Related papers: Point processes on directed linear network

We present a novel Recurrent Graph Network (RGN) approach for predicting discrete marked event sequences by learning the underlying complex stochastic process. Using the framework of Point Processes, we interpret a marked discrete event…

The Hawkes process is a simple point process that has long memory, clustering effect, self-exciting property and is in general non-Markovian. The future evolution of a self-exciting point process is influenced by the timing of the past…

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…

Statistical depths have been well studied for multivariate and functional data over the past few decades, but remain under-explored for point processes. A first attempt on the notion of point process depth was conducted recently where the…

In the last decade Hawkes processes have received much attention as models for functional connectivity in neural spiking networks and other dynamical systems with a cascade behavior. In this paper we establish a renewal approach for…

We construct a general procedure for the Quasi Likelihood Analysis applied to a multivariate point process on the real half line in an ergodic framework. More precisely, we assume that the stochastic intensity of the underlying model…

Advances in modern technology have enabled the simultaneous recording of neural spiking activity, which statistically can be represented by a multivariate point process. We characterise the second order structure of this process via the…

This paper extends the analysis of Muni Toke and Yoshida (2020) to the case of marked point processes. We consider multiple marked point processes with intensities defined by three multiplicative components, namely a common baseline…

Modern high-dimensional point process data, especially those from neuroscience experiments, often involve observations from multiple conditions and/or experiments. Networks of interactions corresponding to these conditions are expected to…

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…

This paper presents an alternative approach of analyzing possibly multitype point patterns in space and space-time that occur on network structures, and introduces several different graph-related intensity measures. The proposed formalism…

The last decade has witnessed an increase of interest in the spatial analysis of structured point patterns over networks whose analysis is challenging because of geometrical complexities and unique methodological problems. In this context,…

We give general sufficient conditions to prove the convergence of marked point processes that keep record of the occurrence of rare events and of their impact for non-autonomous dynamical systems. We apply the results to sequential…

In the past decades, the growing amount of network data has lead to many novel statistical models. In this paper we consider so called geometric networks. Typical examples are road networks or other infrastructure networks. But also the…

We develop a new family of marked point processes by focusing the characteristic properties of marked Hawkes processes exclusively to the space of marks, providing the freedom to specify a different model for the occurrence times. This is…

We propose a novel class of network models for temporal dyadic interaction data. Our goal is to capture a number of important features often observed in social interactions: sparsity, degree heterogeneity, community structure and…

While Multiple Instance (MI) data are point patterns -- sets or multi-sets of unordered points -- appropriate statistical point pattern models have not been used in MI learning. This article proposes a framework for model-based MI learning…

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…

Hawkes processes are a class of point processes that have the ability to model the self- and mutual-exciting phenomena. Although the classic Hawkes processes cover a wide range of applications, their expressive ability is limited due to…

In real-world scenario, many phenomena produce a collection of events that occur in continuous time. Point Processes provide a natural mathematical framework for modeling these sequences of events. In this survey, we investigate…