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.
Preface. Part I: Extensions of Basic Models. 1. The Solidarity of Markov Renewal Processes R. Pyke. 2. A Generalization of Semi-Markov Processes M. Iosifescu. 3. Quasi-stationary Phenomena for Semi-Markov Processes M. Gyllenberg, D.S. Silvestrov. 4. Semi-Markov Random Walks V.S. Korolyuk. 5. Diffusion Approximation for Processes with Semi-Markov Switches V.V. Anisimov. 6. Approximations for Semi-Markov Single Ion Channel Models S.M. Pitts. Part II: Statistical Estimation. 7. Log-likelihood in Stochastic Processes G.G. Rousas, D. Bhattacharya. 8. Some Asymptotic Results and Exponential Approximation in Semi-Markov Models G.G. Roussas, D. Bhattacharya. 9. Markov Renewal Processes and Exponential Families V.T. Stefanov. 10. On Homogeneity of Two Semi-Markov Samples L. Afanasyeva, P. Radchenko. 11. Product-Type Estimator of Convolutions I. Gertsbakh, I. Spungin. 12. Failure Rate Estimation of Semi-Markov Systems B. Ouhbi, N. Limnios. 13. Estimation for Semi-Markov Manpower Models in a Stochastic Environment S. McClean, E. Montgomery. 14. Semi-Markov Models for Lifetime Data Analysis R. Perez-Ocon, et al Part III: Non-Homogeneous Models. 15. Continuous Time Non Homogeneous Semi-Markov Systems A.A. Papadopoulou, P.C.G. Vassiliou. 16. The Perturbed Non-Homogeneous Semi-Markov System P.C.G. Vassiliou, H. Tsakiridou. Part IV: Queueing Systems Theory. 17. Semi-Markov Queues with Heavy Tails S. Asmussen.18. MR Modelling of Poisson Traffic at Intersections Having Separate Turn Lanes R. Gideon, R. Pyke. Part V: Financial Models. 19. Stochastic Stability and Optimal Control in Insurance Mathematics A. Swishchuk. 20. Option Pricing with Semi-Markov Volatility J. Janssen, et al Part VI: Controlled Processes & Maintenance. 21. Applications of Semi-Markov Processes in Reliability and Maintenance M. Abdel-Hameed. 22. Controlled Queueing Systems with Recovery Functions T. Dohi, et al Part VII: Chromatography & Fluid Mechanics. 23. Continuous Semi-Markov Models for Chromatography B.P. Harlamov. 24. The Stress Tensor of the Closed Semi-Markov System. Energy and Entropy G.M. Tsaklidis. Index. This paper is concerned with algorithms for prediction of discrete sequences over a finite alphabet, using variable order Markov models. The class of such algorithms is large and in principle includes any lossless compression algorithm. We focus on six prominent prediction algorithms, including Context Tree Weighting (CTW), Prediction by Partial Match (PPM) and Probabilistic Suffix Trees (PSTs). We discuss the properties of these algorithms and compare their performance using real life sequences from three domains: proteins, English text and music pieces. The comparison is made with respect to prediction quality as measured by the average log-loss. We also compare classification algorithms based on these predictors with respect to a number of large protein classification tasks. Our results indicate that a "decomposed" CTW (a variant of the CTW algorithm) and PPM outperform all other algorithms in sequence prediction tasks. Somewhat surprisingly, a different algorithm, which is a modification of the Lempel-Ziv compression algorithm, significantly outperforms all algorithms on the protein classification problems.