A variety of real-world processes (over networks) produce sequences of data whose complex temporal dynamics need to be studied. More especially, the event timestamps can carry important information about the underlying network dynamics, which otherwise are not available from the time-series evenly sampled from continuous signals. Moreover, in most complex processes, event sequences and evenly-sampled times series data can interact with each other, which renders joint modeling of those two sources of data necessary. To tackle the above problems, in this paper, we utilize the rich framework of (temporal) point processes to model event data and timely update its intensity function by the synergic twin Recurrent Neural Networks (RNNs). In the proposed architecture, the intensity function is synergistically modulated by one RNN with asynchronous events as input and another RNN with time series as input. Furthermore, to enhance the interpretability of the model, the attention mechanism for the neural point process is introduced. The whole model with event type and timestamp prediction output layers can be trained end-to-end and allows a black-box treatment for modeling the intensity. We substantiate the superiority of our model in synthetic data and three real-world benchmark datasets.
4) @cite_19 : it can be regarded as a generalization of the Hawkes process by adding a self-inhibiting term to account for the inhibiting effects from history events.
@cite_19
1999735946 138372711 2950604469 2137644567
A maximum likelihood estimation procedure of Hawkes' self-exciting point process model is proposed with explicit presentations of the log-likelihood of the model and its gradient and Hessian. A simulation method of the process is also presented. Some numerical results are given. IN contagious processes (e.g. measles, hijacking, etc.) the occurrence of events increases the probability of further events occurring in the near future. Also several series of events may interact with each other, for example one might consider notifications of some disease in a number of adjacent regions which would interact through infectives or carriers moving between the regions. In this paper we postulate a model for such processes and derive a general expression for the point spectral matrices. These theoretical spectra are useful for comparison with spectra estimated from data and thus provide a means of evaluating the fit of such a model in the manner of Bartlett (1963). The model studied was put forward in an earlier paper (Hawkes, 1971) but the solution was obtained only in special cases. In this paper an elegant solution is obtained for the. general case. Consider a stationary k-variate point process N(t), where Ni(t) represents the cumulative number of events in the ith process up to time t, with intensity vector X = of dN(t) dt and covariance density matrix 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 a rat. Clusters in document streams, such as online news articles, can be induced by their textual contents, as well as by the temporal dynamics of their arriving patterns. Can we leverage both sources of information to obtain a better clustering of the documents, and distill information that is not possible to extract using contents only? In this paper, we propose a novel random process, referred to as the Dirichlet-Hawkes process, to take into account both information in a unified framework. A distinctive feature of the proposed model is that the preferential attachment of items to clusters according to cluster sizes, present in Dirichlet processes, is now driven according to the intensities of cluster-wise self-exciting temporal point processes, the Hawkes processes. This new model establishes a previously unexplored connection between Bayesian Nonparametrics and temporal Point Processes, which makes the number of clusters grow to accommodate the increasing complexity of online streaming contents, while at the same time adapts to the ever changing dynamics of the respective continuous arrival time. We conducted large-scale experiments on both synthetic and real world news articles, and show that Dirichlet-Hawkes processes can recover both meaningful topics and temporal dynamics, which leads to better predictive performance in terms of content perplexity and arrival time of future documents.