Efficient Inference of Flexible Interaction in Spiking-neuron Networks
Efficient Inference of Flexible Interaction in Spiking-neuron Networks
复制标题
尖峰神经元网络中灵活交互的有效推理
DOI：
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发表时间：
2021
期刊：
影响因子：
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通讯作者：
Jun Zhu
中科院分区：
文献类型：
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作者：
Feng Zhou;Yixuan Zhang;Jun Zhu
霍克斯过程为分析神经元锋电位活动的时间依赖性相互作用提供了有效的统计框架。虽然在许多真实的应用中使用，但经典的Hawkes过程无法模拟神经元之间的抑制性相互作用。相反，非线性霍克斯过程允许更灵活的影响模式与兴奋或抑制的相互作用。在本文中，三组辅助潜变量（Polya-Gamma变量，潜在的标记泊松过程和稀疏变量）的增广功能连接权重的高斯形式，这使得一个简单的迭代算法与分析更新。因此，一个有效的期望最大化（EM）算法推导出获得最大后验（MAP）估计。我们证明了我们的算法的准确性和效率性能的合成和真实的数据。对于真实的神经记录，我们表明我们的算法可以估计相互作用的时间动态，并揭示可解释的功能连接的神经尖峰列车。
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 (Polya-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.