Department of Physics and Center for Brains, Minds and Machines, Massachusetts Institute of Technology, Cambridge, MA 02139, USA.
Phys Rev E. 2019 Mar;99(3-1):032408. doi: 10.1103/PhysRevE.99.032408.
The pairwise maximum entropy model, also known as the Ising model, has been widely used to analyze the collective activity of neurons. However, controversy persists in the literature about seemingly inconsistent findings, whose significance is unclear due to lack of reliable error estimates. We therefore develop a method for accurately estimating parameter uncertainty based on random walks in parameter space using adaptive Markov-chain Monte Carlo after the convergence of the main optimization algorithm. We apply our method to the activity patterns of excitatory and inhibitory neurons recorded with multielectrode arrays in the human temporal cortex during the wake-sleep cycle. Our analysis shows that the Ising model captures neuronal collective behavior much better than the independent model during wakefulness, light sleep, and deep sleep when both excitatory (E) and inhibitory (I) neurons are modeled; ignoring the inhibitory effects of I neurons dramatically overestimates synchrony among E neurons. Furthermore, information-theoretic measures reveal that the Ising model explains about 80-95% of the correlations, depending on sleep state and neuron type. Thermodynamic measures show signatures of criticality, although we take this with a grain of salt as it may be merely a reflection of long-range neural correlations.
成对最大熵模型，也称为伊辛模型，已被广泛用于分析神经元的集体活动。然而，文献中仍然存在争议，似乎相互矛盾的发现意义不明确，因为缺乏可靠的误差估计。因此，我们开发了一种方法，该方法基于主要优化算法收敛后在参数空间中使用自适应马尔可夫链蒙特卡罗进行随机游走，从而可以准确估计参数不确定性。我们将我们的方法应用于在清醒-睡眠周期中用多电极阵列记录的人颞叶皮层中的兴奋性和抑制性神经元的活动模式。我们的分析表明，在清醒、轻度睡眠和深度睡眠期间，当同时建模兴奋性（E）和抑制性（I）神经元时，伊辛模型比独立模型更好地捕获神经元的集体行为；忽略 I 神经元的抑制作用会极大地高估 E 神经元之间的同步性。此外，信息论度量揭示了伊辛模型可以解释约 80-95％的相关性，具体取决于睡眠状态和神经元类型。热力学度量显示出临界性的特征，尽管我们对此持保留态度，因为它可能仅仅反映了长程神经相关性。
