Fisher and Shannon Information in Finite Neural Populations

Stuart Yarrow, Peggy Series

Research output: Contribution to conferencePosterpeer-review


The precision of the neural code is commonly investigated using two different families of statistical measures: (i) Shannon mutual information and derived quantities when investigating very small populations of neurons and (ii) Fisher information when studying large populations. These statistical tools are no longer the preserve of theorists, and are being applied by experimental research groups in the analysis of empirical data. Although the relationship between information theoretic and Fisher-based measures in the limit of infinite neural populations is relatively well understood, how these measures compare in finite size populations has not yet been systematically explored. We aim to close this gap. We are particularly interested in understanding which stimuli are best encoded (in terms of discrimination) by a given neuron within a population and how this depends on the chosen measure. We use a novel Monte Carlo approach to compute a stimulus-specific decomposition of the mutual information (the stimulus-specific information) for model populations of up to 256 neurons and show that Fisher information can be
used to accurately estimate both mutual information and stimulus-specific information (SSI) for populations of the order of 100 neurons, even in the presence of biologically realistic variability, noise correlations and experimentally relevant integration times. According to both measures, the stimuli that are best encoded are then those falling at the flanks of the neuron’s tuning curve. In populations of less than around 50 neurons, however, Fisher information can be misleading.
Original languageEnglish
Number of pages1
Publication statusPublished - Feb 2012
Event9th Annual Annual Computational and Systems Neurscience Meeting (COSYNE 2012) - Salt Lake City, United States
Duration: 23 Feb 201226 Feb 2012


Conference9th Annual Annual Computational and Systems Neurscience Meeting (COSYNE 2012)
Country/TerritoryUnited States
CitySalt Lake City


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