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Minimum mean square error estimation of connectivity in biological neural networks

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Abstract

A minimum mean square error (MMSE) estimation scheme is employed to identify the synaptic connectivity in neural networks. This new approach can substantially reduce the amount of data and the computational cost involved in the conventional correlation methods, and is suitable for both nonstationary and stationary neuronal firings. Two algorithms are proposed to estimate the synaptic connectivities recursively, one for nonlinear filtering, the other for linear filtering. In addition, the lower and upper bounds for the MMSE estimator are determined. It is shown that the estimators are consistent in quadratic mean. We also demonstrate that the conventional cross-interval histogram is an asymptotic linear MMSE estimator with an inappropriate initial value. Finally, simulations of both nonlinear and linear (Kalman filter) estimates demonstrate that the true connectivity values are approached asymptotically.

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Authors and Affiliations

  1. Systems Research Center, University of Maryland, 20742, College Park, MD, USA

    X. Yang & Shihab A. Shamma

  2. Electrical Engineering Department, University of Maryland, 20742, College Park, MD, USA

    Shihab A. Shamma

  3. The University of Maryland Institute for Advanced Computer Studies, University of Maryland, 20742, College Park, MD, USA

    Shihab A. Shamma

Authors
  1. X. Yang
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  2. Shihab A. Shamma
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Yang, X., Shamma, S.A. Minimum mean square error estimation of connectivity in biological neural networks. Biol. Cybern. 65, 171–179 (1991). https://doi.org/10.1007/BF00198088

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  • DOI: https://doi.org/10.1007/BF00198088

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