相关论文: A Parameter Estimation Method for Multivariate Agg…

Nowadays, the confidentiality of data and information is of great importance for many companies and organizations. For this reason, they may prefer not to release exact data, but instead to grant researchers access to approximate data. For…

The expectation maximization (EM) algorithm is a widespread method for empirical Bayesian inference, but its expectation step (E-step) is often intractable. Employing a stochastic approximation scheme with Markov chain Monte Carlo (MCMC)…

We introduce the Hawkes process with renewal immigration and make its statistical estimation possible with two Expectation Maximization (EM) algorithms. The standard Hawkes process introduces immigrant points via a Poisson process, and each…

In this paper, we consider the sigmoid Gaussian Hawkes process model: the baseline intensity and triggering kernel of Hawkes process are both modeled as the sigmoid transformation of random trajectories drawn from Gaussian processes (GP).…

Many multivariate statistical analysis methods and their corresponding probabilistic counterparts have been adopted to develop process monitoring models in recent decades. However, the insightful connections between them have rarely been…

A novel multi-task Gaussian process (GP) framework is proposed, by using a common mean process for sharing information across tasks. In particular, we investigate the problem of time series forecasting, with the objective to improve…

The Hawkes process is a model for counting the number of arrivals to a system which exhibits the self-exciting property - that one arrival creates a heightened chance of further arrivals in the near future. The model, and its…

Finite mixture models are powerful tools for modelling and analyzing heterogeneous data. Parameter estimation is typically carried out using maximum likelihood estimation via the Expectation-Maximization (EM) algorithm. Recently, the…

Expectation Maximization (EM) is among the most popular algorithms for maximum likelihood estimation, but it is generally only guaranteed to find its stationary points of the log-likelihood objective. The goal of this article is to present…

We show that the jumps correlation matrix of a multivariate Hawkes process is related to the Hawkes kernel matrix through a system of Wiener-Hopf integral equations. A Wiener-Hopf argument allows one to prove that this system (in which the…

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…

We have established a sparse estimation method for the generalized exponential marked Hawkes process by the penalized method to the ordinary method (P-O) estimator. Furthermore, we evaluated the probability of correct variable selection. In…

Expectation Maximization (EM) is among the most popular algorithms for estimating parameters of statistical models. However, EM, which is an iterative algorithm based on the maximum likelihood principle, is generally only guaranteed to find…

Modeling the time-varying covariance structures of high-dimensional variables is critical across diverse scientific and industrial applications; however, existing approaches exhibit notable limitations in either modeling flexibility or…

We consider the problem of estimating the parameters of a non-stationary Hawkes process with time-dependent reproduction rate and baseline intensity. Our approach relies on the standard maximum likelihood estimator (MLE), coinciding with…

Finite mixture models have been widely used for the modelling and analysis of data from heterogeneous populations. Maximum likelihood estimation of the parameters is typically carried out via the Expectation-Maximization (EM) algorithm. The…

We present a new CUSUM procedure for sequentially detecting change-point in the self and mutual exciting processes, a.k.a. Hawkes networks using discrete events data. Hawkes networks have become a popular model for statistics and machine…

The stochastic block model (SBM) is one of the most widely used generative models for network data. Many continuous-time dynamic network models are built upon the same assumption as the SBM: edges or events between all pairs of nodes are…

Asynchronous events on the continuous time domain, e.g., social media actions and stock transactions, occur frequently in the world. The ability to recognize occurrence patterns of event sequences is crucial to predict which typeof events…

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.…