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.
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