Related papers: Uncertainty Quantification for Inferring Hawkes Ne…
The Hawkes model is a past-dependent point process, widely used in various fields for modeling temporal clustering of events. Extending this framework, the multidimensional marked Hawkes process incorporates multiple interacting event types…
Learning Granger causality for general point processes is a very challenging task. In this paper, we propose an effective method, learning Granger causality, for a special but significant type of point processes --- Hawkes process. We…
The Hawkes process has become a standard method for modeling self-exciting event sequences with different event types. A recent work has generalized the Hawkes process to a neurally self-modulating multivariate point process, which enables…
While neural networks have demonstrated impressive performance across various tasks, accurately quantifying uncertainty in their predictions is essential to ensure their trustworthiness and enable widespread adoption in critical systems.…
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…
Multi-dimensional Hawkes process (MHP) is a class of self and mutually exciting point processes that find wide range of applications -- from prediction of earthquakes to modelling of order books in high frequency trading. This paper makes…
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…
Learning the influence structure of multiple time series data is of great interest to many disciplines. This paper studies the problem of recovering the causal structure in network of multivariate linear Hawkes processes. In such processes,…
The Hawkes process is a class of point processes whose future depends on their own history. Previous theoretical work on the Hawkes process is limited to a special case in which a past event can only increase the occurrence of future…
Multivariate Hawkes processes are a widely used class of self-exciting point processes, but maximum likelihood estimation naively scales as $O(N^2)$ in the number of events. The canonical linear exponential Hawkes process admits a faster…
Multivariate Hawkes process provides a powerful framework for modeling temporal dependencies and event-driven interactions in complex systems. While existing methods primarily focus on uncovering causal structures among observed…
We consider the problem of learning the network of mutual excitations (i.e., the dependency graph) in a non-stationary, multivariate Hawkes process. We consider a general setting where baseline rates at each node are time-varying and delay…
To better understand the theoretical behavior of large neural networks, several works have analyzed the case where a network's width tends to infinity. In this regime, the effect of random initialization and the process of training a neural…
Event-driven systems in fields such as neuroscience, social networks, and finance often exhibit dynamics influenced by continuously evolving external covariates. Motivated by these applications, we introduce a new class of multivariate…
Event data consisting of time of occurrence of the events arises in several real-world applications. Recent works have introduced neural network based point processes for modeling event-times, and were shown to provide state-of-the-art…
Causality is crucial to understanding the mechanisms behind complex systems and making decisions that lead to intended outcomes. Event sequence data is widely collected from many real-world processes, such as electronic health records, web…
Granger causality has been employed to investigate causality relations between components of stationary multiple time series. We generalize this concept by developing statistical inference for local Granger causality for multivariate…
Identifying key influencers from time series data without a known prior network structure is a challenging problem in various applications, from crime analysis to social media. While much work has focused on event-based time series…
Networks - collections of interacting elements or nodes - abound in the natural and manmade worlds. For many networks, complex spatiotemporal dynamics stem from patterns of physical interactions unknown to us. To infer these interactions,…
In this paper, we develop an efficient nonparametric Bayesian estimation of the kernel function of Hawkes processes. The non-parametric Bayesian approach is important because it provides flexible Hawkes kernels and quantifies their…