论文标题
推断具有抑制和应用神经元活性的多元指数霍克斯过程
Inference of multivariate exponential Hawkes processes with inhibition and application to neuronal activity
论文作者
论文摘要
多元霍克斯的过程是一个过去的依赖点过程，用于模拟事件发生之间的关系，尽管引入了霍克斯的过程来描述激发效应，尽管霍克斯的过程最初会增加另一个事件的机会，但在这种情况下，人们越来越兴趣对相反的效果，我们已知的依赖性，我们将其置于互惠率的范围。和抑制作用。我们的第一个结果是在一些足够的假设下证明该模型的可识别性。然后，我们提出了一种最大的似然方法来估计相互作用函数，据我们所知，在频繁式框架中的第一个精确推理过程。我们的方法包括一个可变选择步骤，以恢复相互作用的支持，因此可以推断我们方法的好处，以评估符合日志的良好性，该效果是在良好的情况下进行良好的效果，该功能是良好的，该功能是良好的，该效果是一个良好的效果，该效果是一个良好的效果，该效果是一个良好的效果。将我们的方法与在线性框架中开发的标准方法进行比较，并且不是专门设计用于处理抑制效果的专门设计的。我们表明，所提出的估计器在合成数据上的性能要比替代方法更好。我们还说明了我们的程序在神经元活动数据集中的应用，这突出了神经元之间令人兴奋和抑制作用的存在。
The multivariate Hawkes process is a past-dependent point process used to model the relationship of event occurrences between different phenomena.Although the Hawkes process was originally introduced to describe excitation effects, which means that one event increases the chances of another occurring, there has been a growing interest in modelling the opposite effect, known as inhibition.In this paper, we focus on how to infer the parameters of a multidimensional exponential Hawkes process with both excitation and inhibition effects. Our first result is to prove the identifiability of this model under a few sufficient assumptions. Then we propose a maximum likelihood approach to estimate the interaction functions, which is, to the best of our knowledge, the first exact inference procedure in the frequentist framework.Our method includes a variable selection step in order to recover the support of interactions and therefore to infer the connectivity graph.A benefit of our method is to provide an explicit computation of the log-likelihood, which enables in addition to perform a goodness-of-fit test for assessing the quality of estimations.We compare our method to standard approaches, which were developed in the linear framework and are not specifically designed for handling inhibiting effects.We show that the proposed estimator performs better on synthetic data than alternative approaches. We also illustrate the application of our procedure to a neuronal activity dataset, which highlights the presence of both exciting and inhibiting effects between neurons.
