Temporal point process is widely used for sequential data modeling. In this paper, we focus on the problem of modeling sequential event propagation in graph, such as retweeting by social network users, news transmitting between websites, etc. Given a collection of event propagation sequences, conventional point process model consider only the event history, i.e. embed event history into a vector, not the latent graph structure. We propose a Graph Biased Temporal Point Process (GBTPP) leveraging the structural information from graph representation learning, where the direct influence between nodes and indirect influence from event history is modeled respectively. Moreover, the learned node embedding vector is also integrated into the embedded event history as side information. Experiments on a synthetic dataset and two real-world datasets show the efficacy of our model compared to conventional methods and state-of-the-art.
When dealing with event propagation sequences, a major limitation of these existing studies is that the structural information of the latent graph @math is not utilized. Conventional TPP models including state-of-the-art method in @cite_4 solve event propagation modeling as general event sequences modeling and take input @math , while our GBTPP model leverage the structural information and node proximity of graph @math taking input @math , where @math is the node embedding vector obtained by a graph representation learning method for @math .
@cite_4
2169415915 1961165281 1938647246 2950857600
Important inference problems in statistical physics, computer vision, error-correcting coding theory, and artificial intelligence can all be reformulated as the computation of marginal probabilities on factor graphs. The belief propagation (BP) algorithm is an efficient way to solve these problems that is exact when the factor graph is a tree, but only approximate when the factor graph has cycles. We show that BP fixed points correspond to the stationary points of the Bethe approximation of the free energy for a factor graph. We explain how to obtain region-based free energy approximations that improve the Bethe approximation, and corresponding generalized belief propagation (GBP) algorithms. We emphasize the conditions a free energy approximation must satisfy in order to be a "valid" or "maxent-normal" approximation. We describe the relationship between four different methods that can be used to generate valid approximations: the "Bethe method", the "junction graph method", the "cluster variation method", and the "region graph method". Finally, we explain how to tell whether a region-based approximation, and its corresponding GBP algorithm, is likely to be accurate, and describe empirical results showing that GBP can significantly outperform BP. This work presents a novel modeling and analysis framework for graph sequences which addresses the challenge of detecting and contextualizing anomalies in labeled, streaming graph data. We introduce a generalization of the BTER model of by adding flexibility to community structure, and use this model to perform multi-scale graph anomaly detection. Specifically, probability models describing coarse subgraphs are built by aggregating node probabilities, and these related hierarchical models simultaneously detect deviations from expectation. This technique provides insight into the graphs' structure and helps contextualized detected event. For evaluation, two new hierarchical detectors are tested against a baseline Gaussian method on a synthetic graph sequence with seeded anomalies. We demonstrate that in a labeled setting with community structure, our graph statistics-based approach outperforms both a distribution-based detector and the baseline, accurately detecting anomalies at the node, subgraph, and graph levels. Determinantal point processes (DPP) serve as a practicable modeling for many applications of repulsive point processes. A known approach for simulation was proposed in Hough(2006) , which generate the desired distribution point wise through rejection sampling. Unfortunately, the size of rejection could be very large. In this paper, we investigate the application of perfect simulation via coupling from the past (CFTP) on DPP. We give a general framework for perfect simulation on DPP model. It is shown that the limiting sequence of the time-to-coalescence of the coupling is bounded by @math An application is given to the stationary models in DPP. We present a Bayesian tensor factorization model for inferring latent group structures from dynamic pairwise interaction patterns. For decades, political scientists have collected and analyzed records of the form "country @math took action @math toward country @math at time @math "---known as dyadic events---in order to form and test theories of international relations. We represent these event data as a tensor of counts and develop Bayesian Poisson tensor factorization to infer a low-dimensional, interpretable representation of their salient patterns. We demonstrate that our model's predictive performance is better than that of standard non-negative tensor factorization methods. We also provide a comparison of our variational updates to their maximum likelihood counterparts. In doing so, we identify a better way to form point estimates of the latent factors than that typically used in Bayesian Poisson matrix factorization. Finally, we showcase our model as an exploratory analysis tool for political scientists. We show that the inferred latent factor matrices capture interpretable multilateral relations that both conform to and inform our knowledge of international affairs.