Energy-Based Dependence Measures

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) .


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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.

EDMeasure 1.2.0

  • Add R functions:

    • conditional mean dependence measures: mddm
  • Add R tests:

    • conditional mean dependence measures: test-mddm

Reference manual

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install.packages("EDMeasure")

1.2.0 by Ze Jin, a year ago


Browse source code at https://github.com/cran/EDMeasure


Authors: Ze Jin [aut, cre] , Shun Yao [aut] , David S. Matteson [aut] , Xiaofeng Shao [aut]


Documentation:   PDF Manual  


GPL (>= 2) license


Imports energy, dHSIC, rBayesianOptimization

Suggests testthat


See at CRAN