非局部随机神经元动力学的自主学习
Autonomous learning of nonlocal stochastic neuron dynamics
AI总结：
针对生物学合理的有色噪声驱动下神经元动力学PDF方程需闭合近似的问题，提出改进非局部大涡扩散率闭合和稀疏回归数据驱动闭合两种方法，在两类神经元模型上验证并计算了相关信息论量。
摘要：
神经元动力学由外部施加或内部产生的随机激励/噪声驱动，通常用随机常微分方程组来描述。这类系统存在解的分布，其（部分）特征由系统状态的单时间联合概率密度函数（PDF）表征。该PDF可用于计算信息论量，例如随机刺激与神经元各内部状态（如膜电位）之间的互信息，以及各类尖峰统计量。当随机激励被建模为高斯白噪声时，神经元状态的联合PDF精确满足Fokker-Planck方程。然而，大多数具备生物学合理性的噪声源是相关的（有色噪声），此时得到的PDF方程需要闭合近似。我们提出两种闭合这类方程的方法：一种是改进的非局部大涡扩散率闭合方法，另一种是依赖稀疏回归学习相关特征的数据驱动闭合方法。我们在由sine-Wiener噪声驱动的随机非尖峰泄漏积分点火神经元与FitzHugh-Nagumo（FHN）神经元上测试了这些闭合方法，并针对FHN神经元计算了随机刺激与神经元内部状态之间的互信息和总相关性。
英文摘要：
Neuronal dynamics is driven by externally imposed or internally generated random excitations/noise, and is often described by systems of random or stochastic ordinary differential equations. Such systems admit a distribution of solutions, which is (partially) characterized by the single-time joint probability density function (PDF) of system states. It can be used to calculate such information-theoretic quantities as the mutual information between the stochastic stimulus and various internal states of the neuron (e.g., membrane potential), as well as various spiking statistics. When random excitations are modeled as Gaussian white noise, the joint PDF of neuron states satisfies exactly a Fokker-Planck equation. However, most biologically plausible noise sources are correlated (colored). In this case, the resulting PDF equations require a closure approximation. We propose two methods for closing such equations: a modified nonlocal large-eddy-diffusivity closure and a data-driven closure relying on sparse regression to learn relevant features. The closures are tested for the stochastic non-spiking leaky integrate-and-fire and FitzHugh-Nagumo (FHN) neurons driven by sine-Wiener noise. Mutual information and total correlation between the random stimulus and the internal states of the neuron are calculated for the FHN neuron.
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