众筹平台动态的互激点过程

A Multivariate Hawkes Process Model for Stablecoin-Cryptocurrency Depegging Event Dynamics

Stablecoins, digital assets pegged to a specific currency or commodity value, are heavily involved in transactions of major cryptocurrencies. The effects of deviations from their desired fixed values (depeggings) on the cryptocurrencies for which they are frequently used in transactions are therefore of interest to study. We propose a model for this phenomenon using a multivariate mutually-exciting Hawkes process, and present a numerical example applying this model to Tether (USDT) and Bitcoin (BTC).

聚合Hawkes过程的贝叶斯推断

Bayesian inference for aggregated Hawkes processes

针对时间戳和空间信息被聚合的Hawkes过程，提出贝叶斯参数估计方法，理论证明参数可识别性，并在模拟数据与真实暴力事件数据上验证有效性。

Graphical Modeling for Multivariate Hawkes Processes with Nonparametric Link Functions

Hawkes (1971) introduced a powerful multivariate point process model of mutually exciting processes to explain causal structure in data. In this paper it is shown that the Granger causality structure of such processes is fully encoded in the corresponding link functions of the model. A new nonparametric estimator of the link functions based on a time-discretized version of the point process is introduced by using an infinite order autoregression. Consistency of the new estimator is derived. The estimator is applied to simulated data and to neural spike train data from the spinal dorsal horn of…

Fine-Grained $ε$-Margin Closed-Form Stabilization of Parametric Hawkes Processes

Hawkes Processes have undergone increasing popularity as default tools for modeling self- and mutually exciting interactions of discrete events in continuous-time event streams. A Maximum Likelihood Estimation (MLE) unconstrained optimization procedure over parametrically assumed forms of the triggering kernels of the corresponding intensity function are a widespread cost-effective modeling strategy, particularly suitable for data with few and/or short sequences. However, the MLE optimization lacks guarantees, except for strong assumptions on the parameters of the triggering kernels, and may l…

基于多模态数据的时空野火预测

Spatio-Temporal Wildfire Prediction using Multi-Modal Data

本文提出一个基于多模态时间序列数据的时空野火预测框架，利用相互激励点过程预测野火风险，并结合无分布共形预测构建规模预测集，在加州数据上验证了有效性与可扩展性。

A neural network based model for multi-dimensional nonlinear Hawkes processes

This paper introduces the Neural Network for Nonlinear Hawkes processes (NNNH), a non-parametric method based on neural networks to fit nonlinear Hawkes processes. Our method is suitable for analyzing large datasets in which events exhibit both mutually-exciting and inhibitive patterns. The NNNH approach models the individual kernels and the base intensity of the nonlinear Hawkes process using feed forward neural networks and jointly calibrates the parameters of the networks by maximizing the log-likelihood function. We utilize Stochastic Gradient Descent to search for the optimal parameters a…

A Parameter Estimation Method for Multivariate Aggregated Hawkes Processes

It is often assumed that events cannot occur simultaneously when modelling data with point processes. This raises a problem as real-world data often contains synchronous observations due to aggregation or rounding, resulting from limitations on recording capabilities and the expense of storing high volumes of precise data. In order to gain a better understanding of the relationships between processes, we consider modelling the aggregated event data using multivariate Hawkes processes, which offer a description of mutually-exciting behaviour and have found wide applications in areas including s…

Neural Spectral Marked Point Processes

Self- and mutually-exciting point processes are popular models in machine learning and statistics for dependent discrete event data. To date, most existing models assume stationary kernels (including the classical Hawkes processes) and simple parametric models. Modern applications with complex event data require more general point process models that can incorporate contextual information of the events, called marks, besides the temporal and location information. Moreover, such applications often require non-stationary models to capture more complex spatio-temporal dependence. To tackle these …

伯恩斯坦-冯·米塞定理与多变量海克斯过程中的半参数推断效率

The Bernstein-von Mises theorem and efficiency for semiparametric inference in multivariate Hawkes processes

本文研究了线性多变量海克斯过程的半参数推断，通过建立卷积定理和半参数伯恩斯坦-冯·米塞定理，证明了在贝叶斯设置下非参数随机级数先验的最优行为。

基于霍克斯过程的异质事件动态下的短期时间依赖检测

Short-term Temporal Dependency Detection under Heterogeneous Event Dynamic with Hawkes Processes

本文针对异质事件动态下的短期时间依赖检测问题，提出一种改进MLE的鲁棒高效方法，无需先验估计异质强度，适用于少样本场景，并在多数据集实验中显著优于现有方法。

一种面向带动态潜图神经时间点过程的变分自编码器

A Variational Autoencoder for Neural Temporal Point Processes with Dynamic Latent Graphs

针对事件动力学的时变混合特征，提出一种带动态潜图的神经时间点过程变分自编码器，通过分子区间学习维度依赖图剔除无关影响，提升了事件间隔与类型的预测精度。

Prediction with Spatio-temporal Point Processes with Self Organizing Decision Trees

We study the spatio-temporal prediction problem, which has attracted the attention of many researchers due to its critical real-life applications. In particular, we introduce a novel approach to this problem. Our approach is based on the Hawkes process, which is a non-stationary and self-exciting point process. We extend the formulations of a standard point process model that can represent time-series data to represent a spatio-temporal data. We model the data as nonstationary in time and space. Furthermore, we partition the spatial region we are working on into subregions via an adaptive deci…

时间网络的依赖社区Hawkes过程模型的谱聚类

Spectral clustering for dependent community Hawkes process models of temporal networks

针对时间网络中的社区结构与节点对依赖性，提出依赖社区Hawkes（DCH）模型，结合随机块模型与相互激发Hawkes过程，推导了谱聚类误聚类误差的非渐近上界，并提出基于广义矩估计的高可扩展参数估计方法。