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The Journal of Neuroscience, May 25, 2005, 25(21):5195-5206; doi:10.1523/JNEUROSCI.5319-04.2005

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Behavioral/Systems/Cognitive
Synergy, Redundancy, and Independence in Population Codes, Revisited

Peter E. Latham¹ and Sheila Nirenberg²

¹Gatsby Computational Neuroscience Unit, University College London, London WC1N 3AR, United Kingdom, and ²Department of Neurobiology, University of California at Los Angeles, Los Angeles, California 90095-1763

Decoding the activity of a population of neurons is a fundamental problem in neuroscience. A key aspect of this problem is determining whether correlations in the activity, i.e., noise correlations, are important. If they are important, then the decoding problem is high dimensional: decoding algorithms must take the correlational structure in the activity into account. If they are not important, or if they play a minor role, then the decoding problem can be reduced to lower dimension and thus made more tractable. The issue of whether correlations are important has been a subject of heated debate. The debate centers around the validity of the measures used to address it. Here, we evaluate three of the most commonly used ones: synergy, I_shuffled, and I. We show that synergy and I_shuffled are confounded measures: they can be zero when correlations are clearly important for decoding and positive when they are not. In contrast, I is not confounded. It is zero only when correlations are not important for decoding and positive only when they are; that is, it is zero only when one can decode exactly as well using a decoder that ignores correlations as one can using a decoder that does not, and it is positive only when one cannot decode as well. Finally, we show that I has an information theoretic interpretation; it is an upper bound on the information lost when correlations are ignored.

Key words: retina; encoding; decoding; neural code; information theory; population coding; signal correlations; noise correlations

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Received Dec 31, 2004; revised March 11, 2005; accepted March 29, 2005.

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