aps2020

This is the code for the paper 'Variable Selection with Copula Entropy' published on Chinese Journal of Applied Probability and Statistics. The preprint paper is available at here on ArXiv.

• Ma, Jian. “Variable Selection with Copula Entropy.” Chinese Journal of Applied Probability and Statistics, 2021, 37(4): 405-420. See also arXiv preprint arXiv:1910.12389 (2019).

In the paper, three methods for variable selection are compared on the UCI heart disease data:

• Copula Entropy [1],
• Hilbert-Schimdt Independence Criterion (HSIC) [2,3],
• Distance Correlation [4].

The following additional independence measures are also considered in this version of comparison experiment:

• Heller-Heller-Gorfine Tests of Independence [5],
• Hoeffding's D test [6],
• Bergsma-Dassios T* sign covariance [7],
• Ball correlation [8],
• BET: Binary Expansion Testing [9],
• qad: Quantification of Asymmetric Dependence [10],
• MixedIndTests [11],
• NNS: Nonlinear Nonparametric Statistics [12],
• subcopula based dependence measures [13],
• MDM: Mutual Independence Measure [14].

Copula Entropy does better than all the others measures in terms of predictibility and interpretability.

References

1. Ma, J., & Sun, Z. (2011). Mutual Information Is Copula Entropy. Tsinghua Science & Technology, 16(1), 51–54. See also arXiv preprint arXiv:0808.0845 (2008).
2. Gretton, A., Fukumizu, K., Teo, C. H., Song, L., Schölkopf, B., & Smola, A. J. (2007). A Kernel Statistical Test of Independence. In Advances in Neural Information Processing Systems 20 (Vol. 20, pp. 585–592).
3. Pfister, N., Bühlmann, P., Schölkopf, B., & Peters, J. (2018). Kernel-based Tests for Joint Independence. Journal of The Royal Statistical Society Series B-Statistical Methodology, 80(1), 5–31.
4. Székely, G. J., Rizzo, M. L., & Bakirov, N. K. (2007). Measuring and testing dependence by correlation of distances. Annals of Statistics, 35(6), 2769–2794.
5. Heller, R., Heller, Y., Kaufman, S., Brill, B., & Gorfine, M. (2016). Consistent distribution-free K-sample and independence tests for univariate random variables. Journal of Machine Learning Research, 17(1), 978–1031.
6. Hoeffding, W. (1948). A Non-Parametric Test of Independence. Annals of Mathematical Statistics, 19(4), 546–557.
7. Bergsma, W., & Dassios, A. (2014). A consistent test of independence based on a sign covariance related to Kendall’s tau. Bernoulli, 20(2), 1006–1028.
8. Wenliang Pan, Xueqin Wang, Heping Zhang, Hongtu Zhu & Jin Zhu (2019). Ball Covariance: A Generic Measure of Dependence in Banach Space. Journal of the American Statistical Association, 115, 307-317.
9. Zhang, K. (2019).BET on Independence. Journal of the American Statistical Association, Taylor & Francis, 114, 1620-1637.
10. Junker, R. R.; Griessenberger, F. & Trutschnig, W. (2021). Estimating scale-invariant directed dependence of bivariate distributions. Computational Statistics & Data Analysis, 153, 107058.
11. Genest, C.; Nešlehová, J. G.; Rémillard, B. & Murphy, O. A. Testing for independence in arbitrary distributions. Biometrika, 2019, 106, 47-68.
12. Viole, Fred and Nawrocki, David N., Deriving Nonlinear Correlation Coefficients from Partial Moments (September 18, 2012). Available at SSRN: https://ssrn.com/abstract=2148522 or http://dx.doi.org/10.2139/ssrn.2148522
13. Arturo Erdely. A subcopula based dependence measure. Kybernetika, 53(2), 231-243, 2017.
14. Ze Jin, David S. Matteson. Generalizing Distance Covariance to Measure and Test Multivariate Mutual Dependence. arXiv preprint arXiv:1709.02532, 2017.