Related papers: Hawkes Processes on Graphons

Hawkes Processes on Graphons

URL: http://arxiv.org/abs/2102.02741v1
Date: Thu, 4 Feb 2021 17:09:50 GMT
Title: Hawkes Processes on Graphons
Authors: Hongteng Xu and Dixin Luo and Hongyuan Zha
Abstract summary: We study Hawkes processes and their variants that are associated with Granger causality graphs. We can generate the corresponding Hawkes processes and simulate event sequences. We learn the proposed model by minimizing the hierarchical optimal transport distance between the generated event sequences and the observed ones.
Score: 85.6759041284472
License: http://creativecommons.org/licenses/by/4.0/
Abstract: We propose a novel framework for modeling multiple multivariate point processes, each with heterogeneous event types that share an underlying space and obey the same generative mechanism. Focusing on Hawkes processes and their variants that are associated with Granger causality graphs, our model leverages an uncountable event type space and samples the graphs with different sizes from a nonparametric model called {\it graphon}. Given those graphs, we can generate the corresponding Hawkes processes and simulate event sequences. Learning this graphon-based Hawkes process model helps to 1) infer the underlying relations shared by different Hawkes processes; and 2) simulate event sequences with different event types but similar dynamics. We learn the proposed model by minimizing the hierarchical optimal transport distance between the generated event sequences and the observed ones, leading to a novel reward-augmented maximum likelihood estimation method. We analyze the properties of our model in-depth and demonstrate its rationality and effectiveness in both theory and experiments.

Related papers

IFH: a Diffusion Framework for Flexible Design of Graph Generative Models [53.219279193440734]
Graph generative models can be classified into two prominent families: one-shot models, which generate a graph in one go, and sequential models, which generate a graph by successive additions of nodes and edges. This paper proposes a graph generative model, called Insert-Fill-Halt (IFH), that supports the specification of a sequentiality degree.
arXiv Detail & Related papers (2024-08-23T16:24:40Z)
von Mises Quasi-Processes for Bayesian Circular Regression [57.88921637944379]
We explore a family of expressive and interpretable distributions over circle-valued random functions. The resulting probability model has connections with continuous spin models in statistical physics. For posterior inference, we introduce a new Stratonovich-like augmentation that lends itself to fast Markov Chain Monte Carlo sampling.
arXiv Detail & Related papers (2024-06-19T01:57:21Z)
Interacting Diffusion Processes for Event Sequence Forecasting [20.380620709345898]
We introduce a novel approach that incorporates a diffusion generative model. The model facilitates sequence-to-sequence prediction, allowing multi-step predictions based on historical event sequences. We demonstrate that our proposal outperforms state-of-the-art baselines for long-horizon forecasting of TPP.
arXiv Detail & Related papers (2023-10-26T22:17:25Z)
Geometric Neural Diffusion Processes [55.891428654434634]
We extend the framework of diffusion models to incorporate a series of geometric priors in infinite-dimension modelling. We show that with these conditions, the generative functional model admits the same symmetry.
arXiv Detail & Related papers (2023-07-11T16:51:38Z)
Beyond Conjugacy for Chain Event Graph Model Selection [0.0]
Chain event graphs are a family of probabilistic graphical models that generalise Bayesian networks. We propose a mixture modelling approach to model selection in chain event graphs that does not rely on conjugacy.
arXiv Detail & Related papers (2022-11-07T10:33:01Z)
Visually-aware Acoustic Event Detection using Heterogeneous Graphs [39.90352230010103]
Perception of auditory events is inherently multimodal relying on both audio and visual cues. We employ heterogeneous graphs to capture the spatial and temporal relationships between the modalities. We show efficiently modelling of intra- and inter-modality relationships both at spatial and temporal scales.
arXiv Detail & Related papers (2022-07-16T13:09:25Z)
CEP3: Community Event Prediction with Neural Point Process on Graph [59.434777403325604]
We propose a novel model combining Graph Neural Networks and Marked Temporal Point Process (MTPP) Our experiments demonstrate the superior performance of our model in terms of both model accuracy and training efficiency.
arXiv Detail & Related papers (2022-05-21T15:30:25Z)
THP: Topological Hawkes Processes for Learning Granger Causality on Event Sequences [31.895008425796792]
We propose a Granger causality learning method on Topological Hawkes processes (THP) in a likelihood framework. The proposed method is featured with the graph convolution-based likelihood function of THP and a sparse optimization scheme with an Expectation-Maximization of the likelihood function.
arXiv Detail & Related papers (2021-05-23T08:33:46Z)
A Twin Neural Model for Uplift [59.38563723706796]
Uplift is a particular case of conditional treatment effect modeling. We propose a new loss function defined by leveraging a connection with the Bayesian interpretation of the relative risk. We show our proposed method is competitive with the state-of-the-art in simulation setting and on real data from large scale randomized experiments.
arXiv Detail & Related papers (2021-05-11T16:02:39Z)
Graph Hawkes Neural Network for Forecasting on Temporal Knowledge Graphs [38.56057203198837]
Hawkes process has become a standard method for modeling self-exciting event sequences with different event types. We propose the Graph Hawkes Neural Network that can capture the dynamics of evolving graph sequences and can predict the occurrence of a fact in a future time instance.
arXiv Detail & Related papers (2020-03-30T12:56:50Z)

This list is automatically generated from the titles and abstracts of the papers in this site.