Abstract
Synergy is a fundamental concept in complex systems that has received much attention in computational biology (Narayanan et al. 2005; Balduzzi and Tononi 2008). Several papers (Schneidman et al. 2003a; Bell 2003; Nirenberg et al. 2001;Williams and Beer 2010) have proposed measures for quantifying synergy, but there remains no consensus which measure is most valid.
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References
Amari, S.: Information geometry on hierarchical decomposition of stochastic interactions. IEEE Transaction on Information Theory 47, 1701–1711 (1999)
Anastassiou, D.: Computational analysis of the synergy among multiple interacting genes. Molecular Systems Biology 3, 83 (2007)
Balduzzi, D., Tononi, G.: Integrated information in discrete dynamical systems: motivation and theoretical framework. PLoS Computational Biology 4(6), e1000091 (2008)
Bell, A.J.: The co-information lattice. In: Amari, S., Cichocki, A., Makino, S., Murata, N. (eds.) Fifth International Workshop on Independent Component Analysis and Blind Signal Separation, Springer (2003)
Bertschinger, N., Rauh, J., Olbrich, E., Jost, J.: Shared information – new insights and problems in decomposing information in complex systems. CoRR, abs/1210.5902 (2012)
Chechik, G., Globerson, A., Anderson, M.J., Young, E.D., Nelken, I., Tishby, N.: Group redundancy measures reveal redundancy reduction in the auditory pathway. In: Dietterich, T.G., Becker, S., Ghahramani, Z. (eds.) NIPS 2002, pp. 173–180. MIT Press, Cambridge (2002)
Comtet, L.: Advanced Combinatorics: The Art of Finite and Infinite Expansions. Reidel, Dordrecht (1998)
Cover, T.M., Thomas, J.A.: Elements of Information Theory. John Wiley, New York (1991)
DeWeese, M.R., Meister, M.: How to measure the information gained from one symbol. Network 10, 325–340 (1999)
Gat, I., Tishby, N.: Synergy and redundancy among brain cells of behaving monkeys. In: Advances in Neural Information Proceedings systems, pp. 465–471. MIT Press (1999)
Gawne, T.J., Richmond, B.J.: How independent are the messages carried by adjacent inferior temporal cortical neurons? Journal of Neuroscience 13, 2758–2771 (1993)
Han, T.S.: Nonnegative entropy measures of multivariate symmetric correlations. Information and Control 36(2), 133–156 (1978)
Harder, M., Salge, C., Polani, D.: A bivariate measure of redundant information. Physical Review E 87(1), 012130 (2013)
Latham, P.E., Nirenberg, S.: Synergy, redundancy, and independence in population codes, revisited. Journal of Neuroscience 25(21), 5195–5206 (2005)
Lei, W., Xu, G., Chen, B.: The common information of n dependent random variables. In: Forty-Eighth Annual Allerton Conference on Communication, Control, and Computing (2010), doi:abs/1010.3613:836–843
Lizier, J.T., Flecker, B., Williams, P.L.: Towards a synergy-based approach to measuring information modification. In: IEEE Symposium Series on Computational Intelligence (SSCI 2013) — IEEE Symposium on Artificial Life, Singapore. IEEE Press (April 2013)
Maurer, U.M., Wolf, S.: Unconditionally secure key agreement and the intrinsic conditional information. IEEE Transactions on Information Theory 45(2), 499–514 (1999)
Narayanan, N.S., Kimchi, E.Y., Laubach, M.: Redundancy and synergy of neuronal ensembles in motor cortex. The Journal of Neuroscience 25(17), 4207–4216 (2005)
Nirenberg, S., Carcieri, S.M., Jacobs, A.L., Latham, P.E.: Retinal ganglion cells act largely as independent encoders. Nature 411(6838), 698–701 (2001)
Nirenberg, S., Latham, P.E.: Decoding neuronal spike trains: How important are correlations? Proceedings of the National Academy of Sciences 100(12), 7348–7353 (2003)
Panzeri, S., Treves, A., Schultz, S., Rolls, E.T.: On decoding the responses of a population of neurons from short time windows. Neural Comput. 11(7), 1553–1577 (1999)
Pola, G., Thiele, A., Hoffmann, K.P., Panzeri, S.: An exact method to quantify the information transmitted by different mechanisms of correlational coding. Network 14(1), 35–60 (2003)
Schneidman, E., Bialek, W., Berry II, M.: Synergy, redundancy, and independence in population codes. Journal of Neuroscience 23(37), 11539–11553 (2003a)
Schneidman, E., Still, S., Berry, M.J., Bialek, W.: Network information and connected correlations. Phys. Rev. Lett. 91(23), 238701–238705 (2003b)
Weisstein, E.W.: Antichain (2011), http://mathworld.wolfram.com/Antichain.html
White, D., Rabago-Smith, M.: Genotype-phenotype associations and human eye color. Journal of Human Genetics 56(1), 5–7 (2011)
Williams, P.L., Beer, R.D.: Nonnegative decomposition of multivariate information. CoRR, abs/1004.2515 (2010)
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Griffith, V., Koch, C. (2014). Quantifying Synergistic Mutual Information. In: Prokopenko, M. (eds) Guided Self-Organization: Inception. Emergence, Complexity and Computation, vol 9. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-53734-9_6
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