Linking Across Data Granularity: Fitting Multivariate Hawkes Processes to Partially Interval-Censored Data

• URL: http://arxiv.org/abs/2111.02062v3
• Date: Thu, 5 Oct 2023 04:55:06 GMT
• Title: Linking Across Data Granularity: Fitting Multivariate Hawkes Processes to Partially Interval-Censored Data
• Authors: Pio Calderon, Alexander Soen, Marian-Andrei Rizoiu
• Abstract summary: In certain applications, the timestamps of individual events in some dimensions are unobservable. We introduce the Partial Mean Behavior Poisson (PMBP) process, a novel point process which shares parameter equivalence with the MHP. We demonstrate the capabilities of the PMBP process using synthetic and real-world datasets.
• Score: 55.31692043677966
• License: http://creativecommons.org/licenses/by-nc-sa/4.0/
• Abstract: The multivariate Hawkes process (MHP) is widely used for analyzing data streams that interact with each other, where events generate new events within their own dimension (via self-excitation) or across different dimensions (via cross-excitation). However, in certain applications, the timestamps of individual events in some dimensions are unobservable, and only event counts within intervals are known, referred to as partially interval-censored data. The MHP is unsuitable for handling such data since its estimation requires event timestamps. In this study, we introduce the Partial Mean Behavior Poisson (PMBP) process, 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 PMBP process using synthetic and real-world datasets. Firstly, we illustrate that the PMBP process can approximate MHP parameters and recover the spectral radius using synthetic event histories. Next, we assess the performance of the PMBP process in predicting YouTube popularity and find that it surpasses state-of-the-art methods. Lastly, we leverage the PMBP process to gain qualitative insights from a dataset comprising daily COVID-19 case counts from multiple countries and COVID-19-related news articles. By clustering the PMBP-modeled countries, we unveil hidden interaction patterns between occurrences of COVID-19 cases and news reporting.

Related papers

• Explaining Categorical Feature Interactions Using Graph Covariance and LLMs [18.44675735926458]
  This paper focuses on the global synthetic dataset from the Counter Trafficking Data Collaborative. It contains over 200,000 anonymized records spanning from 2002 to 2022 with numerous categorical features for each record. We propose a fast and scalable method for analyzing and extracting significant categorical feature interactions.
  arXiv  Detail & Related papers  (2025-01-24T21:41:26Z)
• MTSCI: A Conditional Diffusion Model for Multivariate Time Series Consistent Imputation [41.681869408967586]
  Key research question is how to ensure imputation consistency, i.e., intra-consistency between observed and imputed values. Previous methods rely solely on the inductive bias of the imputation targets to guide the learning process.
  arXiv  Detail & Related papers  (2024-08-11T10:24:53Z)
• Near-Optimal Learning and Planning in Separated Latent MDPs [70.88315649628251]
  We study computational and statistical aspects of learning Latent Markov Decision Processes (LMDPs) In this model, the learner interacts with an MDP drawn at the beginning of each epoch from an unknown mixture of MDPs.
  arXiv  Detail & Related papers  (2024-06-12T06:41:47Z)
• PeFAD: A Parameter-Efficient Federated Framework for Time Series Anomaly Detection [51.20479454379662]
  We propose a. Federated Anomaly Detection framework named PeFAD with the increasing privacy concerns. We conduct extensive evaluations on four real datasets, where PeFAD outperforms existing state-of-the-art baselines by up to 28.74%.
  arXiv  Detail & Related papers  (2024-06-04T13:51:08Z)
• Transformer-Based Neural Marked Spatio Temporal Point Process Model for Football Match Events Analysis [0.6946929968559495]
  We propose a model for football event data based on the neural temporal point processes framework. For verification, we examined the relationship with football teams' final ranking, average goal score, and average xG over season. It was observed that the average HPUS showed significant correlations regardless of not using goal and shot details.
  arXiv  Detail & Related papers  (2023-02-18T10:02:45Z)
• TACTiS: Transformer-Attentional Copulas for Time Series [76.71406465526454]
  estimation of time-varying quantities is a fundamental component of decision making in fields such as healthcare and finance. We propose a versatile method that estimates joint distributions using an attention-based decoder. We show that our model produces state-of-the-art predictions on several real-world datasets.
  arXiv  Detail & Related papers  (2022-02-07T21:37:29Z)
• Interval-censored Hawkes processes [82.87738318505582]
  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.
  arXiv  Detail & Related papers  (2021-04-16T07:29:04Z)
• Learning Multivariate Hawkes Processes at Scale [17.17906360554892]
  We show that our approach allows to compute the exact likelihood and gradients of an MHP -- independently of the ambient dimensions of the underlying network. We show on synthetic and real-world datasets that our model does not only achieve state-of-the-art predictive results, but also improves runtime performance by multiple orders of magnitude.
  arXiv  Detail & Related papers  (2020-02-28T01:18:01Z)
• 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.