{"type":"ScholarlyArticle","title":"Improving Maximum Likelihood Estimation of Temporal Point Process via Discriminative and Adversarial Learning","authors":[{"name":"Junchi Yan","slug":"junchi-yan","given":"Junchi","family":"Yan","affiliation":"Shanghai Jiao Tong University"},{"name":"Xin Liu","slug":"xin-liu","given":"Xin","family":"Liu","affiliation":"East China Normal University"},{"name":"Liangliang Shi","slug":"liangliang-shi","given":"Liangliang","family":"Shi","affiliation":"East China Normal University"},{"name":"Changsheng Li","slug":"changsheng-li","given":"Changsheng","family":"Li","affiliation":"University of Electronic Science and Technology of China"},{"name":"Hongyuan Zha","slug":"hongyuan-zha","given":"Hongyuan","family":"Zha","affiliation":"East China Normal University"}],"abstract":"Point process is an expressive tool in learning temporal event sequence which is ubiquitous in real-world applications. Traditional predictive models are based on maximum likelihood estimation (MLE). This paper aims to improve MLE by discriminative and adversarial learning. The initial model is learned by MLE explaining the joint distribution of the occurred event history. Then it is refined by devising a gradient based learning procedure with two complementary recipes: i) mean square error (MSE) that directly reflects the prediction accuracy of the model; ii) adversarial classification loss which induces the Wasserstein distance loss. The hope is that the adversarial loss can add sharpness to the smooth effect inherently caused by the MSE loss. The method is generic and compatible with different differentiable parametric forms of the intensity function. Empirical results via a variant of the Hawkes processes demonstrate its effectiveness of our method.","doi":"10.24963/ijcai.2018/409","url":"https://ijcai.org/proceedings/2018/409","pdf":"https://ijcai.org/proceedings/2018/0409.pdf","markdown":"https://ijcai.org/proceedings/2018/409.md","bibtex":"https://ijcai.org/proceedings/2018/bibtex/409","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":409,"pages":{"first":2948,"last":2954},"keywords":["Machine Learning: Time-series;Data Streams","Machine Learning Applications: Other Applications"],"videos":[],"references":[{"position":1,"raw":"[Aalen et al., 2008] O. Aalen, O. Borgan, and H. Gjessing. Survival and event history analysis: a process point of view. Springer Science & Business Media, 2008.","title":"Survival and event history analysis: a process point of view","authors":"O Aalen, O Borgan, H Gjessing","year":"2008","venue":null,"doi":null,"url":null,"internal_url":null},{"position":2,"raw":"[Arjovsky et al., 2017] M. Arjovsky, S. Chintala, and L. Bottou. Wasserstein gan. ICML, 2017.","title":"Wasserstein gan. ICML","authors":"M Arjovsky, S Chintala, L Bottou","year":"2017","venue":null,"doi":null,"url":null,"internal_url":null},{"position":3,"raw":"[Bengio et al., 2015] S. Bengio, O. Vinyals, N. Jaitly, and N. Shazeer. Scheduled sampling for sequence prediction with recurrent neural networks. In NIPS, 2015.","title":"Scheduled sampling for sequence prediction with recurrent neural networks","authors":"S Bengio, O Vinyals, N Jaitly, N Shazeer","year":"2015","venue":"NIPS","doi":null,"url":null,"internal_url":null},{"position":4,"raw":"[Dassios et al., 2013] A. Dassios, H. Zhao, et al. Exact simulation of hawkes process with exponentially decaying intensity. Electronic Communications in Probability, 18(62):1-13, 2013.","title":"Exact simulation of hawkes process with exponentially decaying intensity","authors":"A Dassios, H Zhao","year":"2013","venue":"Electronic Communications in Probability","doi":null,"url":null,"internal_url":null},{"position":5,"raw":"[Du et al., 2016] N. Du, H. Dai, R. Trivedi, U. Upadhyay, M. Gomez-Rodriguez, and L. Song. Recurrent marked temporal point processes: Embedding event history to vector. In KDD, 2016.","title":"Recurrent marked temporal point processes: