# aps2020

**Repository Path**: android_fen/aps2020

## Basic Information

- **Project Name**: aps2020
- **Description**: No description available
- **Primary Language**: Unknown
- **License**: GPL-3.0
- **Default Branch**: master
- **Homepage**: None
- **GVP Project**: No

## Statistics

- **Stars**: 1
- **Forks**: 0
- **Created**: 2021-11-10
- **Last Updated**: 2023-03-17

## Categories & Tags

**Categories**: Uncategorized

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## README

# 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](https://arxiv.org/abs/1910.12389) 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](http://archive.ics.uci.edu/ml/datasets/heart+disease):
* Copula Entropy [1],
* Hilbert-Schimdt Independence Criterion (HSIC) [2,3],
* Distance Correlation [4].

 Four 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].

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.