{"type":"ScholarlyArticle","title":"Z-Transforms and its Inference on Partially Observable Point Processes","authors":[{"name":"Young Lee","slug":"young-lee","given":"Young","family":"Lee","affiliation":"National University of Singapore"},{"name":"Thanh Vinh Vo","slug":"thanh-vinh-vo","given":"Thanh Vinh","family":"Vo","affiliation":"National University of Singapore"},{"name":"Kar Wai Lim","slug":"kar-wai-lim","given":"Kar Wai","family":"Lim","affiliation":"National University of Singapore"},{"name":"Harold Soh","slug":"harold-soh","given":"Harold","family":"Soh","affiliation":"National University of Singapore"}],"abstract":"This paper proposes an inference framework based on the Z-transform for a specific class of non-homogeneous point processes. This framework gives an alternative method to maximum likelihood estimation which is omnipresent in the field of point processes. The inference strategy is to couple or match the theoretical Z-transform with its empirical counterpart from the observed samples. This procedure fully characterizes the distribution of the point process since there exists a one-to-one mapping with the Z-transform. We illustrate how to use the methodology to estimate a point process whose intensity is driven by a general neural network.","doi":"10.24963/ijcai.2018/328","url":"https://ijcai.org/proceedings/2018/328","pdf":"https://ijcai.org/proceedings/2018/0328.pdf","markdown":"https://ijcai.org/proceedings/2018/328.md","bibtex":"https://ijcai.org/proceedings/2018/bibtex/328","volume":{"slug":"2018","title":"Proceedings of the Twenty-Seventh International Joint Conference on Artificial Intelligence","short_title":"IJCAI 2018","url":"https://ijcai.org/proceedings/2018/","year":2018,"location":"Stockholm","dates":"13-19 July 2018","editors":"Jérôme Lang","isbn":"978-0-9992411-2-7","publisher":"International Joint Conferences on Artificial Intelligence Organization","doi_prefix":"10.24963/ijcai.2018"},"section":"Machine Learning","track":"Main track","number":328,"pages":{"first":2369,"last":2375},"keywords":["Machine Learning: Neural Networks","Machine Learning: Machine Learning","Machine Learning: Time-series;Data Streams"],"videos":[],"references":[{"position":1,"raw":"[Achab et al., 2017] Massil Achab, Emmanuel Bacry, Stéphane Gaıffas, Iacopo Mastromatteo, and Jean-Franc ¸ois Muzy. Uncovering causality from multivariate Hawkes integrated cumulants. In ICML, pages 1-10, 2017.","title":"Uncovering causality from multivariate Hawkes integrated cumulants","authors":"Achab","year":"2017","venue":"ICML","doi":null,"url":null,"internal_url":null},{"position":2,"raw":"[Aït-Sahalia et al., 2015] Yacine Aït-Sahalia, Julio Cacho- Diaz, and Roger J. A. Laeven. Modeling financial con- tagion using mutually exciting jump processes. Journal of Financial Economics, 17(3):585-606, 2015.","title":"Modeling financial contagion using mutually exciting jump processes","authors":"Yacine Aït-Sahalia, Julio Cacho-Diaz, Roger J A Laeven","year":"2015","venue":"Journal of Financial Economics","doi":null,"url":null,"internal_url":null},{"position":3,"raw":"[Anandkumar et al., 2012] Animashree Anandkumar, Daniel Hsu, and Sham M Kakade. A method of moments for mixture models and hidden Markov models. In Conference on Learning Theory, pages 33-1, 2012.","title":"A method of moments for mixture models and hidden Markov models","authors":"Anandkumar","year":"2012","venue":"Conference on Learning Theory","doi":null,"url":null,"internal_url":null},{"position":4,"raw":"[Brémaud, 1981] Pierre Brémaud. Point Processes and Queues: Martingale Dynamics. Springer-Verlag, 1981.","title":"Point Processes and Queues: Martingale Dynamics","authors":"Pierre Brémaud","year":"1981","venue":null,"doi":null,"url":null,"internal_url":null},{"position":5,"raw":"[Choi