Description
Energy-Based Dependence Measures.
Description
Implementations of (1) mutual dependence measures and mutual independence tests in Jin, Z., and Matteson, D. S. (2017) <arXiv:1709.02532>; (2) independent component analysis methods based on mutual dependence measures in Jin, Z., and Matteson, D. S. (2017) <arXiv:1709.02532> and Pfister, N., et al. (2018) <doi:10.1111/rssb.12235>; (3) conditional mean dependence measures and conditional mean independence tests in Shao, X., and Zhang, J. (2014) <doi:10.1080/01621459.2014.887012>, Park, T., et al. (2015) <doi:10.1214/15-EJS1047>, and Lee, C. E., and Shao, X. (2017) <doi:10.1080/01621459.2016.1240083>.
README.md
EDMeasure
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")