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转移熵

维基百科,自由的百科全书

转移熵(英语:transfer entropy)是测量两个随机过程之间有向(时间不对称)信息转移量的一种非参数统计量[1][2][3]过程X到另一个过程Y的转移熵可定义为:在已知Y过去值的情况下,了解X的过去值所能减少Y未来值不确定性的程度。更具体地说,假定)表示两个随机过程,并用香农熵来度量信息量,则转移熵可定义为:

其中H ( X ) 表示X的香农熵。此外,还可以使用其他类型的度量(例如雷尼熵英语Rényi entropy)对上述定义进行扩展。[3][4]

转移熵可看作一种条件互信息英语Conditional mutual information[5][6],其条件为受影响变量的历史值

向量自回归过程而言,转移熵可简化为格兰杰因果关系[7] 因而,转移熵适用于非线性信号分析等格兰杰因果关系的模型假设不成立的场合。[8][9]然而,它通常需要更多的样本才能进行准确估计。[10]熵公式中的概率可以使用分箱、最近邻等不用方法来估计,或为了降低复杂性而使用非均匀嵌入方法。[11]虽然转移熵的原始定义是建立在双变量分析英语Bivariate analysis基础上的,但后来也扩展到多变量分析中。这种扩展可以以其他潜在源变量为条件[12] ,或考虑从一组源进行转移[13],不过这些都需要更多的样本。

转移熵被用于估计神经元功能连接[13][14][15]社交网络中的社会影响[8]以及武装冲突事件之间的统计因果关系等。[16]转移熵是有向信息英语Directed information的有限形式,于1990年由詹姆斯·马西英语James Massey[17]定义为,其中表示向量则表示 。有向信息在描述具有或没有反馈的通信信道的基本极限(信道容量)中起着关键作用。[18][19]