et al., 2016] Edward Choi, Mohammad Taha Bahadori, Andy Schuetz, Walter F Stewart, and Jimeng Sun. Doctor AI: Predicting clinical events via recurrent neural networks. In ML for Healthcare Conf., pages 301-318, 2016.","title":"Doctor AI: Predicting clinical events via recurrent neural networks","authors":"Edward Choi, Mohammad Taha Bahadori, Andy Schuetz, Walter F Stewart, Jimeng Sun","year":"2016","venue":"ML for Healthcare Conf","doi":null,"url":null,"internal_url":null},{"position":6,"raw":"[Cox and Isham, 1980] David Roxbee Cox and Valerie Isham. Point Processes. Chapman & Hall, 1980.","title":"Point Processes","authors":"Roxbee David, Valerie Cox, Isham","year":"1980","venue":null,"doi":null,"url":null,"internal_url":null},{"position":7,"raw":"[Da Fonseca and Zaatour, 2014] José Da Fonseca and Riadh Zaatour. Hawkes process: Fast calibration, application to trade clustering, and diffusive limit. Journal of Futures Markets, 34(6):548-579, 2014.","title":"José Da Fonseca and Riadh Zaatour. Hawkes process: Fast calibration, application to trade clustering, and diffusive limit","authors":"Da Fonseca, Zaatour","year":"2014","venue":"Journal of Futures Markets","doi":null,"url":null,"internal_url":null},{"position":8,"raw":"[Diggle et al., 2013] Peter J Diggle, Paula Moraga, Barry Rowlingson, and Benjamin M Taylor. Spatial and spatio- temporal log-Gaussian Cox processes: extending the geo- statistical paradigm. Stat. Sci., pages 542-563, 2013.","title":"Spatial and spatiotemporal log-Gaussian Cox processes: extending the geostatistical paradigm","authors":"Paula Peter J Diggle, Barry Moraga, Benjamin M Rowlingson, Taylor","year":"2013","venue":"Stat. Sci","doi":null,"url":null,"internal_url":null},{"position":9,"raw":"[Ding et al., 2017] Hongyi Ding, Issei Sato, and Masashi Sugiyama. Bayesian nonparametric Poisson process al- location. arXiv preprint arXiv:1705.07006, 2017.","title":"Bayesian nonparametric Poisson process allocation","authors":"Hongyi Ding, Issei Sato, Masashi Sugiyama","year":"2017","venue":null,"doi":null,"url":null,"internal_url":null},{"position":10,"raw":"[Du et al., 2015] Nan Du, Yichen Wang, Niao He, and Le Song. Time-sensitive recommendation from recurrent user activities. In NIPS, pages 3474-3482. 2015.","title":"Time-sensitive recommendation from recurrent user activities","authors":"Nan Du, Yichen Wang, Niao He, Le Song","year":"2015","venue":"NIPS","doi":null,"url":null,"internal_url":null},{"position":11,"raw":"[Du et al., 2016] Nan Du, Hanjun Dai, Rakshit Trivedi, Utkarsh Upadhyay, Manuel Gomez-Rodriguez, and Le Song. Recurrent marked temporal point processes: Em- bedding event history to vector. In Proceedings of the 22nd ACM SIGKDD, KDD '16, pages 1555-1564. ACM, 2016.","title":"Recurrent marked temporal point processes: Embedding event history to vector","authors":"Nan Du, Hanjun Dai, Rakshit Trivedi, Utkarsh Upadhyay, Manuel Gomez-Rodriguez, Le Song","year":"2016","venue":"Proceedings of the 22nd ACM SIGKDD, KDD '16","doi":null,"url":null,"internal_url":null},{"position":12,"raw":"[Flaxman et al., 2017] Seth Flaxman, Yee Whye Teh, and Dino Sejdinovic. Poisson intensity estimation with repro- ducing kernels. In Proceedings of the 20th Int. Conf. on Artificial Intelligence and Statistics, volume 54 of Proceed- ings of Machine Learning Research, pages 270-279, 2017.","title":"Poisson intensity estimation with reproducing kernels","authors":"Seth Flaxman, Yee Whye Teh, Dino Sejdinovic","year":"2017","venue":"Proceedings of the 20th Int. Conf. on Artificial Intelligence and Statistics","doi":null,"url":null,"internal_url":null},{"position":13,"raw":"[Gerhardt and Nelson, 2009] Ira Gerhardt and Barry L Nel- son. On capturing dependence in point processes: