Implementations of (1) mutual dependence measures and mutual independence tests in
Jin, Z., and Matteson, D. S. (2017) ;
(2) independent component analysis methods based on mutual dependence measures in
Jin, Z., and Matteson, D. S. (2017)
and Pfister, N., et al. (2018) ;
(3) conditional mean dependence measures and conditional mean independence tests in
Shao, X., and Zhang, J. (2014) ,
Park, T., et al. (2015) ,
and Lee, C. E., and Shao, X. (2017) .
Overview
EDMeasure 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 based on distance covariance
symmetric measure based on distance covariance
complete measure based on complete V-statistics
simplified complete measure based on incomplete V-statistics
asymmetric measure based on complete measure
simplified asymmetric measure based on simplified complete measure
symmetric measure based on complete measure
simplified symmetric measure based on simplified complete measure
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 based on distance covariance
symmetric measure based on distance covariance
simplified complete measure based on incomplete V-statistics
kernel-based maximum mean discrepancies
d-variable Hilbert−Schmidt independence criterion based on
Hilbert−Schmidt independence criterion
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 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.
Installation
# Install the released version from CRAN
install.packages("EDMeasure")
# Or the development version from GitHub:
# install.packages("devtools")
devtools::install_github("zejin/EDMeasure")
News
EDMeasure 1.0.0
Initial commit.
Add R functions:
mutual dependence measures: mdm
mutual independence tests: mdm_test
independent component analysis based on mutual dependence measures: mdm_ica
conditional mean dependence measures: mdd, mdc, pmdd, pmdc
conditional mean independence tests: cmdm_test
Add R tests:
mutual dependence measures: test-mdm
independent component analysis based on mutual dependence measures: test-mdm-ica
conditional mean dependence measures: test-mdd
EDMeasure 1.1.0
Fix the arXiv IDs in the Description field of the DESCRIPTION file.