We propose an extension to Hawkes processes by treating the levels of self-excitation as a stochastic differential equation. Our new point process allows better approximation in application domains where events and intensities accelerate each other with correlated levels of contagion. We generalize a recent algorithm for simulating draws from Hawkes processes whose levels of excitation are stochastic processes, and propose a hybrid Markov chain Monte Carlo approach for model fitting. Our sampling procedure scales linearly with the number of required events and does not require stationarity of the point process. A modular inference procedure consisting of a combination between Gibbs and Metropolis Hastings steps is put forward. We recover expectation maximization as a special case. Our general approach is illustrated for contagion following geometric Brownian motion and exponential Langevin dynamics.
proposed an EM inference algorithm for Hawkes processes and applied to large social network datasets. Inspired by their latent variable set-up, we adapted some of their hidden variable formulation within the marked point process framework into our fully Bayesian inference setting. We have leveraged ideas from previous work on self-exciting processes to consequently treating the levels of excitation as random processes. introduced a multivariate point process combining self (Hawkes) and external (Cox) flavors to study latent networks in the data. These processes have also been proposed and applied in analyzing topic diffusion and user interactions @cite_11 @cite_12 . put forth a temporal point process model with one intensity being modulated by the other. Bounds of self exciting processes are also studied in @cite_4 . Differently from these, we breathe another dimension into Hawkes processes by modeling the contagion parameters as a stochastic differential equation equipped with general procedures for learning. This allows much more latitude in parameterizing the self-exciting processes as a basic building block before incorporating wider families of processes.
@cite_4 @cite_12 @cite_11
2808908091 2950604469 236111108 2137644567
Given the rich real-life applications of network mining as well as the surge of representation learning in recent years, network embedding has become the focal point of increasing research interests in both academic and industrial domains. Nevertheless, the complete temporal formation process of networks characterized by sequential interactive events between nodes has yet seldom been modeled in the existing studies, which calls for further research on the so-called temporal network embedding problem. In light of this, in this paper, we introduce the concept of neighborhood formation sequence to describe the evolution of a node, where temporal excitation effects exist between neighbors in the sequence, and thus we propose a Hawkes process based Temporal Network Embedding (HTNE) method. HTNE well integrates the Hawkes process into network embedding so as to capture the influence of historical neighbors on the current neighbors. In particular, the interactions of low-dimensional vectors are fed into the Hawkes process as base rate and temporal influence, respectively. In addition, attention mechanism is also integrated into HTNE to better determine the influence of historical neighbors on current neighbors of a node. Experiments on three large-scale real-life networks demonstrate that the embeddings learned from the proposed HTNE model achieve better performance than state-of-the-art methods in various tasks including node classification, link prediction, and embedding visualization. In particular, temporal recommendation based on arrival rate inferred from node embeddings shows excellent predictive power of the proposed model. 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. We present a novel probabilistic approach for fitting a statistical model to an image. A 3D Morphable Model (3DMM) of faces is interpreted as a generative (Top-Down) Bayesian model. Random Forests are used as noisy detectors (Bottom-Up) for the face and facial landmark positions. The Top-Down and Bottom-Up parts are then combined using a Data-Driven Markov Chain Monte Carlo Method (DDMCMC). As core of the integration, we use the Metropolis-Hastings algorithm which has two main advantages. First, the algorithm can handle unreliable detections and therefore does not need the detectors to take an early and possible wrong hard decision before fitting. Second, it is open for integration of various cues to guide the fitting process. Based on the proposed approach, we implemented a completely automatic, pose and illumination invariant face recognition application. We are able to train and test the building blocks of our application on different databases. The system is evaluated on the Multi-PIE database and reaches state of the art performance. 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.