Matching moments and other techniques. Technical report, North- western university, 2009.","title":"On capturing dependence in point processes: Matching moments and other techniques","authors":"Ira Gerhardt, Barry L Nelson","year":"2009","venue":null,"doi":null,"url":null,"internal_url":null},{"position":14,"raw":"[Hall, 2005] Alastair R Hall. Generalized method of moments. Oxford University Press, 2005.","title":"Generalized method of moments","authors":"Alastair R Hall","year":"2005","venue":null,"doi":null,"url":null,"internal_url":null},{"position":15,"raw":"[Heath et al., 2013] Robert W Heath, Marios Kountouris, and Tianyang Bai. Modeling heterogeneous network interfer- ence using Poisson point processes. IEEE Transactions on Signal Processing, 61(16):4114-4126, 2013.","title":"Modeling heterogeneous network interference using Poisson point processes","authors":"Robert W Heath, Marios Kountouris, Tianyang Bai","year":"2013","venue":"IEEE Transactions on Signal Processing","doi":null,"url":null,"internal_url":null},{"position":16,"raw":"[Kallenberg, 2006] Olav Kallenberg. Foundations of modern probability. Springer Science & Business Media, 2006.","title":"Foundations of modern probability","authors":"Olav Kallenberg, Kallenberg","year":"2006","venue":null,"doi":null,"url":null,"internal_url":null},{"position":17,"raw":"[Kim et al., 2011] Sanggyun Kim, David Putrino, Soumya Ghosh, and Emery N Brown. A granger causality measure for point process models of ensemble neural spiking activity. PLoS computational biology, 7(3):e1001110, 2011.","title":"A granger causality measure for point process models of ensemble neural spiking activity","authors":"Kim","year":"2011","venue":"PLoS computational biology","doi":null,"url":null,"internal_url":null},{"position":18,"raw":"[Kumar et al., 2006] Vipin Kumar, Jaideep Srivastava, and Aleksandar Lazarevic. Managing Cyber Threats: Issues, Approaches, and Challenges, volume 5. Springer, 2006.","title":"Managing Cyber Threats: Issues, Approaches, and Challenges","authors":"Vipin Kumar, Jaideep Srivastava, Aleksandar Lazarevic","year":"2006","venue":null,"doi":null,"url":null,"internal_url":null},{"position":19,"raw":"[Linderman and Adams, 2014] Scott W. Linderman and Ryan P. Adams. Discovering latent network structure in point process data. In ICML, pages 1413-1421, 2014.","title":"Discovering latent network structure in point process data","authors":"Scott W Linderman, Ryan P Adams","year":"2014","venue":"ICML","doi":null,"url":null,"internal_url":null},{"position":20,"raw":"[Mei and Eisner, 2016] Hongyuan Mei and Jason Eisner. The neural Hawkes process: A neurally self-modulating multi- variate point process. CoRR, abs/1612.09328, 2016.","title":"The neural Hawkes process: A neurally self-modulating multivariate point process","authors":"Eisner ; ] Hongyuan Mei, Jason Mei, Eisner","year":"2016","venue":null,"doi":null,"url":null,"internal_url":null},{"position":21,"raw":"[Menon and Lee, 2017] Aditya Krishna Menon and Young Lee. Predicting short-term public transport demand via inhomogeneous Poisson processes. In Proceedings of the 2017 ACM on CIKM, pages 2207-2210. ACM, 2017.","title":"Predicting short-term public transport demand via inhomogeneous Poisson processes","authors":"Lee ; Menon, Aditya, Krishna Menon, Young Lee","year":"2017","venue":"Proceedings of the 2017 ACM on CIKM","doi":null,"url":null,"internal_url":null},{"position":22,"raw":"[Ogata, 1981] Yosihiko Ogata. On Lewis' simulation method for point processes. IEEE TIT, 27(1):23-31, 1981.","title":"Yosihiko Ogata. On Lewis' simulation method for point processes","authors":"Ogata","year":"1981","venue":"IEEE TIT","doi":null,"url":null,"internal_url":null},{"position":23,"raw":"[Pitman, 1997] Jim Pitman. Some