Embedding event history to vector","authors":"N Du, H Dai, R Trivedi, U Upadhyay, M Gomez-Rodriguez, L Song","year":"2016","venue":"KDD","doi":null,"url":null,"internal_url":null},{"position":6,"raw":"[Dziugaite et al., 2015] G. K. Dziugaite, D. M. Roy, and Z. Ghahra- mani. Training generative neural networks via maximum mean discrepancy optimization. In UAI, 2015.","title":"Training generative neural networks via maximum mean discrepancy optimization","authors":"G K Dziugaite, D M Roy, Z Ghahramani","year":"2015","venue":"UAI","doi":null,"url":null,"internal_url":null},{"position":7,"raw":"[Eichler et al., 2017] M. Eichler, R. Dahlhaus, and J. Dueck. Graph- ical modeling for multivariate hawkes processes with nonparamet- ric link functions. Journal of Time Series Analysis, 2017.","title":"Graphical modeling for multivariate hawkes processes with nonparametric link functions","authors":"M Eichler, R Dahlhaus, J Dueck","year":"2017","venue":"Journal of Time Series Analysis","doi":null,"url":null,"internal_url":null},{"position":8,"raw":"[Ertekin et al., 2015a] S. Ertekin, C. Rudin, and T. McCormick. Re- active point processes: A new approach to predicting power fail- ures in underground electrical systems. The Annals of Applied Statistics, 9(1):122-144, 2015.","title":"Reactive point processes: A new approach to predicting power failures in underground electrical systems","authors":"Ertekin","year":"2015","venue":"The Annals of Applied Statistics","doi":null,"url":null,"internal_url":null},{"position":9,"raw":"[Ertekin et al., 2015b] S. Ertekin, C. Rudin, and T. H McCormick. Reactive point processes: A new approach to predicting power failures in underground electrical systems. The Annals of Applied Statistics, 2015.","title":"Reactive point processes: A new approach to predicting power failures in underground electrical systems","authors":"Ertekin","year":"2015","venue":"The Annals of Applied Statistics","doi":null,"url":null,"internal_url":null},{"position":10,"raw":"[Goodfellow et al., 2014] I.","title":null,"authors":"Goodfellow","year":"2014","venue":null,"doi":null,"url":null,"internal_url":null},{"position":11,"raw":"Goodfellow, J. Pouget-Abadie, M. Mirza, B. Xu, D. Warde-Farley, S. Ozair, A. Courville, and Y. Bengio. Generative adversarial nets. In NIPS, 2014.","title":"Generative adversarial nets","authors":"J Goodfellow, M Pouget-Abadie, B Mirza, D Xu, S Warde-Farley, A Ozair, Y Courville, Bengio","year":"2014","venue":"NIPS","doi":null,"url":null,"internal_url":null},{"position":12,"raw":"[Gulrajani et al., 2017] I. Gulrajani, F. Ahmed, M. Arjovsky, V. Du- moulin, and A. Courville. Improved training of wasserstein gans. In NIPS, 2017.","title":"Improved training of wasserstein gans","authors":"Gulrajani","year":"2017","venue":"NIPS","doi":null,"url":null,"internal_url":null},{"position":13,"raw":"[Hawkes, 1971] A. Hawkes. Point spectra of some mutually exciting point processes. Journal of the Royal Statistical Society. Series B (Methodological), pages 438-443, 1971.","title":"Point spectra of some mutually exciting point processes","authors":"A Hawkes","year":"1971","venue":"Journal of the Royal Statistical Society. Series B (Methodological)","doi":null,"url":null,"internal_url":null},{"position":14,"raw":"[Isham and Westcott, 1979] V. Isham and M. Westcott. A self- correcting point process. Stochastic Processes and Their Ap- plications, 8(3):335-347, 1979.","title":"A selfcorrecting point process","authors":"V Isham, M Westcott","year":"1979","venue":"Stochastic Processes and Their Applications","doi":null,"url":null,"internal_url":null},{"position":15,"raw":"[LeCun et al., 1998] Y. LeCun, L. Bottou, Y. Bengio, and P. Haffner. Gradient-based learning applied to document recognition. Pro- ceedings of the IEEE, 86(11):2278-2324, 1998.","title":"Gradient-based learning applied to document recognition","authors":"Y Lecun, L Bottou, Y Bengio, P Haffner","year":"1998","venue":"Proceedings