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Relational time series forecasting

  • Ryan A. Rossi (a1)

Networks encode dependencies between entities (people, computers, proteins) and allow us to study phenomena across social, technological, and biological domains. These networks naturally evolve over time by the addition, deletion, and changing of links, nodes, and attributes. Despite the importance of modeling these dynamics, existing work in relational machine learning has ignored relational time series data. Relational time series learning lies at the intersection of traditional time series analysis and statistical relational learning, and bridges the gap between these two fundamentally important problems. This paper formulates the relational time series learning problem, and a general framework and taxonomy for representation discovery tasks of both nodes and links including predicting their existence, label, and weight (importance), as well as systematically constructing features. We also reinterpret the prediction task leading to the proposal of two important relational time series forecasting tasks consisting of (i) relational time series classification (predicts a future class or label of an entity), and (ii) relational time series regression (predicts a future real-valued attribute or weight). Relational time series models are designed to leverage both relational and temporal dependencies to minimize forecasting error for both relational time series classification and regression. Finally, we discuss challenges and open problems that remain to be addressed.

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Acar, E., Dunlavy, D. & Kolda, T. 2009. Link prediction on evolving data using matrix and tensor factorizations. In Proceedings of the 9th IEEE International Conference on Data Mining Workshops, 262–269.
Agami, N., Atiya, A., Saleh, M. & El-Shishiny, H. 2009. A neural network based dynamic forecasting model for trend impact analysis. Technological Forecasting and Social Change 76(7), 952962.
Ahmed, N., Atiya, A., El Gayar, N. & El-Shishiny, H. 2010. An empirical comparison of machine learning models for time series forecasting. Econometric Reviews 29(5–6), 594621.
Albert, R., Jeong, H. & Barabási, A. 1999. Internet: diameter of the world-wide web. Nature 401(6749), 130131.
Al Hasan, M. & Zaki, M. J. 2011. A survey of link prediction in social networks. In Social Network Data Analytics, 243–275. Springer.
Anderson, J. R., Michalski, R. S., Michalski, R. S., Carbonell, J. G. & Mitchell, T. M. 1986. Machine Learning: An Artificial Intelligence Approach, 2. Morgan Kaufmann.
Bengio, Y. 2009. Learning deep architectures for AI. Foundations and Trends in Machine Learning 2(1), 1127.
Ben Taieb, S., Bontempi, G., Atiya, A. F. & Sorjamaa, A. 2012. A review and comparison of strategies for multi-step ahead time series forecasting based on the NN5 forecasting competition. Expert Systems with Applications 39(8), 70677083.
Bhadra, S. & Ferreira, A. 2003. Complexity of connected components in evolving graphs and the computation of multicast trees in dynamic networks. In Ad-Hoc, Mobile, and Wireless Networks, 259–270.
Bifet, A., Holmes, G., Pfahringer, B., Kirkby, R. & Gavaldà, R. 2009. New ensemble methods for evolving data streams. In Proceeding of the 15th ACM SIGKDD International Conference on Knowledge Discovery in Data Mining, 139–148.
Bishop, C. M. 2006. Pattern Recognition and Machine Learning. Springer.
Bock, J., Cooray, A., Hanany, S., Keating, B., Lee, A., Matsumura, T., Milligan, M., Ponthieu, N., Renbarger, T. & Tran, H. 2008. The experimental probe of inflationary cosmology (EPIC): a mission concept study for NASA’s Einstein inflation probe. arXiv:0805.4207.
Boureau, Y.-L., Bach, F., LeCun, Y. & Ponce, J. 2010. Learning mid-level features for recognition. In IEEE Conference on Computer Vision and Pattern Recognition, 2559–2566.
Box, G. E., Jenkins, G. M. & Reinsel, G. C. 2013. Time Series Analysis: Forecasting and Control. John Wiley & Sons.
Brockwell, P. J. & Davis, R. A. 2002. Introduction to Time Series and Forecasting, 1. Taylor & Francis.
Broder, A., Kumar, R., Maghoul, F., Raghavan, P., Rajagopalan, S., Stata, R., Tomkins, A. & Wiener, J. 2000. Graph structure in the web. Computer Networks 33(1–6), 309320.
Bunke, H. & Kraetzl, M. 2004. Classification and detection of abnormal events in time series of graphs. In Mark Last, Abraham Kandel, Horst Bunke, Data Mining in Time Series Databases, Last, M., Kandel, A. & Bunke H (eds). World Scientific, 127–148.
