based on distance covariance \(\mathcal{V}_n\)
symmetric measure \(\mathcal{S}_n\) based on distance covariance \(\mathcal{V}_n\)
simplified complete measure \(\mathcal{Q}_n^\star\) based on incomplete V-statistics
kernel-based maximum mean discrepancies
d-variable Hilbert--Schmidt independence criterion dHSIC\(_n\) based on Hilbert--Schmidt independence criterion HSIC\(_n\)
Initializing local optimization methods
The initialization methods include:
Latin hypercube sampling
Bayesian optimization
Measuring conditional mean dependence
The conditional mean dependence measures include:
conditional mean dependence of Y given X
martingale difference divergence
martingale difference correlation
martingale difference divergence matrix
conditional mean dependence of Y given X adjusting for the dependence on Z
partial martingale difference divergence
partial martingale difference correlation
Testing conditional mean independence
The conditional mean independence tests include:
conditional mean independence of Y given X conditioning on Z
martingale difference divergence under a linear assumption
partial martingale difference divergence
The conditional mean independence tests based on the conditional mean dependence measures are implemented as permutation tests.
The EDMeasure package provides measures of mutual dependence and tests of mutual independence, independent component analysis methods based on mutual dependence measures, and measures of conditional mean dependence and tests of conditional mean independence.
The three main parts are:
mutual dependence measures via energy statistics
measuring mutual dependence
testing mutual independence
independent component analysis via mutual dependence measures
applying mutual dependence measures
initializing local optimization methods
conditional mean dependence measures via energy statistics
measuring conditional mean dependence
testing conditional mean independence