TY - JOUR
T1 - Adaptive stimulus design for dynamic recurrent neural network models
AU - Doruk, R. Ozgur
AU - Zhang, Kechen
N1 - Funding Information:
Supported by Turkish Scientific and Technological Research Council (TÜBİTAK) 2219 Research Program and NIH grant R01 DC013698. All the computer codes in Matlab for the simulations in this paper are freely available upon request for scientific research and education or any noncommercial use.
Publisher Copyright:
© 2019 Doruk and Zhang.
PY - 2019/1/22
Y1 - 2019/1/22
N2 - We present an adaptive stimulus design method for efficiently estimating the parameters of a dynamic recurrent network model with interacting excitatory and inhibitory neuronal populations. Although stimuli that are optimized for model parameter estimation should, in theory, have advantages over nonadaptive random stimuli, in practice it remains unclear in what way and to what extent an optimal design of time-varying stimuli may actually improve parameter estimation for this common type of recurrent network models. Here we specified the time course of each stimulus by a Fourier series whose amplitudes and phases were determined by maximizing a utility function based on the Fisher information matrix. To facilitate the optimization process, we have derived differential equations that govern the time evolution of the gradients of the utility function with respect to the stimulus parameters. The network parameters were estimated by maximum likelihood from the spike train data generated by an inhomogeneous Poisson process from the continuous network state. The adaptive design process was repeated in a closed loop, alternating between optimal stimulus design and parameter estimation from the updated stimulus-response data. Our results confirmed that, compared with random stimuli, optimally designed stimuli elicited responses with significantly better likelihood values for parameter estimation. Furthermore, all individual parameters, including the time constants and the connection weights, were recovered more accurately by the optimal design method. We also examined how the errors of different parameter estimates were correlated, and proposed heuristic formulas to account for the correlation patterns by an approximate parameter-confounding theory. Our results suggest that although adaptive optimal stimulus design incurs considerable computational cost even for the simplest excitatory-inhibitory recurrent network model, it may potentially help save time in experiments by reducing the number of stimuli needed for network parameter estimation.
AB - We present an adaptive stimulus design method for efficiently estimating the parameters of a dynamic recurrent network model with interacting excitatory and inhibitory neuronal populations. Although stimuli that are optimized for model parameter estimation should, in theory, have advantages over nonadaptive random stimuli, in practice it remains unclear in what way and to what extent an optimal design of time-varying stimuli may actually improve parameter estimation for this common type of recurrent network models. Here we specified the time course of each stimulus by a Fourier series whose amplitudes and phases were determined by maximizing a utility function based on the Fisher information matrix. To facilitate the optimization process, we have derived differential equations that govern the time evolution of the gradients of the utility function with respect to the stimulus parameters. The network parameters were estimated by maximum likelihood from the spike train data generated by an inhomogeneous Poisson process from the continuous network state. The adaptive design process was repeated in a closed loop, alternating between optimal stimulus design and parameter estimation from the updated stimulus-response data. Our results confirmed that, compared with random stimuli, optimally designed stimuli elicited responses with significantly better likelihood values for parameter estimation. Furthermore, all individual parameters, including the time constants and the connection weights, were recovered more accurately by the optimal design method. We also examined how the errors of different parameter estimates were correlated, and proposed heuristic formulas to account for the correlation patterns by an approximate parameter-confounding theory. Our results suggest that although adaptive optimal stimulus design incurs considerable computational cost even for the simplest excitatory-inhibitory recurrent network model, it may potentially help save time in experiments by reducing the number of stimuli needed for network parameter estimation.
KW - Excitatory-inhibitory network
KW - Fisher information matrix
KW - Fourier series
KW - Inhomogeneous poisson spike train
KW - Maximum likelihood estimation
KW - Optimal stimulus design
KW - Parameter confounding
KW - Sensory coding
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U2 - 10.3389/fncir.2018.00119
DO - 10.3389/fncir.2018.00119
M3 - Article
C2 - 30723397
AN - SCOPUS:85061116101
SN - 1662-5110
VL - 12
JO - Frontiers in neural circuits
JF - Frontiers in neural circuits
M1 - 119
ER -