Interval-censored Hawkes processes

• URL: http://arxiv.org/abs/2104.07932v1
• Date: Fri, 16 Apr 2021 07:29:04 GMT
• Title: Interval-censored Hawkes processes
• Authors: Marian-Andrei Rizoiu, Alexander Soen, Shidi Li, Leanne Dong, Aditya Krishna Menon and Lexing Xie
• Abstract summary: We propose a model to estimate the parameters of a Hawkes process in interval-censored settings. We show how a non-homogeneous approximation to the Hawkes admits a tractable likelihood in the interval-censored setting.
• Score: 82.87738318505582
• License: http://creativecommons.org/licenses/by-nc-sa/4.0/
• Abstract: Hawkes processes are a popular means of modeling the event times of self-exciting phenomena, such as earthquake strikes or tweets on a topical subject. Classically, these models are fit to historical event time data via likelihood maximization. However, in many scenarios, the exact times of historical events are not recorded for either privacy (e.g., patient admittance to hospitals) or technical limitations (e.g., most transport data records the volume of vehicles passing loop detectors but not the individual times). The interval-censored setting denotes when only the aggregate counts of events at specific time intervals are observed. Fitting the parameters of interval-censored Hawkes processes requires designing new training objectives that do not rely on the exact event times. In this paper, we propose a model to estimate the parameters of a Hawkes process in interval-censored settings. Our model builds upon the existing Hawkes Intensity Process (HIP) of in several important directions. First, we observe that while HIP is formulated in terms of expected intensities, it is more natural to work instead with expected counts; further, one can express the latter as the solution to an integral equation closely related to the defining equation of HIP. Second, we show how a non-homogeneous Poisson approximation to the Hawkes process admits a tractable likelihood in the interval-censored setting; this approximation recovers the original HIP objective as a special case, and allows for the use of a broader class of Bregman divergences as loss function. Third, we explicate how to compute a tighter approximation to the ground truth in the likelihood. Finally, we show how our model can incorporate information about varying interval lengths. Experiments on synthetic and real-world data confirm our HIPPer model outperforms HIP and several other baselines on the task of interval-censored inference.

Related papers

• Interacting Diffusion Processes for Event Sequence Forecasting [20.380620709345898]
  We introduce a novel approach that incorporates a diffusion generative model. The model facilitates sequence-to-sequence prediction, allowing multi-step predictions based on historical event sequences. We demonstrate that our proposal outperforms state-of-the-art baselines for long-horizon forecasting of TPP.
  arXiv  Detail & Related papers  (2023-10-26T22:17:25Z)
• SMURF-THP: Score Matching-based UnceRtainty quantiFication for Transformer Hawkes Process [76.98721879039559]
  We propose SMURF-THP, a score-based method for learning Transformer Hawkes process and quantifying prediction uncertainty. Specifically, SMURF-THP learns the score function of events' arrival time based on a score-matching objective. We conduct extensive experiments in both event type prediction and uncertainty quantification of arrival time.
  arXiv  Detail & Related papers  (2023-10-25T03:33:45Z)
• Deep Representation Learning for Prediction of Temporal Event Sets in the Continuous Time Domain [9.71405768795797]
  Temporal Point Processes play an important role in predicting or forecasting events. We propose a scalable and efficient approach based on TPPs to solve this problem.
  arXiv  Detail & Related papers  (2023-09-29T06:46:31Z)
• CenTime: Event-Conditional Modelling of Censoring in Survival Analysis [49.44664144472712]
  We introduce CenTime, a novel approach to survival analysis that directly estimates the time to event. Our method features an innovative event-conditional censoring mechanism that performs robustly even when uncensored data is scarce. Our results indicate that CenTime offers state-of-the-art performance in predicting time-to-death while maintaining comparable ranking performance.
  arXiv  Detail & Related papers  (2023-09-07T17:07:33Z)
• Generative Time Series Forecasting with Diffusion, Denoise, and Disentanglement [51.55157852647306]
  Time series forecasting has been a widely explored task of great importance in many applications. It is common that real-world time series data are recorded in a short time period, which results in a big gap between the deep model and the limited and noisy time series. We propose to address the time series forecasting problem with generative modeling and propose a bidirectional variational auto-encoder equipped with diffusion, denoise, and disentanglement.
  arXiv  Detail & Related papers  (2023-01-08T12:20:46Z)
• Cox-Hawkes: doubly stochastic spatiotemporal Poisson processes [2.6599014990168834]
  We develop a new class of inference Hawkes processes that can both trigger and clustering and behavior we provide an efficient method for performing inference. We show the efficacy and flexibility of our approach in experiments on simulated data and use our methods to uncover the trends in a dataset of reported crimes in the US.
  arXiv  Detail & Related papers  (2022-10-21T09:47:34Z)
• Linking Across Data Granularity: Fitting Multivariate Hawkes Processes to Partially Interval-Censored Data [50.63666649894571]
  In some applications, timestamps of individual events in some dimensions are unobservable, and only event counts within intervals are known. In this study, we introduce a novel point process which shares parameter equivalence with the MHP and can effectively model both timestamped and interval-censored data. We demonstrate the capabilities of the PCMHP using synthetic and real-world datasets.
  arXiv  Detail & Related papers  (2021-11-03T08:25:35Z)
• Transformer Hawkes Process [79.16290557505211]
  We propose a Transformer Hawkes Process (THP) model, which leverages the self-attention mechanism to capture long-term dependencies. THP outperforms existing models in terms of both likelihood and event prediction accuracy by a notable margin. We provide a concrete example, where THP achieves improved prediction performance for learning multiple point processes when incorporating their relational information.
  arXiv  Detail & Related papers  (2020-02-21T13:48:13Z)

This list is automatically generated from the titles and abstracts of the papers in this site.

This site does not guarantee the quality of this site (including all information) and is not responsible for any consequences.