Related papers: Hawkes Processes with Variable Length Memory: Exis…
Human activities generate various event sequences such as taxi trip records, bike-sharing pick-ups, crime occurrence, and infectious disease transmission. The point process is widely used in many applications to predict such events related…
This paper addresses nonparametric estimation of nonlinear multivariate Hawkes processes, where the interaction functions are assumed to lie in a reproducing kernel Hilbert space (RKHS). Motivated by applications in neuroscience, the model…
The Hawkes process is a model for counting the number of arrivals to a system which exhibits the self-exciting property - that one arrival creates a heightened chance of further arrivals in the near future. The model, and its…
Multivariate Hawkes processes (MHP) are a class of point processes in which events at different coordinates interact through mutual excitation. The weighted adjacency matrix of the MHP encodes the strength of the relations, and shares its…
Non-linear Hawkes processes with memory kernels given by the sum of Erlang kernels are considered. It is shown that their stability properties can be studied in terms of an associated class of piecewise deterministic Markov processes,…
We show that the jumps correlation matrix of a multivariate Hawkes process is related to the Hawkes kernel matrix through a system of Wiener-Hopf integral equations. A Wiener-Hopf argument allows one to prove that this system (in which the…
The order flow in high-frequency financial markets has been of particular research interest in recent years, as it provides insights into trading and order execution strategies and leads to better understanding of the supply-demand…
This paper proposes a new meta-learning method -- named HARMLESS (HAwkes Relational Meta LEarning method for Short Sequences) for learning heterogeneous point process models from short event sequence data along with a relational network.…
The marked Hawkes risk process is a compound point process for which the occurrence and amplitude of past events impact the future. Thanks to its autoregressive properties, it found applications in various fields such as neuosciences,…
Modeling event sequences of multiple event types with marked temporal point processes (MTPPs) provides a principled way to uncover governing dynamical rules and predict future events. Current neural network approaches to MTPP inference rely…
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…
We address the problem of identifying functional interactions among stochastic neurons with variable-length memory from their spiking activity. The neuronal network is modeled by a stochastic system of interacting point processes with…
Hawkes processes have seen a number of applications in finance, due to their ability to capture event clustering behaviour typically observed in financial systems. Given a calibrated Hawkes process, of concern is the statistical fit to…
Mobile health applications, including those that track activities such as exercise, sleep, and diet, are becoming widely used. Accurately predicting human actions is essential for targeted recommendations that could improve our health and…
There is often latent network structure in spatial and temporal data and the tools of network analysis can yield fascinating insights into such data. In this paper, we develop a nonparametric method for network reconstruction from…
We study the spatio-temporal prediction problem, which has attracted the attention of many researchers due to its critical real-life applications. In particular, we introduce a novel approach to this problem. Our approach is based on the…
Memory is the fundamental form of temporal complexity: when present but uncontrollable, it manifests as non-Markovian noise; conversely, if controllable, memory can be a powerful resource for information processing. Memory effects arise…
In this paper, we study a discrete-time analogue of a Hawkes process, modelled as a Poisson autoregressive process whose parameters depend on the past of the trajectory. The model is characterized to allow these parameters to take negative…
We are interested in the problem of classifying Multivariate Hawkes Processes (MHP) paths coming from several classes. MHP form a versatile family of point processes that models interactions between connected individuals within a network.…
We study statistical aspects of state-dependent Hawkes processes, which are an extension of Hawkes processes where a self- and cross-exciting counting process and a state process are fully coupled, interacting with each other. The…