参见

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参考文献

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  1. ^ Schreiber, Thomas. Measuring information transfer. Physical Review Letters. 1 July 2000, 85 (2): 461–464. Bibcode:2000PhRvL..85..461S. PMID 10991308. S2CID 7411376. arXiv:nlin/0001042可免费查阅. doi:10.1103/PhysRevLett.85.461. 
  2. ^ Seth, Anil. Granger causality. Scholarpedia. 2007, 2 (7): 1667. Bibcode:2007SchpJ...2.1667S. doi:10.4249/scholarpedia.1667可免费查阅. 
  3. ^ 3.0 3.1 Hlaváčková-Schindler, Katerina; Palus, M; Vejmelka, M; Bhattacharya, J. Causality detection based on information-theoretic approaches in time series analysis. Physics Reports. 1 March 2007, 441 (1): 1–46. Bibcode:2007PhR...441....1H. CiteSeerX 10.1.1.183.1617可免费查阅. doi:10.1016/j.physrep.2006.12.004. 
  4. ^ Jizba, Petr; Kleinert, Hagen; Shefaat, Mohammad. Rényi's information transfer between financial time series. Physica A: Statistical Mechanics and Its Applications. 2012-05-15, 391 (10): 2971–2989. Bibcode:2012PhyA..391.2971J. ISSN 0378-4371. S2CID 51789622. arXiv:1106.5913可免费查阅. doi:10.1016/j.physa.2011.12.064 (英语). 
  5. ^ Wyner, A. D. A definition of conditional mutual information for arbitrary ensembles. Information and Control. 1978, 38 (1): 51–59. doi:10.1016/s0019-9958(78)90026-8可免费查阅. 
  6. ^ Dobrushin, R. L. General formulation of Shannon's main theorem in information theory. Uspekhi Mat. Nauk. 1959, 14: 3–104. 
  7. ^ Barnett, Lionel. Granger Causality and Transfer Entropy Are Equivalent for Gaussian Variables. Physical Review Letters. 1 December 2009, 103 (23): 238701. Bibcode:2009PhRvL.103w8701B. PMID 20366183. S2CID 1266025. arXiv:0910.4514可免费查阅. doi:10.1103/PhysRevLett.103.238701. 
  8. ^ 8.0 8.1 Ver Steeg, Greg; Galstyan, Aram. Information transfer in social media. Proceedings of the 21st international conference on World Wide Web (WWW '12). ACM: 509–518. 2012. Bibcode:2011arXiv1110.2724V. arXiv:1110.2724可免费查阅. 
  9. ^ Lungarella, M.; Ishiguro, K.; Kuniyoshi, Y.; Otsu, N. Methods for quantifying the causal structure of bivariate time series. International Journal of Bifurcation and Chaos. 1 March 2007, 17 (3): 903–921. Bibcode:2007IJBC...17..903L. CiteSeerX 10.1.1.67.3585可免费查阅. doi:10.1142/S0218127407017628. 
  10. ^ Pereda, E; Quiroga, RQ; Bhattacharya, J. Nonlinear multivariate analysis of neurophysiological signals.. Progress in Neurobiology. Sep–Oct 2005, 77 (1–2): 1–37. Bibcode:2005nlin.....10077P. PMID 16289760. S2CID 9529656. arXiv:nlin/0510077可免费查阅. doi:10.1016/j.pneurobio.2005.10.003. 
  11. ^ Montalto, A; Faes, L; Marinazzo, D. MuTE: A MATLAB Toolbox to Compare Established and Novel Estimators of the Multivariate Transfer Entropy.. PLOS ONE. Oct 2014, 9 (10): e109462. Bibcode:2014PLoSO...9j9462M. PMC 4196918可免费查阅. PMID 25314003. doi:10.1371/journal.pone.0109462可免费查阅. 
  12. ^ Lizier, Joseph; Prokopenko, Mikhail; Zomaya, Albert. Local information transfer as a spatiotemporal filter for complex systems. Physical Review E. 2008, 77 (2): 026110. Bibcode:2008PhRvE..77b6110L. PMID 18352093. S2CID 15634881. arXiv:0809.3275可免费查阅. doi:10.1103/PhysRevE.77.026110. 
  13. ^ 13.0 13.1 Lizier, Joseph; Heinzle, Jakob; Horstmann, Annette; Haynes, John-Dylan; Prokopenko, Mikhail. Multivariate information-theoretic measures reveal directed information structure and task relevant changes in fMRI connectivity. Journal of Computational Neuroscience. 2011, 30 (1): 85–107. PMID 20799057. S2CID 3012713. doi:10.1007/s10827-010-0271-2. 
  14. ^ Vicente, Raul; Wibral, Michael; Lindner, Michael; Pipa, Gordon. Transfer entropy—a model-free measure of effective connectivity for the neurosciences. Journal of Computational Neuroscience. February 2011, 30 (1): 45–67. PMC 3040354可免费查阅. PMID 20706781. doi:10.1007/s10827-010-0262-3. 
  15. ^ Shimono, Masanori; Beggs, John. Functional clusters, hubs, and communities in the cortical microconnectome. Cerebral Cortex. October 2014, 25 (10): 3743–57. PMC 4585513可免费查阅. PMID 25336598. doi:10.1093/cercor/bhu252. 
  16. ^ Kushwaha, Niraj; Lee, Edward D. Discovering the mesoscale for chains of conflict. PNAS Nexus. July 2023, 2 (7). ISSN 2752-6542. PMC 10392960可免费查阅. PMID 37533894. doi:10.1093/pnasnexus/pgad228. 
  17. ^ Massey, James. Causality, Feedback And Directed Information (ISITA). 1990. CiteSeerX 10.1.1.36.5688可免费查阅. 
  18. ^ Permuter, Haim Henry; Weissman, Tsachy; Goldsmith, Andrea J. Finite State Channels With Time-Invariant Deterministic Feedback. IEEE Transactions on Information Theory. February 2009, 55 (2): 644–662. S2CID 13178. arXiv:cs/0608070可免费查阅. doi:10.1109/TIT.2008.2009849. 
  19. ^ Kramer, G. Capacity results for the discrete memoryless network. IEEE Transactions on Information Theory. January 2003, 49 (1): 4–21. doi:10.1109/TIT.2002.806135.