Department of Electrical and Electronic Engineering, Atilim University, Golbasi, Turkey.
Department of Biomedical Engineering, Johns Hopkins University School of Medicine, Baltimore, MD, United States.
Front Neural Circuits. 2019 Jan 22;12:119. doi: 10.3389/fncir.2018.00119. eCollection 2018.
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.
我们提出了一种自适应刺激设计方法，用于有效地估计具有相互作用的兴奋性和抑制性神经元群体的动态递归网络模型的参数。尽管理论上，针对模型参数估计而优化的刺激应该比非自适应随机刺激具有优势，但在实践中，对于这种常见类型的递归网络模型，最佳时变刺激设计实际上在哪些方面以及在何种程度上可以改善参数估计，仍然不清楚。在这里，我们通过傅里叶级数来指定每个刺激的时间过程，其幅度和相位通过最大化基于 Fisher 信息矩阵的效用函数来确定。为了便于优化过程，我们推导出了控制效用函数梯度随刺激参数的时间演化的微分方程。通过来自连续网络状态的非均匀泊松过程产生的尖峰序列数据，从最大似然法估计网络参数。自适应设计过程在闭环中重复进行，在最优刺激设计和从更新的刺激-反应数据进行参数估计之间交替进行。我们的结果证实，与随机刺激相比，最优设计的刺激引起的响应更有利于参数估计的似然值。此外，通过最优设计方法可以更准确地恢复所有个体参数，包括时间常数和连接权重。我们还研究了不同参数估计的误差如何相关，并通过近似参数混淆理论提出了启发式公式来解释相关模式。我们的结果表明，尽管即使对于最简单的兴奋性抑制性递归网络模型，自适应最优刺激设计也会带来相当大的计算成本，但它可能通过减少网络参数估计所需的刺激数量，有助于在实验中节省时间。