probabilistic aspects of set partitions. The American mathematical monthly, 104(3):201-209, 1997.","title":"Jim Pitman. Some probabilistic aspects of set partitions","authors":"Pitman","year":"1997","venue":"The American mathematical monthly","doi":null,"url":null,"internal_url":null},{"position":24,"raw":"[Privacy Rights Clearinghouse, 2018] Privacy Rights Clear- inghouse. Data breaches, 2018.","title":"Privacy Rights Clearinghouse","authors":null,"year":"2018","venue":"Data breaches","doi":null,"url":null,"internal_url":null},{"position":25,"raw":"[Soh and Demiris, 2015] Harold Soh and Yiannis Demiris. Spatio-temporal learning with the online finite and infi- nite echo-state Gaussian processes. IEEE Trans. on Neural Networks and Learning Systems, 26(3):522-536, 2015.","title":"Spatio-temporal learning with the online finite and infinite echo-state Gaussian processes","authors":"Demiris Soh, Harold Soh, Yiannis Demiris","year":"2015","venue":"IEEE Trans. on Neural Networks and Learning Systems","doi":null,"url":null,"internal_url":null},{"position":26,"raw":"[Soufiani et al., 2013] Hossein Azari Soufiani, William Chen, David C Parkes, and Lirong Xia. Generalized method- of-moments for rank aggregation. In Advances in Neural Information Processing Systems, pages 2706-2714, 2013.","title":"Generalized methodof-moments for rank aggregation","authors":"Hossein Azari Soufiani, William Chen, David C Parkes, Lirong Xia","year":"2013","venue":"Advances in Neural Information Processing Systems","doi":null,"url":null,"internal_url":null},{"position":27,"raw":"[The Internet Traffic Archive, 2018] The Internet Traffic Archive, 2018. http://ita.ee.lbl.gov/html/traces.html.","title":"The Internet Traffic Archive","authors":null,"year":"2018","venue":null,"doi":null,"url":"http://ita.ee.lbl.gov/html/traces.html","internal_url":null},{"position":28,"raw":"[Wang et al., 2017] Yongqing Wang, Shenghua Liu, Huawei Shen, Jinhua Gao, and Xueqi Cheng. Marked temporal dy- namics modeling based on recurrent neural network. In Ad- vances in Knowledge Discovery and Data Mining, PAKDD 2017, pages 786-798. Springer, 2017.","title":"Marked temporal dynamics modeling based on recurrent neural network","authors":"Yongqing Wang, Shenghua Liu, Huawei Shen, Jinhua Gao, Xueqi Cheng","year":"2017","venue":"Advances in Knowledge Discovery and Data Mining, PAKDD 2017","doi":null,"url":null,"internal_url":null},{"position":29,"raw":"[Xiao et al., 2017] Shuai Xiao, Junchi Yan, Xiaokang Yang, Hongyuan Zha, and Stephen M. Chu. Modeling the inten- sity function of point process via recurrent neural networks. In Proceedings of the Thirty-First AAAI Conference on Artificial Intelligence, pages 1597-1603, 2017.","title":"Modeling the intensity function of point process via recurrent neural networks","authors":"Shuai Xiao, Junchi Yan, Xiaokang Yang, Hongyuan Zha, Stephen M Chu","year":"2017","venue":"Proceedings of the Thirty-First AAAI Conference on Artificial Intelligence","doi":null,"url":null,"internal_url":null},{"position":30,"raw":"[Yu, 2004] Jun Yu. Empirical characteristic function estima- tion and its applications. Econometric Reviews, 23(2):93- 123, 2004.","title":"Empirical characteristic function estimation and its applications","authors":"Jun Yu","year":"2004","venue":"Econometric Reviews","doi":null,"url":null,"internal_url":null},{"position":31,"raw":"[Zhang et al., 2012] Tonglin Zhang, Zuoyi Zhang, and Ge Lin. Spatial scan statistics with overdispersion. Statis- tics in medicine, 31(8):762-774, 2012.","title":"Spatial scan statistics with overdispersion","authors":"Zhang","year":"2012","venue":"Statistics in medicine","doi":null,"url":null,"internal_url":null}],"license_note":"Copyright International Joint Conferences on Artificial Intelligence."}