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While the standard network description of complex systems is based on quantifying links between pairs of system units, higher-order interactions (HOIs) involving three or more units play a major role in governing the collective network…

We develop a Bayesian nonparametric framework for inference in spatio-temporal Hawkes processes, extending existing theoretical results beyond the purely temporal setting. Our framework encompasses modelling both the background and…

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…

Previous work has shown that popular trending events are important external factors which pose significant influence on user search behavior and also provided a way to computationally model this influence. However, their problem formulation…

The richness of many complex systems stems from the interactions among their components. The higher-order nature of these interactions, involving many units at once, and their temporal dynamics constitute crucial properties that shape the…

Hawkes (1971) introduced a powerful multivariate point process model of mutually exciting processes to explain causal structure in data. In this paper it is shown that the Granger causality structure of such processes is fully encoded in…

Forecasting relations between entities is paramount in the current era of data and AI. However, it is often overlooked that real-world relationships are inherently directional, involve more than two entities, and can change with time. In…

Although the bipartite shopping graphs are straightforward to model search behavior, they suffer from two challenges: 1) The majority of items are sporadically searched and hence have noisy/sparse query associations, leading to a…

Self-exciting processes of Hawkes type have been used to model various phenomena including earthquakes, neural activities, and views of online videos. Studies of temporal networks have revealed that sequences of social interevent times for…

High-energy physics experiments face extreme data rates, requiring real-time trigger systems to reduce event throughput while preserving sensitivity to rare processes. Trigger systems are typically constructed as modular chains of…

We aim to explicitly model the delayed Granger causal effects based on multivariate Hawkes processes. The idea is inspired by the fact that a causal event usually takes some time to exert an effect. Studying this time lag itself is of…

The exponential growth of scientific knowledge has made the automated generation of scientific hypotheses that combine novelty, feasibility, and research value a core challenge. Existing methods based on large language models fail to…

We characterize a Hawkes point process with kernel proportional to the probability density function of Mittag-Leffler random variables. This kernel decays as a power law with exponent $\beta +1 \in (1,2]$. Several analytical results can be…

We study a multivariate Hawkes process as a model for time-continuous relational event networks. The model does not assume the network to be known, it includes covariates, and it allows for both common drivers, parameters common to all the…

Biological systems represent time from microseconds to years. An important gap in our knowledge concerns the mechanisms for encoding time intervals of hundreds of milliseconds to minutes that matter for tasks like navigation, communication,…

The Hilbert-Huang transform (HHT) consists of empirical mode decomposition (EMD), which is a template-free method that represents the combination of different intrinsic modes on a time-frequency map (i.e., the Hilbert spectrum). The…

Complex systems frequently exhibit multi-way, rather than pairwise, interactions. These group interactions cannot be faithfully modeled as collections of pairwise interactions using graphs and instead require hypergraphs. However, methods…

Inference and testing in general point process models such as the Hawkes model is predominantly based on asymptotic approximations for likelihood-based estimators and tests. As an alternative, and to improve finite sample performance, this…

A range of systems across the social and natural sciences generate datasets consisting of interactions between two distinct categories of items at various instances in time. Online shopping, for example, generates purchasing events of the…

Physiological signal analysis often involves identifying events crucial to understanding biological dynamics. Traditional methods rely on handcrafted procedures or supervised learning, presenting challenges such as expert dependence, lack…