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 partially censored multivariate Hawkes process (PCMHP), a novel point process that 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. First, we illustrate that the PCMHP can approximate MHP parameters and recover the spectral radius using synthetic event histories. Next, we assess the performance of the PCMHP in predicting YouTube popularity and find that the PCMHP outperforms the popularity estimation algorithm Hawkes intensity process (HIP)[1]. Comparing with the fully interval-censored HIP, we show that the PCMHP improves prediction performance by accounting for point process dimensions, particularly when there exist significant cross-dimension interactions. Last, we leverage the PCMHP 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 PCMHP-modeled countries, we unveil hidden interaction patterns between occurrences of COVID-19 cases and news reporting.

Online extremism has severe societal consequences, including normalizing hate speech, user radicalization, and increased social divisions. Various mitigation strategies have been explored to address these consequences. One such strategy uses positive interventions: controlled signals that add attention to the opinion ecosystem to boost certain opinions. To evaluate the effectiveness of positive interventions, we introduce the Opinion Market Model (OMM), a two-tier online opinion ecosystem model that considers both inter-opinion interactions and the role of positive interventions. The size of the opinion attention market is modeled in the first tier using the multivariate discrete-time Hawkes process; in the second tier, opinions cooperate and compete for market share, given limited attention using the market share attraction model. We demonstrate the convergence of our proposed estimation scheme on a synthetic dataset. Next, we test OMM on two learning tasks, applying to two real-world datasets to predict attention market shares and uncover latent relationships between online items. The first dataset comprises Facebook and Twitter discussions containing moderate and far-right opinions about bushfires and climate change. The second dataset captures popular VEVO artists' YouTube and Twitter attention volumes. OMM outperforms the state-of-the-art predictive models on both datasets and captures latent cooperation-competition relations. We uncover (1) self- and cross-reinforcement between far-right and moderate opinions on the bushfires and (2) pairwise artist relations that correlate with real-world interactions such as collaborations and long-lasting feuds. Lastly, we use OMM as a testbed for positive interventions and show how media coverage modulates the spread of far-right opinions.

Social media is being increasingly weaponized by state-backed actors to elicit reactions, push narratives and sway public opinion. These are known as Information Operations (IO). The covert nature of IO makes their detection difficult. This is further amplified by missing data due to the user and content removal and privacy requirements. This work advances the hypothesis that the very reactions that Information Operations seek to elicit within the target social systems can be used to detect them. We propose an Interval-censored Transformer Hawkes (IC-TH) architecture and a novel data encoding scheme to account for both observed and missing data. We derive a novel log-likelihood function that we deploy together with a contrastive learning procedure. We showcase the performance of IC-TH on three real-world Twitter datasets and two learning tasks: future popularity prediction and item category prediction. The latter is particularly significant. Using the retweeting timing and patterns solely, we can predict the category of YouTube videos, guess whether news publishers are reputable or controversial and, most importantly, identify state-backed IO agent accounts. Additional qualitative investigations uncover that the automatically discovered clusters of Russian-backed agents appear to coordinate their behavior, activating simultaneously to push specific narratives.

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. We find that our MBPP outperforms HIP on real-world datasets for the task of popularity prediction. This work makes it possible to efficiently fit the Hawkes process to interval-censored data.