具有可变记忆长度的Hawkes过程：存在性、推断及应用于神经活动
Hawkes Processes with Variable Length Memory: Existence, Inference and Application to Neuronal Activity
AI总结：
本文提出一种具有可变记忆长度的非线性Hawkes过程，证明其存在性并推导出可行的似然最大化方法，应用于神经活动数据集以验证有效性。
摘要：
多变量Hawkes过程是依赖过去事件的点过程，最初用于建模激发效应，后扩展为非线性框架以考虑抑制效应。受神经科学应用启发，我们引入了一种新的非线性Hawkes过程，具有可变长度记忆。该模型扩展了经典Hawkes过程，描述事件在给定子过程中发生概率可能对历史前后的不同事件依赖性不同。特别地，如果子过程不依赖于其最后一次事件前的历史，则称为具有可变长度记忆。本文的主要贡献是证明此类过程的存在性，并推导出可行的似然最大化方法，能够识别经典和可变记忆动态。我们通过合成数据和神经活动数据集验证了该方法的有效性。
英文摘要：
Multivariate Hawkes processes are past-dependant point processes originally introduced to model excitation effects, later extended to a nonlinear framework to account for the opposite effect, known as inhibition. Motivated by applications in neuroscience, where the memory of a neuron may reset upon firing, we introduce a new class of nonlinear Hawkes processes with variable length memory. Our model generalises classical Hawkes processes, with or without inhibition, describing the situation where the probability of an event occurring within a given subprocess may depend differently on the history before and after its last event. In particular, if the subprocess does not depend on the history before its last event, it is said to have a variable length memory. Our main contributions are to prove existence of such processes, and to derive a workable likelihood maximisation method, capable of identifying both classical and variable memory dynamics. We demonstrate the effectiveness of our approach both on synthetic data, and on a neuronal activity dataset.
机构、总结、中文摘要均由AI分析而来，可能存在错误，请以论文正文为准。
