Related papers: Hawkes Processes with Delayed Granger Causality
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…
The multivariate Hawkes process is a past-dependent point process used to model the relationship of event occurrences between different phenomena.Although the Hawkes process was originally introduced to describe excitation effects, which…
Multivariate Hawkes processes are past-dependant point processes originally introduced to model excitation effects, later extended to a nonlinear framework to account for the opposite effect, known as inhibition. Motivated by applications…
Identifying causal relations among simultaneously acquired signals is an important problem in multivariate time series analysis. For linear stochastic systems Granger proposed a simple procedure called the Granger causality to detect such…
Dynamic systems described by differential equations often involve feedback among system components. When there are time delays for components to sense and respond to feedback, delay differential equation (DDE) models are commonly used. This…
Learning causal structure among event types on multi-type event sequences is an important but challenging task. Existing methods, such as the Multivariate Hawkes processes, mostly assumed that each sequence is independent and identically…
The self-exciting Hawkes process is widely used to model events which occur in bursts. However, many real world data sets contain missing events and/or noisily observed event times, which we refer to as data distortion. The presence of such…
Existing spatio-temporal Hawkes process models typically rely on either parametric or semiparametric assumptions, limiting the model's ability to capture complex endogenous and exogenous event dynamics. We propose a fully Bayesian…
The event sequence of many diverse systems is represented as a sequence of discrete events in a continuous space. Examples of such an event sequence are earthquake aftershock events, financial transactions, e-commerce transactions, social…
Granger causality, commonly used for inferring causal structures from time series data, has been adopted in widespread applications across various fields due to its intuitive explainability and high compatibility with emerging deep neural…
In this paper, we propose an extension of the Hawkes process by incorporating a kernel based on the tempered Mittag-Leffler distribution. This is the generalization of the work presented in [10]. We derive analytical results for the…
We introduce a rigorous mathematical framework for Granger causality in extremes, designed to identify causal links from extreme events in time series. Granger causality plays a pivotal role in uncovering directional relationships among…
Granger causality is a statistical notion of causal influence based on prediction via vector autoregression. For Gaussian variables it is equivalent to transfer entropy, an information-theoretic measure of time-directed information transfer…
Univariate marked Hawkes processes are used to model a range of real-world phenomena including earthquake aftershock sequences, contagious disease spread, content diffusion on social media platforms, and order book dynamics. This paper…
Temporal point process as the stochastic process on continuous domain of time is commonly used to model the asynchronous event sequence featuring with occurrence timestamps. Thanks to the strong expressivity of deep neural networks, they…
Sequences of events including infectious disease outbreaks, social network activities, and crimes are ubiquitous and the data on such events carry essential information about the underlying diffusion processes between communities (e.g.,…
Multivariate Hawkes Processes (MHPs) are an important class of temporal point processes that have enabled key advances in understanding and predicting social information systems. However, due to their complex modeling of temporal…
Introduced more than a half century ago, Granger causality has become a popular tool for analyzing time series data in many application domains, from economics and finance to genomics and neuroscience. Despite this popularity, the validity…
Hawkes processes are often applied to model dependence and interaction phenomena in multivariate event data sets, such as neuronal spike trains, social interactions, and financial transactions. In the nonparametric setting, learning the…
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…