of the IEEE","doi":null,"url":null,"internal_url":null},{"position":16,"raw":"[Ledig et al., 2017] C. Ledig, L. Theis, F. Huszar, J. Caballero, and A. Cunningham. Photo realistic single image super resolution using a generative adversarial network. In CVPR, 2017.","title":"Photo realistic single image super resolution using a generative adversarial network","authors":"C Ledig, L Theis, F Huszar, J Caballero, A Cunningham","year":"2017","venue":"CVPR","doi":null,"url":null,"internal_url":null},{"position":17,"raw":"[Lewis and Mohler, 2011] E. Lewis and E. Mohler. A nonparamet- ric em algorithm for multiscale hawkes processes. Journal of Nonparametric Statistics, 2011.","title":"A nonparametric em algorithm for multiscale hawkes processes","authors":"E Lewis, E Mohler","year":"2011","venue":"Journal of Nonparametric Statistics","doi":null,"url":null,"internal_url":null},{"position":18,"raw":"[Liu et al., 2017] X. Liu, J. Yan, S. Xiao, X. Wang, H. Zha, and S. Chu. On predictive patent valuation: Forecasting patent cita- tions and their types. In AAAI, 2017.","title":"On predictive patent valuation: Forecasting patent citations and their types","authors":"Liu","year":"2017","venue":"AAAI","doi":null,"url":null,"internal_url":null},{"position":19,"raw":"[Mathieu et al., 2015] Michael Mathieu, Camille Couprie, and Yann LeCun. Deep multi-scale video prediction beyond mean square error. In ICLR, 2015.","title":"Deep multi-scale video prediction beyond mean square error","authors":"Michael Mathieu, Camille Couprie, Yann Lecun","year":"2015","venue":"ICLR","doi":null,"url":null,"internal_url":null},{"position":20,"raw":"[Mohler et al., 2011] G. Mohler, M. Short, J. Brantingham, F. Schoenberg, and G. Tita. Self-exciting point process mod- eling of crime. Journal of the American Statistical Association, 2011.","title":"Self-exciting point process modeling of crime","authors":"G Mohler, M Short, J Brantingham, F Schoenberg, G Tita","year":"2011","venue":"Journal of the American Statistical Association","doi":null,"url":null,"internal_url":null},{"position":21,"raw":"[Møller and Rasmussen, 2005] J. Møller and J. G Rasmussen. Per- fect simulation of hawkes processes. Advances in applied proba- bility, 37(03):629-646, 2005.","title":"Perfect simulation of hawkes processes","authors":"J Møller, J G Rasmussen","year":"2005","venue":"Advances in applied probability","doi":null,"url":null,"internal_url":null},{"position":22,"raw":"[Møller and Rasmussen, 2006] J. Møller and J. G Rasmussen. Ap- proximate simulation of hawkes processes. Methodology and Computing in Applied Probability, 8(1):53-64, 2006.","title":"Approximate simulation of hawkes processes","authors":"J Møller, J G Rasmussen","year":"2006","venue":"Methodology and Computing in Applied Probability","doi":null,"url":null,"internal_url":null},{"position":23,"raw":"[Ogata, 1981] Y. Ogata. On lewis' simulation method for point processes. IEEE Transactions on Information Theory, 27(1):23- 31, 1981.","title":"On lewis' simulation method for point processes","authors":"Y Ogata","year":"1981","venue":"IEEE Transactions on Information Theory","doi":null,"url":null,"internal_url":null},{"position":24,"raw":"[Ogata, 1988] Y. Ogata. Statistical models for earthquake occur- rences and residual analysis for point processes. Journal of the American Statistical Association, 1988.","title":"Statistical models for earthquake occurrences and residual analysis for point processes","authors":"Y Ogata","year":"1988","venue":"Journal of the American Statistical Association","doi":null,"url":null,"internal_url":null},{"position":25,"raw":"[Rubin, 1972] I. Rubin. Regular point processes and their detection. IEEE Transactions on Information Theory, 18(5):547-557, 1972.","title":"Regular point processes and their detection","authors":"; I Rubin, Rubin","year":"1972","venue":"IEEE Transactions on Information Theory","doi":null,"url":null,"internal_url":null},{"position":26,"raw":"[Shen