Estimation of the entropy based on its polynomial representation

Physical Review E - Statistical, Nonlinear, and Soft Matter Physics

Volumn 85, Issue 5, 2012, Pages

  Vinck, Martin ^a   Battaglia, Francesco P ^a   Balakirsky, Vladimir B ^b   Vinck, A J Han ^b   Pennartz, Cyriel M A ^a  

^a UNIVERSITY OF AMSTERDAM   (Netherlands)

^b Inst F Experimentelle Mathematik   (Germany)

Author keywords

[No Author keywords available]

Indexed keywords

APPROXIMATION FUNCTION; ENTROPY ESTIMATOR; ENTROPY FUNCTION; ENTROPY-BASED; FINITE SIZE; LINEAR ESTIMATES; NONLINEAR BAYESIAN ESTIMATION; POLYNOMIAL REPRESENTATIONS; POWER SERIES; PRIOR DISTRIBUTION; STATISTICAL BIAS; STATISTICAL SYSTEMS; TAYLOR EXPANSIONS;

BAYESIAN NETWORKS; ENTROPY; INFORMATION THEORY; POLYNOMIAL APPROXIMATION;

ESTIMATION;

EID: 84861946892     PISSN: 15393755     EISSN: 15502376     Source Type: Journal    
DOI: 10.1103/PhysRevE.85.051139     Document Type: Article

References (30)

1. R. Quiroga and S. Panzeri, Nat. Rev. Neurosci. 1471-0048 10.1038/nrn2578 10, 173 (2009).
2. F. Rieke, D. Warland, and W. Bialek, Spikes: Exploring the Neural Code (MIT Press, Cambridge, 1999).
3. P. Dayan, L. Abbott, and L. Abbott, Theoretical Neuroscience: Computational and Mathematical Modeling of Neural Systems (MIT Press, Cambridge, 2001).
4. D. MacKay and W. McCulloch, Bull. Math. Biol. 14, 127 (1952).
5. J. Hertz and S. Panzeri, in The Handbook of Brain Theory and Neural Networks, edited by, M. B. Arbib, (MIT Press, Cambridge, 2002), pp. 1023-1026.
6. A. Borst and F. Theunissen, Nat. Neurosci. NANEFN 1097-6256 10.1038/14731 2, 947 (1999). (Pubitemid 30599556)
7. W. Bialek and F. Rieke, Trends Neurosci. TNSCDR 0166-2236 10.1016/0166-2236(92)90005-S 15, 428 (1992).
8. S. Ma, J. Stat. Phys. JSTPBS 0022-4715 10.1007/BF01013169 26, 221 (1981).
9. S. Panzeri, R. Senatore, M. A. Montemurro, and R. S. Petersen, J. Neurocytol. 98, 1064 (2007).
10. A. Treves and S. Panzeri, Neural Comput. NEUCEB 0899-7667 10.1162/neco.1995.7.2.399 7, 399 (1995).
11. J. Victor, Neural Comput. NEUCEB 0899-7667 10.1162/089976600300014728 12, 2797 (2000).
12. G. Miller, in Information Theory in Psychology; Problems and Methods II-B, edited by, H. Quastler, (Free Press, Glencoe, IL, 1955), pp. 95-100.
13. P. Grassberger, arXiv: physics/0307138.
14. J. D. Victor, Phys. Rev. E PLEEE8 1539-3755 10.1103/PhysRevE.66.051903 66, 051903 (2002). (Pubitemid 40618506)
15. S. P. Strong, R. Koberle, R. R. de Ruyter van Steveninck, and W. Bialek, Phys. Rev. Lett. PRLTAO 0031-9007 10.1103/PhysRevLett.80.197 80, 197 (1998).
16. A. Kraskov, H. Stögbauer, and P. Grassberger, Phys. Rev. E PLEEE8 1539-3755 10.1103/PhysRevE.69.066138 69, 066138 (2004).
17. L. Kozachenko and N. Leonenko, Problems Inform. Trans. 23, 95 (1987).
18. L. Paninski, Neural Comput. NEUCEB 0899-7667 10.1162/089976603321780272 15, 1191 (2003). (Pubitemid 37049793)
19. J. Bonachela, H. Hinrichsen, and M. Muñoz, J. Phys. A: Math. Theor. 1751-8113 10.1088/1751-8113/41/20/202001 41, 202001 (2008).
20. T. Schürmann, J. Phys. A: Math. Gen. JPHAC5 0305-4470 10.1088/0305-4470/37/27/L02 37, L295 (2004). (Pubitemid 38904275)
21. I. Nemenman, W. Bialek, and R. de Ruyter van Steveninck, Phys. Rev. E PLEEE8 1539-3755 10.1103/PhysRevE.69.056111 69, 056111 (2004).
22. I. Nemenman, F. Shafee, and W. Bialek, arXiv: physics/0108025.
23. D. H. Wolpert and D. R. Wolf, Phys. Rev. E PLEEE8 1539-3755 10.1103/PhysRevE.52.6841 52, 6841 (1995).
24. I. Nemenman, G. Lewen, W. Bialek, and R. van Steveninck, PLoS Comput. Biol. 1553-734X 10.1371/journal.pcbi.1000025 4, e1000025 (2008). (Pubitemid 351497532)
25. F. Montani, A. Kohn, M. A. Smith, and S. R. Schultz, J. Neurosci. JNRSDS 0270-6474 10.1523/JNEUROSCI.3417-06.2007 27, 2338 (2007). (Pubitemid 46340967)
26. C. Shannon, Bell Syst. Tech. J. 27, 379 (1948).
27. S. Panzeri and A. Treves, Netw., Comput. Neural Syst. NEWKEB 0954-898X 10.1088/0954-898X/7/1/006 7, 87 (1996).
28. C. Magri, K. Whittingstall, V. Singh, N. Logothetis, and S. Panzeri, BMC Neurosci. 1471-2202 10.1186/1471-2202-10-81 10, 81 (2009).
29. P. Grassberger, Phys. Lett. A PYLAAG 0375-9601 10.1016/0375-9601(88) 90193-4 128, 369 (1988).
30. I. Nemenman, Entropy ENTRFG 1099-4300 10.3390/e13122013 13, 2013 (2011).