EDMeasure-package {EDMeasure} | R Documentation |
Energy-Based Dependence Measures
Description
EDMeasure: A package for energy-based dependence measures
Details
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
Mutual Dependence Measures via Energy Statistics
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-statisticssimplified complete measure
\mathcal{Q}_n^\star
based on incomplete V-statisticsasymmetric 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.
Independent Component Analysis via Mutual Dependence Measures
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
Conditional Mean Dependence Measures via Energy Statistics
Measuring conditional mean dependence
The conditional mean dependence measures include:
conditional mean dependence of
Y
givenX
martingale difference divergence
martingale difference correlation
martingale difference divergence matrix
conditional mean dependence of
Y
givenX
adjusting for the dependence onZ
partial martingale difference divergence
partial martingale difference correlation
Testing conditional mean independence
The conditional mean independence tests include:
conditional mean independence of
Y
givenX
conditioning onZ
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.
Author(s)
Ze Jin zj58@cornell.edu,
Shun Yao shunyao2@illinois.edu,
David S. Matteson matteson@cornell.edu,
Xiaofeng Shao xshao@illinois.edu