论文标题
有效推断峰值 - 神经网络中灵活相互作用
Efficient Inference of Flexible Interaction in Spiking-neuron Networks
论文作者
论文摘要
霍克斯工艺提供了一个有效的统计框架，用于分析神经元尖峰活动的时间依赖性相互作用。尽管在许多实际应用中使用，但经典的霍克斯过程无法对神经元之间的抑制作用进行建模。取而代之的是，非线性鹰队过程允许通过兴奋性或抑制性相互作用产生更灵活的影响模式。在本文中，增强了三组辅助潜在变量（Pólya-Gamma变量，潜在标记的Poisson过程和稀疏变量），以使高斯形式的功能连接权重以高斯形式提供功能连接权重，从而允许使用分析更新的简单迭代算法。结果，得出有效的期望最大化（EM）算法以获得最大后验（MAP）估计值。我们证明了算法在合成和真实数据上的准确性和效率性能。对于真实的神经记录，我们显示我们的算法可以估计相互作用的时间动力学，并揭示神经尖峰列车的可解释功能连通性。
Hawkes process provides an effective statistical framework for analyzing the time-dependent interaction of neuronal spiking activities. Although utilized in many real applications, the classic Hawkes process is incapable of modelling inhibitory interactions among neurons. Instead, the nonlinear Hawkes process allows for a more flexible influence pattern with excitatory or inhibitory interactions. In this paper, three sets of auxiliary latent variables (Pólya-Gamma variables, latent marked Poisson processes and sparsity variables) are augmented to make functional connection weights in a Gaussian form, which allows for a simple iterative algorithm with analytical updates. As a result, an efficient expectation-maximization (EM) algorithm is derived to obtain the maximum a posteriori (MAP) estimate. We demonstrate the accuracy and efficiency performance of our algorithm on synthetic and real data. For real neural recordings, we show our algorithm can estimate the temporal dynamics of interaction and reveal the interpretable functional connectivity underlying neural spike trains.
