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System Identification of Neuronal Behaviors

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If you have a question about this talk, please contact Alberto Padoan.

In order to estimate reliable models from noisy input-output data, system identification techniques usually require that the data be generated by a process with a fading memory. Non-equilibrium systems such as neuronal and chaotic models lack a fading memory. Their identification is challenging, in particular in the presence of process noise. To approach the problem of neuronal system identification, we build on the fundamental observation that neuronal systems have a global relative degree of one, and a contracting internal dynamics. In particular, while a neuronal system does not have a fading memory, its inverse dynamics does; this allows endowing neuronal systems with fading memory by output feedback. Based on these properties, we first analyze the asymptotic behavior of the prediction-error method when applied to the identification of single-compartment conductance-based models subject to input-additive noise. We show that consistent estimates can be obtained by gathering data under voltage-clamp, when measurement noise (but not process noise) is neglected. We then approach the multiple-input-multiple-output problem of identifying a biophysical neuronal network from a black-box perspective. We propose identifying the MIMO system’s internal dynamics using a universal approximator model structure, given by a filter bank of orthogonal basis transfer functions cascaded with multilayer static artificial neural networks. We show that identification of single neurons and half-center oscillators is successful, and that the identified models capture the localized regions of negative conductance that are characteristic of biophysical neuronal systems.

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