Rank-Based Mixture Models for Temporal Point Processes
Temporal point process, an important area in stochastic process, has been extensively studied in both theory and applications. The classical theory on point process focuses on time-based framework, where a conditional intensity function at each given time can fully describe the process. However, suc...
| Main Authors: | , , |
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| Format: | Article |
| Language: | English |
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Frontiers Media S.A.
2022-04-01
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| Series: | Frontiers in Applied Mathematics and Statistics |
| Subjects: | |
| Online Access: | https://www.frontiersin.org/articles/10.3389/fams.2022.852314/full |
| _version_ | 1818355699594297344 |
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| author | Yang Chen Yijia Ma Wei Wu |
| author_facet | Yang Chen Yijia Ma Wei Wu |
| author_sort | Yang Chen |
| collection | DOAJ |
| description | Temporal point process, an important area in stochastic process, has been extensively studied in both theory and applications. The classical theory on point process focuses on time-based framework, where a conditional intensity function at each given time can fully describe the process. However, such a framework cannot directly capture important overall features/patterns in the process, for example, characterizing a center-outward rank or identifying outliers in a given sample. In this article, we propose a new, data-driven model for regular point process. Our study provides a probabilistic model using two factors: (1) the number of events in the process, and (2) the conditional distribution of these events given the number. The second factor is the key challenge. Based on the equivalent inter-event representation, we propose two frameworks on the inter-event times (IETs) to capture large variability in a given process—One is to model the IETs directly by a Dirichlet mixture, and the other is to model the isometric logratio transformed IETs by a classical Gaussian mixture. Both mixture models can be properly estimated using a Dirichlet process (for the number of components) and Expectation-Maximization algorithm (for parameters in the models). In particular, we thoroughly examine the new models on the commonly used Poisson processes. We finally demonstrate the effectiveness of the new framework using two simulations and one real experimental dataset. |
| first_indexed | 2024-12-13T19:45:28Z |
| format | Article |
| id | doaj.art-8f3061b991a84a53932db71ccb90a56d |
| institution | Directory Open Access Journal |
| issn | 2297-4687 |
| language | English |
| last_indexed | 2024-12-13T19:45:28Z |
| publishDate | 2022-04-01 |
| publisher | Frontiers Media S.A. |
| record_format | Article |
| series | Frontiers in Applied Mathematics and Statistics |
| spelling | doaj.art-8f3061b991a84a53932db71ccb90a56d2022-12-21T23:33:34ZengFrontiers Media S.A.Frontiers in Applied Mathematics and Statistics2297-46872022-04-01810.3389/fams.2022.852314852314Rank-Based Mixture Models for Temporal Point ProcessesYang ChenYijia MaWei WuTemporal point process, an important area in stochastic process, has been extensively studied in both theory and applications. The classical theory on point process focuses on time-based framework, where a conditional intensity function at each given time can fully describe the process. However, such a framework cannot directly capture important overall features/patterns in the process, for example, characterizing a center-outward rank or identifying outliers in a given sample. In this article, we propose a new, data-driven model for regular point process. Our study provides a probabilistic model using two factors: (1) the number of events in the process, and (2) the conditional distribution of these events given the number. The second factor is the key challenge. Based on the equivalent inter-event representation, we propose two frameworks on the inter-event times (IETs) to capture large variability in a given process—One is to model the IETs directly by a Dirichlet mixture, and the other is to model the isometric logratio transformed IETs by a classical Gaussian mixture. Both mixture models can be properly estimated using a Dirichlet process (for the number of components) and Expectation-Maximization algorithm (for parameters in the models). In particular, we thoroughly examine the new models on the commonly used Poisson processes. We finally demonstrate the effectiveness of the new framework using two simulations and one real experimental dataset.https://www.frontiersin.org/articles/10.3389/fams.2022.852314/fulltemporal point processcenter-outward rankDirichlet mixtureGaussian mixtureDirichlet processisometric logratio transformation |
| spellingShingle | Yang Chen Yijia Ma Wei Wu Rank-Based Mixture Models for Temporal Point Processes Frontiers in Applied Mathematics and Statistics temporal point process center-outward rank Dirichlet mixture Gaussian mixture Dirichlet process isometric logratio transformation |
| title | Rank-Based Mixture Models for Temporal Point Processes |
| title_full | Rank-Based Mixture Models for Temporal Point Processes |
| title_fullStr | Rank-Based Mixture Models for Temporal Point Processes |
| title_full_unstemmed | Rank-Based Mixture Models for Temporal Point Processes |
| title_short | Rank-Based Mixture Models for Temporal Point Processes |
| title_sort | rank based mixture models for temporal point processes |
| topic | temporal point process center-outward rank Dirichlet mixture Gaussian mixture Dirichlet process isometric logratio transformation |
| url | https://www.frontiersin.org/articles/10.3389/fams.2022.852314/full |
| work_keys_str_mv | AT yangchen rankbasedmixturemodelsfortemporalpointprocesses AT yijiama rankbasedmixturemodelsfortemporalpointprocesses AT weiwu rankbasedmixturemodelsfortemporalpointprocesses |