基于Inlabru的贝叶斯霍克斯过程模型近似

Nonlinear Hawkes Process with Gaussian Process Self Effects

Traditionally, Hawkes processes are used to model time--continuous point processes with history dependence. Here we propose an extended model where the self--effects are of both excitatory and inhibitory type and follow a Gaussian Process. Whereas previous work either relies on a less flexible parameterization of the model, or requires a large amount of data, our formulation allows for both a flexible model and learning when data are scarce. We continue the line of work of Bayesian inference for Hawkes processes, and our approach dispenses with the necessity of estimating a branching structure…

A Dirichlet Mixture Model of Hawkes Processes for Event Sequence Clustering

We propose an effective method to solve the event sequence clustering problems based on a novel Dirichlet mixture model of a special but significant type of point processes --- Hawkes process. In this model, each event sequence belonging to a cluster is generated via the same Hawkes process with specific parameters, and different clusters correspond to different Hawkes processes. The prior distribution of the Hawkes processes is controlled via a Dirichlet distribution. We learn the model via a maximum likelihood estimator (MLE) and propose an effective variational Bayesian inference algorithm.…

Epidemia: An R Package for Semi-Mechanistic Bayesian Modelling of Infectious Diseases using Point Processes

This article introduces epidemia, an R package for Bayesian, regression-oriented modeling of infectious diseases. The implemented models define a likelihood for all observed data while also explicitly modeling transmission dynamics: an approach often termed as semi-mechanistic. Infections are propagated over time using renewal equations. This approach is inspired by self-exciting, continuous-time point processes such as the Hawkes process. A variety of inferential tasks can be performed using the package. Key epidemiological quantities, including reproduction numbers and latent infections, may…

Scalable Bayesian inference for self-excitatory stochastic processes applied to big American gunfire data

The Hawkes process and its extensions effectively model self-excitatory phenomena including earthquakes, viral pandemics, financial transactions, neural spike trains and the spread of memes through social networks. The usefulness of these stochastic process models within a host of economic sectors and scientific disciplines is undercut by the processes' computational burden: complexity of likelihood evaluations grows quadratically in the number of observations for both the temporal and spatiotemporal Hawkes processes. We show that, with care, one may parallelize these calculations using both c…

A joint Bayesian framework for missing data and measurement error using integrated nested Laplace approximations

Measurement error (ME) and missing values in covariates are often unavoidable in disciplines that deal with data, and both problems have separately received considerable attention during the past decades. However, while most researchers are familiar with methods for treating missing data, accounting for ME in covariates of regression models is less common. In addition, ME and missing data are typically treated as two separate problems, despite practical and theoretical similarities. Here, we exploit the fact that missing data in a continuous covariate is an extreme case of classical ME, allowi…

Semiparametric Bayesian Forecasting of Spatial Earthquake Occurrences

Self-exciting Hawkes processes are used to model events which cluster in time and space, and have been widely studied in seismology under the name of the Epidemic Type Aftershock Sequence (ETAS) model. In the ETAS framework, the occurrence of the mainshock earthquakes in a geographical region is assumed to follow an inhomogeneous spatial point process, and aftershock events are then modelled via a separate triggering kernel. Most previous studies of the ETAS model have relied on point estimates of the model parameters due to the complexity of the likelihood function, and the difficulty in esti…

Meta Learning with Relational Information for Short Sequences

This paper proposes a new meta-learning method -- named HARMLESS (HAwkes Relational Meta LEarning method for Short Sequences) for learning heterogeneous point process models from short event sequence data along with a relational network. Specifically, we propose a hierarchical Bayesian mixture Hawkes process model, which naturally incorporates the relational information among sequences into point process modeling. Compared with existing methods, our model can capture the underlying mixed-community patterns of the relational network, which simultaneously encourages knowledge sharing among seque…

多元霍克斯过程的可扩展随机贝叶斯推理方法改进

Improvements on Scalable Stochastic Bayesian Inference Methods for Multivariate Hawkes Process

针对多元霍克斯过程的贝叶斯推理问题，本文研究三类极少用于该场景的随机梯度算法，提出新的似然近似方法兼顾计算效率与精度，通过模拟和标普500板块日内价格风险研究验证效果。

The Bayesian Echo Chamber: Modeling Social Influence via Linguistic Accommodation

We present the Bayesian Echo Chamber, a new Bayesian generative model for social interaction data. By modeling the evolution of people's language usage over time, this model discovers latent influence relationships between them. Unlike previous work on inferring influence, which has primarily focused on simple temporal dynamics evidenced via turn-taking behavior, our model captures more nuanced influence relationships, evidenced via linguistic accommodation patterns in interaction content. The model, which is based on a discrete analog of the multivariate Hawkes process, permits a fully Bayesi…

Scalable Bayesian Inference for Excitatory Point Process Networks

Networks capture our intuition about relationships in the world. They describe the friendships between Facebook users, interactions in financial markets, and synapses connecting neurons in the brain. These networks are richly structured with cliques of friends, sectors of stocks, and a smorgasbord of cell types that govern how neurons connect. Some networks, like social network friendships, can be directly observed, but in many cases we only have an indirect view of the network through the actions of its constituents and an understanding of how the network mediates that activity. In this work,…

Quasi likelihood analysis of point processes for ultra high frequency data

We introduce a point process regression model that is applicable to price models and limit order book models. Hawkes type autoregression in the intensity process is generalized to a stochastic regression to covariate processes. We establish the so-called quasi likelihood analysis, which gives a polynomial type large deviation estimate for the statistical random field. We derive large sample properties of the maximum likelihood type estimator and the Bayesian type estimator when the intensity processes become large under a finite time horizon. There appears non-ergodic statistics. A classical a…

扩展霍克斯过程

Scaling Hawkes Processes

研究霍克斯过程在多领域传染现象分析中的应用，介绍拟合数据策略，通过高性能计算驱动的贝叶斯推理策略对美国枪支暴力行为做时空分析，探讨模型拟合及未来研究方向。

将Hawkes过程扩展至百万级COVID-19病例规模

Scaling Hawkes processes to one million COVID-19 cases

本研究提出高性能计算策略与两种简化可扩展方法，将时空Hawkes过程应用于美国百万级COVID-19病例的传播分析，突破了原有模型的计算规模限制。