条件独立性度量对比实验

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我在Github分享了拙作"Estimating transfer entropy via copula entropy"一文的代码，网址是：

https://github.com/majianthu/transferentropy/

代码使用多个条件独立性度量的R包（copent, cdcsis, CondIndTests, FOCI, GeneralisedCovarianceMeasure, KPC, ppcor, RCIT），在UCI的北京PM2.5数据上对比了如下条件独立性度量及R包：

• Transfer Entropy via Copula Entropy (TE) [1]; {copent}
• Conditional Distance Correlation (CDC) [2]; {cdcsis}
• Kernel-based Conditional Independence (KCI) [3]; {CondIndTests}
• COnditional DEpendence Coefficient (CODEC) [4]; {FOCI}
• Generalised Covariance Measure (GCM) [5]; {GeneralisedCovarianceMeasure}
• Kernel Partial Correlation (KPC) [6]; {KPC}
• Partial Correlation (pcor); {ppcor}
• Randomized conditional Correlation Test (RCoT) [7]. {RCIT}
  

欢迎大家测试并反馈。

References[color=var(--color-accent-fg)]

• Ma, J. Estimating Transfer Entropy via Copula Entropy. arXiv preprint arXiv:1910.04375, 2019.
• Wang, X.; Pan, W.; Hu, W.; Tian, Y. & Zhang, H. Conditional distance correlation. Journal of the American Statistical Association, 2015, 110, 1726-1734.
• Zhang, K.; Peters, J.; Janzing, D. & Schölkopf, B. Kernel-based conditional independence test and application in causal discovery. Uncertainty in Artificial Intelligence, 2011, 804-813.
• Azadkia, M. & Chatterjee, S. A simple measure of conditional dependence. arXiv preprint arXiv:1910.12327, 2019.
• Shah, R. D. & Peters, J. The hardness of conditional independence testing and the generalised covariance measure. Annals of Statistics, 2020, 48, 1514-1538.
• Huang, Z.; Deb, N. & Sen, B. Kernel Partial Correlation Coefficient -- a Measure of Conditional Dependence. arXiv preprint arXiv:2012.14804, 2020.
• Strobl, E. V., Zhang, K., and Visweswaran, S. (2017). Approximate Kernel-based Conditional Independence Tests for Fast Non-Parametric Causal Discovery. http://arxiv.org/abs/1702.03877
  

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关键词：独立性 independence Intelligence conditional correlation

majianthu 发表于 2021-12-23 15:11
我在Github分享了拙作"Estimating transfer entropy via copula entropy"一文的代码，网址是：https://gith ...

好的好的好的好的好的好的

对比实验中增加RCoT（Randomized conditional Correlation Test）。
论文：Strobl, E. V., Zhang, K., and Visweswaran, S. (2017). Approximate Kernel-based Conditional Independence Tests for Fast Non-Parametric Causal Discovery. http://arxiv.org/abs/1702.03877
R包：https://github.com/ericstrobl/RCIT

对比实验中增加了：
* Fast Conditional Independence Test (fcit) [1];
* Model-Powered Conditional Independence Test (CCIT) [2].

[1] Krzysztof Chalupka, Pietro Perona, Frederick Eberhardt. Fast Conditional Independence Test for Vector Variables with Large Sample Sizes. arXiv preprint arXiv:1804.02747, 2018.
[2] Rajat Sen, Ananda Theertha Suresh, Karthikeyan Shanmugam, Alexandros G. Dimakis, Sanjay Shakkottai. Model-Powered Conditional Independence Test. NIPS 2017: 2951-2961.

对比实验又增加了英国Alan Turing实验室的PCIT：
Predictive Conditional Independence Testing (PCIT) [1]

[1] Samuel Burkart, Franz J Király. Predictive Independence Testing, Predictive Conditional Independence Testing, and Predictive Graphical Modelling. arXiv preprint arXiv:1711.05869, 2017.

更新：对比实验加入了如下条件独立性测试：
weighted Generalised Covariance Measure (wGCM) [1];
Conditional Kendall's Tau (CKT) [2];
Conditional Mean Dependence (CMD) [3].

https://github.com/majianthu/transferentropy

1. Cyrill Scheidegger, Julia Hörrmann, Peter Bühlmann. The Weighted Generalised Covariance Measure. arXiv preprint arXiv:2111.04361, 2021.
2. Alexis Derumigny, Jean-David Fermanian. A classification point-of-view about conditional Kendall’s tau. Computational Statistics & Data Analysis, 135, 70-94, 2019.
3. Xiaofeng Shao, Jingsi Zhang. Martingale Difference Correlation and Its Use in High-Dimensional Variable Screening. Journal of the American Statistical Association, 109(507), 1302-1318, 2014.

更新：增加了 Partial Copula based CI test
https://github.com/majianthu/transferentropy

Petersen, L., & Hansen, N. R. Testing Conditional Independence via Quantile Regression Based Partial Copulas. Journal of Machine Learning Research, 22, 1-47, 2021.