et al., 2014] H. Shen, D. Wang, C. Song, and A. Barabasi. Modeling and predicting popularity dynamics via reinforced pois- son processes. In AAAI, 2014.","title":"Modeling and predicting popularity dynamics via reinforced poisson processes","authors":"H Shen, D Wang, C Song, A Barabasi","year":"2014","venue":"AAAI","doi":null,"url":null,"internal_url":null},{"position":27,"raw":"[Sinha et al., 2015] A. Sinha, Z. Shen, Y. Song, H. Ma, D. Eide, B. Hsu, and K. Wang. An overview of microsoft academic service (mas) and applications. In WWW, pages 243-246, 2015.","title":"An overview of microsoft academic service (mas) and applications","authors":"A Sinha, Z Shen, Y Song, H Ma, D Eide, B Hsu, K Wang","year":"2015","venue":"WWW","doi":null,"url":null,"internal_url":null},{"position":28,"raw":"[Theis et al., 2016] L. Theis, A. van den Oord, and M. Bethge. A note on the evaluation of generative models. In ICLR, 2016.","title":"A note on the evaluation of generative models","authors":"L Theis, A Van Den Oord, M Bethge","year":"2016","venue":"ICLR","doi":null,"url":null,"internal_url":null},{"position":29,"raw":"[Tieleman and Hinton, 2012] T. Tieleman and G. Hinton. Rmsprop: Divide the gradient by a running average of its recent magnitude. COURSERA: Neural Networks for Machine Learning, 2012.","title":"Rmsprop: Divide the gradient by a running average of its recent magnitude","authors":"T Tieleman, G Hinton","year":"2012","venue":"COURSERA: Neural Networks for Machine Learning","doi":null,"url":null,"internal_url":null},{"position":30,"raw":"[Wang et al., 2013] D. Wang, C. Song, and A. Barabási. Quantifying long-term scientific impact. Science, 342(6154):127-132, 2013.","title":"Quantifying long-term scientific impact","authors":"D Wang, C Song, A Barabási","year":"2013","venue":"Science","doi":null,"url":null,"internal_url":null},{"position":31,"raw":"[Xiao et al., 2017a] S. Xiao, M. Farajtabar, X. Ye, J. Yan, L. Song, and H. Zha. Wasserstein learning of deep generative point process models. In NIPS, 2017.","title":"Wasserstein learning of deep generative point process models","authors":"Xiao","year":"2017","venue":"NIPS","doi":null,"url":null,"internal_url":null},{"position":32,"raw":"[Xiao et al., 2017b] S. Xiao, J. Yan, X. Yang, H. Zha, and S. Chu. Modeling the intensity function of point process via recurrent neural networks. In AAAI, 2017.","title":"Modeling the intensity function of point process via recurrent neural networks","authors":"Xiao","year":"2017","venue":"AAAI","doi":null,"url":null,"internal_url":null},{"position":33,"raw":"[Xiao et al., 2018] S. Xiao, J. Yan, C. Li, B. Jin, X. Wang, X. Yang, S. Chu, and H. Zha. Learning conditional generative models for temporal point processes. In AAAI, 2018.","title":"Learning conditional generative models for temporal point processes","authors":"S Xiao, J Yan, C Li, B Jin, X Wang, X Yang, S Chu, H Zha","year":"2018","venue":"AAAI","doi":null,"url":null,"internal_url":null},{"position":34,"raw":"[Yan et al., 2016] J. Yan, S. Xiao, C. Li, B. Jin, X. Wang, B. Ke, X. Yang, and H. Zha. Modeling contagious merger and acquisition via point processes with a profile regression prior. In IJCAI, 2016.","title":"Modeling contagious merger and acquisition via point processes with a profile regression prior","authors":"J Yan, S Xiao, C Li, B Jin, X Wang, B Ke, X Yang, H Zha","year":"2016","venue":"IJCAI","doi":null,"url":null,"internal_url":"/proceedings/2016/382"},{"position":35,"raw":"[Zhou et al., 2013] K. Zhou, H. Zha, and L. Song. Learning social infectivity in sparse low-rank networks using multi-dimensional hawkes processes. In AISTATS, 2013.","title":"Learning social infectivity in sparse low-rank networks using multi-dimensional hawkes processes","authors":"K Zhou, H Zha, L Song","year":"2013","venue":"AISTATS","doi":null,"url":null,"internal_url":null}],"license_note":"Copyright International Joint Conferences on Artificial Intelligence."}