Camacho, J., Guimerà, R. & Nunes Amaral, L. 2002. Robust patterns in food web structure. Physical Review Letters 88(22), 228102: 14.
Chakrabarti, S., Dom, B. & Indyk, P. 1998. Enhanced hypertext categorization using hyperlinks. In Proceedings of the ACM SIGMOD International Conference on Management of Data, 307–318.
Chandola, V., Banerjee, A. & Kumar, V. 2009. Anomaly detection: a survey. ACM Computing Surveys 41(3), 15.
Chen, C., Yin, H., Yao, J. & Cui, B. 2013. TeRec: a temporal recommender system over tweet stream. Proceedings of the VLDB Endowment 6(12), 12541257.
Clements, M. & Hendry, D. 1998. Forecasting Economic Time Series. Cambridge University Press.
Couprie, C., Farabet, C. & LeCun, Y. 2013. Causal graph-based video segmentation. arXiv:1301.1671.
Couprie, C., Farabet, C., LeCun, Y., & Najman, L. 2013, September. Causal graph-based video segmentation. In Image Processing (ICIP), 2013 20th IEEE International Conference on (pp. 4249–4253). IEEE.
Craven, M., DiPasquo, D., Freitag, D., McCallum, A., Mitchell, T., Nigam, K. & Slattery, S. 1998. Learning to extract symbolic knowledge from the World Wide Web. In Proceedings of the 15th AAAI Conference on Artificial Intelligence, 509–516.
Croushore, D. & Stark, T. 2001. A real-time data set for macroeconomists. Journal of Econometrics 105(1), 111130.
Das Sarma, A., Gollapudi, S. & Panigrahy, R. 2008. Estimating PageRank on graph streams. In Proceedings of the ACM SIGMOD International Conference on Management of Data, 69–78.
Deng, L. & Li, X. 2013. Machine learning paradigms for speech recognition: an overview. Transactions on Audio, Speech and Language Processing 21(5), 10601089.
De Raedt, L. & Kersting, K. 2008. Probabilistic Inductive Logic Programming. Springer-Verlag.
Domingos, P. & Richardson, M. 2001. Mining the network value of customers. In Proceeding of the 7th ACM SIGKDD International Conference on Knowledge Discovery in Data Mining, 57–66.
Dunlavy, D. M., Kolda, T. G. & Acar, E. 2011. Temporal link prediction using matrix and tensor factorizations. Transactions on Knowledge Discovery from Data 5(2), 10:110:27.
Dunne, J., Williams, R. & Martinez, N. 2002. Food-web structure and network theory: the role of connectance and size. Proceedings of the National Academy of Sciences of the United States of America 99(20), 12917.
Einstein, A. 1906. Zur theorie der brownschen bewegung. Annalen der Physik 324(2), 371381.
Eldardiry, H. & Neville, J. 2011. Across-model collective ensemble classification. In Proceedings of the 25th AAAI Conference on Artificial Intelligence, 343–349.
Esling, P. & Agon, C. 2012. Time-series data mining. ACM Computing Surveys 45(1), 12.
Faloutsos, M., Faloutsos, P. & Faloutsos, C. 1999. On power-law relationships of the internet topology. In Proceedings of the ACM SIGCOMM International Conference on Applications, Technologies, Architectures, and Protocols for Computer Communication, 251–262.
Friedman, N., Getoor, L., Koller, D. & Pfeffer, A. 1999. Learning probabilistic relational models. In Proceedings of the 16th International Joint Conference on Artificial Intelligence, 1300–1309. Springer-Verlag.
Getoor, L. & Taskar, B. (eds) 2007. Introduction to Statistical Relational Learning. MIT Press.
Güneş, İ, Çataltepe, Z. & Öğüdücü, Ş. G. 2011. GA-TVRC: a novel relational time varying classifier to extract temporal information using genetic algorithms. In Machine Learning and Data Mining in Pattern Recognition, 568–583. Springer.
Hasan, M. A., Chaoji, V., Salem, S. & Zaki, M. 2006. Link prediction using supervised learning. In Proceedings of the SDM Workshop on Link Analysis, Counterterrorism and Security.
Hearst, M. A., Dumais, S., Osman, E., Platt, J. & Scholkopf, B. 1998. Support vector machines. Intelligent Systems and their Applications 13(4), 1828.
