Related papers: Granger Causal Inference in Multivariate Hawkes Pr…
Multivariate point processes are widely applied to model event-type data such as natural disasters, online message exchanges, financial transactions or neuronal spike trains. One very popular point process model in which the probability of…
While most classical approaches to Granger causality detection assume linear dynamics, many interactions in real-world applications, like neuroscience and genomics, are inherently nonlinear. In these cases, using linear models may lead to…
When the data are sparse, optimization of hyperparameters of the kernel in Gaussian process regression by the commonly used maximum likelihood estimation (MLE) criterion often leads to overfitting. We show that choosing hyperparameters (in…
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…
The kernel function and its hyperparameters are the central model selection choice in a Gaussian proces (Rasmussen and Williams, 2006). Typically, the hyperparameters of the kernel are chosen by maximising the marginal likelihood, an…
Modern health care systems are conducting continuous, automated surveillance of the electronic medical record (EMR) to identify adverse events with increasing frequency; however, many events such as sepsis do not have elucidated prodromes…
Learning causal structure among event types from discrete-time event sequences is a particularly important but challenging task. Existing methods, such as the multivariate Hawkes processes based methods, mostly boil down to learning the…
It is often assumed that events cannot occur simultaneously when modelling data with point processes. This raises a problem as real-world data often contains synchronous observations due to aggregation or rounding, resulting from…
The Hawkes process is a widely used model in many areas, such as finance, seismology, neuroscience, epidemiology, and social sciences. Estimation of the Hawkes process from continuous observations of a sample path is relatively…
In this paper, we address the problem of fitting multivariate Hawkes processes to potentially large-scale data in a setting where series of events are not only mutually-exciting but can also exhibit inhibitive patterns. We focus on…
Minimum message length is a general Bayesian principle for model selection and parameter estimation that is based on information theory. This paper applies the minimum message length principle to a small-sample model selection problem…
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…
The multivariate Hawkes process (MHP) is widely used for analyzing data streams that interact with each other, where events generate new events within their own dimension (via self-excitation) or across different dimensions (via…
Mixture modelling involves explaining some observed evidence using a combination of probability distributions. The crux of the problem is the inference of an optimal number of mixture components and their corresponding parameters. This…
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.…
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…
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…
Hawkes process are very popular mathematical tools for modelling phenomena exhibiting a \textit{self-exciting} or \textit{self-correcting} behaviour. Typical examples are earthquakes occurrence, wild-fires, drought, capture-recapture, crime…
A major challenge for causal inference from time-series data is the trade-off between computational feasibility and accuracy. Motivated by process motifs for lagged covariance in an autoregressive model with slow mean-reversion, we propose…
Driven by the recent surge in neural-inspired modeling, point processes have gained significant traction in systems and control. While the Hawkes process is the standard model for characterizing random event sequences with memory,…