# Interval-censored Hawkes processes arXiv: https://arxiv.org/abs/2104.07932 ยท HTML: https://mlsanity.com/paper/2104.07932/ ## Key facts - Cited by 5 papers in the map (data through 14 Oct 2026). - Builds on 25 of its 109 references that are in the map. - First posted on arXiv 16 Apr 2021. ## Builds on (most cited first, 25 of 25) - [SEISMIC: A Self-Exciting Point Process Model for Predicting Tweet Popularity](https://mlsanity.com/paper/1506.02594/) (2015) - [A Review of Self-Exciting Spatio-Temporal Point Processes and Their Applications](https://mlsanity.com/paper/1708.02647/) (2017) - [Discovering Latent Network Structure in Point Process Data](https://mlsanity.com/paper/1402.0914/) (2014) - [Expecting to be HIP: Hawkes Intensity Processes for Social Media Popularity](https://mlsanity.com/paper/1602.06033/) (2016) - [Feature Driven and Point Process Approaches for Popularity Prediction](https://mlsanity.com/paper/1608.04862/) (2016) - [SIR-Hawkes: Linking Epidemic Models and Hawkes Processes to Model Diffusions in Finite Populations](https://mlsanity.com/paper/1711.01679/) (2017) - [TiDeH: Time-Dependent Hawkes Process for Predicting Retweet Dynamics](https://mlsanity.com/paper/1603.09449/) (2016) - [Efficient Non-parametric Bayesian Hawkes Processes](https://mlsanity.com/paper/1810.03730/) (2018) - [#DebateNight: The Role and Influence of Socialbots on Twitter During the 1st 2016 U.S. Presidential Debate](https://mlsanity.com/paper/1802.09808/) (2018) - [Estimating Attention Flow in Online Video Networks](https://mlsanity.com/paper/1908.07123/) (2019) - [Learning Hawkes Processes from Short Doubly-Censored Event Sequences](https://mlsanity.com/paper/1702.07013/) (2017) - [Steering Social Activity: A Stochastic Optimal Control Point Of View](https://mlsanity.com/paper/1802.07244/) (2018) - [Modeling Information Cascades with Self-exciting Processes via Generalized Epidemic Models](https://mlsanity.com/paper/1910.05451/) (2019) - [Online Popularity under Promotion: Viral Potential, Forecasting, and the Economics of Time](https://mlsanity.com/paper/1703.01012/) (2017) - [PoPPy: A Point Process Toolbox Based on PyTorch](https://mlsanity.com/paper/1810.10122/) (2018) - [Modeling Popularity in Asynchronous Social Media Streams with Recurrent Neural Networks](https://mlsanity.com/paper/1804.02101/) (2018) - [Quantile Propagation for Wasserstein-Approximate Gaussian Processes](https://mlsanity.com/paper/1912.10200/) (2019) - [Variation across Scales: Measurement Fidelity under Twitter Data Sampling](https://mlsanity.com/paper/2003.09557/) (2020) - [Evolution of Privacy Loss in Wikipedia](https://mlsanity.com/paper/1512.03523/) (2015) - [THAP: A Matlab Toolkit for Learning with Hawkes Processes](https://mlsanity.com/paper/1708.09252/) (2017) - [A Monte Carlo EM Algorithm for the Parameter Estimation of Aggregated Hawkes Processes](https://mlsanity.com/paper/2001.07160/) (2020) - [Birdspotter: A Tool for Analyzing and Labeling Twitter Users](https://mlsanity.com/paper/2012.02370/) (2020) - [A Stochastic Differential Equation Framework for Guiding Online User Activities in Closed Loop](https://mlsanity.com/paper/1603.09021/) (2016) - [RedQueen: An Online Algorithm for Smart Broadcasting in Social Networks](https://mlsanity.com/paper/1610.05773/) (2016) - [Variational Inference for Gaussian Process with Panel Count Data](https://mlsanity.com/paper/1803.04232/) (2018) ## Built on by (most cited first, 5 of 5) - [Before It's Too Late: A State Space Model for the Early Prediction of Misinformation and Disinformation Engagement](https://mlsanity.com/paper/2502.04655/) (2025) - [Opinion Market Model: Stemming Far-Right Opinion Spread using Positive Interventions](https://mlsanity.com/paper/2208.06620/) (2022) - [Linking Across Data Granularity: Fitting Multivariate Hawkes Processes to Partially Interval-Censored Data](https://mlsanity.com/paper/2111.02062/) (2021) - [Estimating Online Influence Needs Causal Modeling! Counterfactual Analysis of Social Media Engagement](https://mlsanity.com/paper/2505.19355/) (2025) - [On the Efficient Marginalization of Probabilistic Sequence Models](https://mlsanity.com/paper/2403.04005/) (2024) ## Abstract (arXiv) Interval-censored data solely records the aggregated counts of events during specific time intervals - such as the number of patients admitted to the hospital or the volume of vehicles passing traffic loop detectors - and not the exact occurrence time of the events. It is currently not understood how to fit the Hawkes point processes to this kind of data. Its typical loss function (the point process log-likelihood) cannot be computed without exact event times. Furthermore, it does not have the independent increments property to use the Poisson likelihood. This work builds a novel point process, a set of tools, and approximations for fitting Hawkes processes within interval-censored data scenarios. First, we define the Mean Behavior Poisson process (MBPP), a novel Poisson process with a direct parameter correspondence to the popular self-exciting Hawkes process. We fit MBPP in the interval-censored setting using an interval-censored Poisson log-likelihood (IC-LL). We use the parameter equivalence to uncover the parameters of the associated Hawkes process. Second, we introduce two novel exogenous functions to distinguish the exogenous from the endogenous events. We propose the multi-impulse exogenous function - for when the exogenous events are observed as event time - and the latent homogeneous Poisson process exogenous function - for when the exogenous events are presented as interval-censored volumes. Third, we provide several approximation methods to estimate the intensity and compensator function of MBPP when no analytical solution exists. Fourth and finally, we connect the interval-censored loss of MBPP to a broader class of Bregman divergence-based functions. Using the connection, we show that the popularity estimation algorithm Hawkes Intensity Process (HIP) is a particular case of the MBPP. We verify our models through empirical testing on synthetic data and real-world data.