Hinton, G. E., Osindero, S. & Teh, Y.-W. 2006. A fast learning algorithm for deep belief nets. Neural Computation 18(7), 15271554.
Holme, P. & Saramäki, J. 2012. Temporal networks. Physics Reports.
Hornik, K., Stinchcombe, M. & White, H. 1989. Multilayer feedforward networks are universal approximators. Neural Networks 2(5), 359366.
Ide, T. & Kashima, H. 2004. Eigenspace-based anomaly detection in computer systems. In Proceedings of the 10th ACM SIGKDD International Conference on Knowledge Discovery and Data Mining, 440–449.
Jensen, D., Neville, J. & Gallagher, B. 2004. Why collective inference improves relational classification. In Proceedings of the 10th ACM SIGKDD International Conference on Knowledge Discovery and Data Mining, 593–598.
Jeong, H., Mason, S. P., Barabási, A. L. & Oltvai, Z. N. 2001. Lethality and centrality in protein networks. Nature, 411(6833), 41.
Jeong, H., Mason, S., Barabasi, A. & Oltvai, Z. 2001. Lethality and centrality in protein networks. arXiv preprint cond-mat/0105306.
Jeong, H., Tombor, B., Albert, R., Oltvai, Z. & Barabási, A. 2000. The large-scale organization of metabolic networks. Nature 407(6804), 651654.
Kleczkowski, A. & Grenfell, B. 1999. Mean-field-type equations for spread of epidemics: the small world model. Physica A: Statistical Mechanics and its Applications 274(1–2), 355360.
Koren, Y. 2010. Collaborative filtering with temporal dynamics. Communications of the ACM 53(4), 8997.
Koren, Y., Bell, R. & Volinsky, C. 2009. Matrix factorization techniques for recommender systems. IEEE Computer 42(8), 3037.
Kovanen, L., Karsai, M., Kaski, K., Kertész, J. & Saramäki, J. 2011. Temporal motifs in time-dependent networks. Journal of Statistical Mechanics: Theory and Experiment 2011(11), P11005.
Krebs, V. 2002. Mapping networks of terrorist cells. Connections 24(3), 4352.
Lahiri, M. & Berger-Wolf, T. 2008. Mining periodic behavior in dynamic social networks. In Proceedings of the 8th IEEE International Conference on Data Mining, 373–382.
Lahiri, M. & Berger-Wolf, T. Y. 2007. Structure prediction in temporal networks using frequent subgraphs. In IEEE Symposium on Computational Intelligence and Data Mining, 35–42.
Lassez, J.-L., Rossi, R. & Jeev, K. 2008. Ranking links on the web: search and surf engines. In Proceedings of the IEA/AIE International Conference, 199–208. Springer.
LeCun, Y., Bottou, L., Bengio, Y. & Haffner, P. 1998. Gradient-based learning applied to document recognition. Proceedings of the IEEE 86(11), 22782324.
Lee, H., Grosse, R., Ranganath, R. & Ng, A. Y. 2009. Convolutional deep belief networks for scalable unsupervised learning of hierarchical representations. In Proceedings of the 26th International Conference on Machine Learning, 609–616.
Leskovec, J., Adamic, L. & Huberman, B. 2007a. The dynamics of viral marketing. Transactions on the Web 1(1), 139.
Leskovec, J., Kleinberg, J. & Faloutsos, C. 2007b. Graph evolution: densification and shrinking diameters. Transactions on Knowledge Discovery from Data 1(1), 141.
Lezama, J., Alahari, K., Sivic, J. & Laptev, I. 2011. Track to the future: spatio-temporal video segmentation with long-range motion cues. In IEEE Conference on Computer Vision and Pattern Recognition.
Li, L., Zheng, L., Yang, F. & Li, T. 2014. Modeling and broadening temporal user interest in personalized news recommendation. Expert Systems with Applications 41(7), 31683177.
Liben-Nowell, D. & Kleinberg, J. 2007. The link-prediction problem for social networks. Journal of the American Society for Information Science and Technology 58(7), 10191031.
Liu, N. N., He, L. & Zhao, M. 2013. Social temporal collaborative ranking for context aware movie recommendation. ACM Transactions on Intelligent Systems and Technology 4(1), 15.
Lu, Q. & Getoor, L. 2003. Link-based classification. In Proceedings of the 20th International Conference on Machine Learning, 496–503.
Ma, H., Yang, H., Lyu, M. R. & King, I. 2008. SoRec: social recommendation using probabilistic matrix factorization. In Proceedings of the 17th ACM Conference on Information and Knowledge Management, 931–940.
Macskassy, S. & Provost, F. 2003. A simple relational classifier. In Proceedings of the SIGKDD 2nd Workshop on Multi-Relational Data Mining, 64–76.
Marc’Aurelio Ranzato, Y., Boureau, L. & LeCun, Y. 2007. Sparse feature learning for deep belief networks. Advances in Neural Information Processing Systems 20, 11851192.
Marcellino, M., Stock, J. H. & Watson, M. W. 2006. A comparison of direct and iterated multistep are methods for forecasting macroeconomic time series. Journal of Econometrics 135(1), 499526.
Maslov, S. & Sneppen, K. 2002. Specificity and stability in topology of protein networks. Science 296(5569), 910913.
May, R. & Lloyd, A. 2001. Infection dynamics on scale-free networks. Physical Review E 64(6), 66112.
McDowell, L., Gupta, K. & Aha, D. 2010. Meta-prediction for collective classification. In Proceedings of the 23rd International FLAIRS Conference.
McDowell, L. K., Gupta, K. M. & Aha, D. W. 2009. Cautious collective classification. Journal of Machine Learning Research 10, 27772836.
McGovern, A., Collier, N., Matthew Gagne, I., Brown, D. & Rodger, A. 2008. Spatiotemporal relational probability trees: an introduction. In Proceedings of the 8th IEEE International Conference on Data Mining, 935–940.
McGovern, A., Friedland, L., Hay, M., Gallagher, B., Fast, A., Neville, J. & Jensen, D. 2003. Exploiting relational structure to understand publication patterns in high-energy physics. SIGKDD Explorations 5(2), 165172.
McPherson, M., Smith-Lovin, L. & Cook, J. M. 2001. Birds of a feather: homophily in social networks. Annual Review of Sociology 27(1), 415444.
Menon, A. & Elkan, C. 2011. Link prediction via matrix factorization. In Proceedings of the European Conference on Machine Learning and Principles and Practice of Knowledge Discovery in Databases, 437–452.
Moore, C. & Newman, M. 2000. Epidemics and percolation in small-world networks. Physical Review E 61(5), 56785682.
Neville, J., Jensen, D. & Gallagher, B. 2003. Simple estimators for relational Bayesian classifers. In Proceedings of the 3rd IEEE International Conference on Data Mining, 609–612.
Neville, J., Simsek, O., Jensen, D., Komoroske, J., Palmer, K. & Goldberg, H. 2005. Using relational knowledge discovery to prevent securities fraud. In Proceedings of the 11th ACM SIGKDD International Conference on Knowledge Discovery in Data Mining, 449–458.
Newman, M. 2001. The structure of scientific collaboration networks. Proceedings of the National Academy of Sciences 98(2), 404409.
Newman, M., Barabasi, A.-L. & Watts, D. J. 2006. The Structure and Dynamics of Networks. Princeton University Press.
Nguyen, G. H., Lee, J. B., Rossi, R. A., Ahmed, N. K., Koh, E. & Kim, S. 2018. Continuous-time dynamic network embeddings. In 3rd International Workshop on Learning Representations for Big Networks (WWW BigNet).
Noble, C. & Cook, D. 2003. Graph-based anomaly detection. In Proceedings of the 9th ACM SIGKDD International Conference on Knowledge Discovery and Data Mining, 631–636.
O’Madadhain, J. & Smyth, P. 2005. EventRank: a framework for ranking time-varying networks. In Proceedings of the LinkKDD Workshop, 9–16.
Oyama, S., Hayashi, K. & Kashima, H. 2011. Cross-temporal link prediction. In Proceedings of the 11th International Conference on Data Mining, 1188–1193.
Pastor-Satorras, R. & Vespignani, A. 2001. Epidemic spreading in scale-free networks. Physical Review Letters 86(14), 32003203.
Pindyck, R. S. & Rubinfeld, D. L. 1981. Econometric Models and Economic Forecasts, 2. McGraw-Hill New York.
Preisach, C. & Schmidt-Thieme, L. 2006. Relational ensemble classification. In Proceedings of the 6th International Conference on Data Mining, 499–509.
Preisach, C. & Schmidt-Thieme, L. 2008. Ensembles of relational classifiers. Knowledge and Information Systems 14(3), 249272.
Redmond, U., Harrigan, M. & Cunningham, P. 2012. Identifying time-respecting subgraphs in temporal networks. In Proceedings of the 3rd International Workshop on Mining Ubiquitous and Social Environments, 51–63.
Rossi, R. A. 2014. Fast triangle core decomposition for mining large graphs. In Advances in Knowledge Discovery and Data Mining, 8443, 310–322.
Rossi, R. A. 2015. Improving Relational Machine Learning by Modeling Temporal Dependencies. PhD thesis, Purdue University.
Rossi, R. A., Gallagher, B., Neville, J. & Henderson, K. 2013a. Modeling dynamic behavior in large evolving graphs. In Proceedings of the Sixth ACM International Conference on Web Search and Data Mining, 667–676.
Rossi, R. A. & Gleich, D. 2012. Dynamic PageRank using evolving teleportation. Algorithms and Models for the Web Graph 7323, 126137.
Rossi, R. A., Gleich, D. & Gebremedhin, A. 2013b. Triangle core decomposition and maximum cliques. In SIAM Network Science Workshop, 1–2.
Rossi, R. A., Gleich, D. F., Gebremedhin, A. H. & Patwary, M. A. 2012a. What if clique were fast? Maximum cliques in information networks and strong components in temporal networks. arXiv:1210.5802, 1–11.
Rossi, R. A., Gleich, D. F., Gebremedhin, A. H. & Patwary, M. A. 2013c. A fast parallel maximum clique algorithm for large sparse graphs and temporal strong components. arXiv:1302.6256, 1–9.
Rossi, R. A., McDowell, L. K., Aha, D. W. & Neville, J. 2012b. Transforming graph data for statistical relational learning. Journal of Artificial Intelligence Research 45, 363441.
Rossi, R. A. & Neville, J. 2010. Modeling the evolution of discussion topics and communication to improve relational classification. In Proceedings of the ACM SIGKDD 1st Workshop on Social Media Analytics, 89–97.
Rossi, R. A. & Neville, J. 2012. Time-evolving relational classification and ensemble methods. In Advances in Knowledge Discovery and Data Mining 7301, 1–13. Springer.
Salakhutdinov, R. & Hinton, G. E. 2009. Deep Boltzmann machines. In International Conference on Artificial Intelligence and Statistics, 448–455.
Schall, D. 2014. Link prediction in directed social networks. Social Network Analysis and Mining 4(1), 114.
Sharan, U. & Neville, J. 2008. Temporal-relational classifiers for prediction in evolving domains. In Proceedings of the 8th IEEE International Conference on Data Mining, 540–549.
Tang, J., Musolesi, M., Mascolo, C. & Latora, V. 2009. Temporal distance metrics for social network analysis. In Proceedings of the 2nd ACM Workshop on Online Social Networks, 31–36.
Tang, J., Musolesi, M., Mascolo, C., Latora, V. & Nicosia, V. 2010. Analysing information flows and key mediators through temporal centrality metrics. In Proceedings of the 3rd Workshop on Social Network Systems, 1–6.
Tong, H. & Lin, C. 2011. Non-negative residual matrix factorization with application to graph anomaly detection. In Proceedings of the 7th SIAM International Conference on Data Mining.
Wagner, A. & Fell, D. 2001. The small world inside large metabolic networks. Proceedings of the Royal Society of London. Series B: Biological Sciences 268(1478), 18031810.
Watts, D. J. & Strogatz, S. H. 1998. Collective dynamics of ‘small-world’ networks. Nature 393(6684), 440442.
Xiang, L., Yuan, Q., Zhao, S., Chen, L., Zhang, X., Yang, Q. & Sun, J. 2010a. Temporal recommendation on graphs via long-and short-term preference fusion. In Proceedings of the 16th ACM SIGKDD International Conference on Knowledge Discovery and Data Mining, 723–732.
Xiang, R., Neville, J. & Rogati, M. 2010b. Modeling relationship strength in online social networks. In Proceedings of the 19th International World Wide Web Conference, 981–990.
Xuan, B., Ferreira, A. & Jarry, A. 2003. Computing shortest, fastest, and foremost journeys in dynamic networks. International Journal of Foundations of Computer Science 14(2), 267285.
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