Mutually Exciting Point Process Graphs for Modeling Dynamic Networks

Passino, Francesco Sanna; Heard, Nicholas A.

doi:10.1080/10618600.2022.2096048

Cited by 8 publications

(11 citation statements)

References 30 publications

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“…However, this temporal aggregation step leads to some information loss, and it could thus be interesting to directly model individual interactions between hosts instead. The stream of interactions could for instance be modelled as a marked point process, in a way similar to previous contributions on recommender systems [37] and computer network monitoring [34]. The source separation approach would then consist in modelling the stochastic intensity of this point process as a time-dependent linear combination of simpler functions representing the activity sources.…”

Section: Discussion and Future Workmentioning

confidence: 99%

A source separation approach to temporal graph modelling for computer networks

Larroche¹

2023

Preprint

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Detecting malicious activity within an enterprise computer network can be framed as a temporal link prediction task: given a sequence of graphs representing communications between hosts over time, the goal is to predict which edges should-or should not-occur in the future. However, standard temporal link prediction algorithms are illsuited for computer network monitoring as they do not take account of the peculiar short-term dynamics of computer network activity, which exhibits sharp seasonal variations. In order to build a better model, we propose a source separation-inspired description of computer network activity: at each time step, the observed graph is a mixture of subgraphs representing various sources of activity, and short-term dynamics result from changes in the mixing coefficients. Both qualitative and quantitative experiments demonstrate the validity of our approach.

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Section: Discussion and Future Workmentioning

confidence: 99%

A source separation approach to temporal graph modelling for computer networks

Larroche¹

2023

Preprint

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“…is property makes the model tractable and scalable. In [20], the mutual point process (Hawkes process) and latent space model are used to model the intensity of interactions. Although these models have interpretable intensity functions, considering a predefined generative model for interactions might cause them not to be applicable for more datasets.…”

Section: Continuous-time Dynamic Network Modelsmentioning

confidence: 99%

“…According to different network sizes, various values for hyperparameters have been set. e sizes of the hidden layer of neural networks are set to the values in the range of [20,100]. e sequences of lengths 20 to 100 have been used for modeling events dependency on their history.…”

Section: Experimental Settingsmentioning

confidence: 99%

“…As was mentioned, modeling continuous-time networks demands higher computational complexity. Several continuous-time models have been proposed, such as Stochastic Actor Oriented Models (SAOM) [5][6][7][8][9], Relational Event Models (REM) [10][11][12][13][14], point process models [15][16][17][18][19][20], and deep learning models [3,[21][22][23]. REMs and SAOMs are statistical methods where defined statistics are used for modeling network interactions.…”

Section: Introductionmentioning

confidence: 99%

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A Comparative Study of Some Point Process Models for Dynamic Networks

2022

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Modeling dynamic networks has attracted much interest in recent years, which helps understand networks’ behavior. Many works have been dedicated to modeling discrete-time networks, but less work is done for continuous-time networks. Point processes as powerful tools for modeling discrete events in continuous time have been widely used for modeling events over networks and their dynamics. These models have solid mathematical assumptions, making them interpretable but decreasing their generalizability for different datasets. Hence, neural point processes were introduced that don’t have strong assumptions on generative functions. However, these models can be impractical in the case of a large number of event types. This research presents a comparative study of different point process (Hawkes) models for continuous-time networks. Furthermore, a previously introduced neural point process (neural Hawkes) model is applied for modeling network interactions. In this work, network clustering is used for specifying interaction types. These methods are compared using different synthetic and real-world datasets, and their efficiency is evaluated on these datasets. The experiments represent that each model is appropriate for a group of datasets. In addition, the effect of clustering on results is discussed, and experiments for different clusters are presented.

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“…In many fields of applications, the requirement of a common connection probability in the Erdős-Rényi model is too stringent, as edges or vertices may have heterogeneous attributes. Some examples of Hawkes processes on more complex graphs deal with estimation of the model parameters, [21], [24], [26], or perform simulations, [27], both for a fixed size of the graph. In the present paper we focus on the Erdős-Rényi model, as it allows to derive rigorous mathematical results in the mean-field setting, i.e.…”

Section: Introductionmentioning

confidence: 99%

Mean-field limits for non-linear Hawkes processes with inhibition on a Erdős-Rényi-graph

Stiefel¹

2022

Preprint

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We study a multivariate, non-linear Hawkes process Z N on a q-Erdős-Rényi-graph with N nodes. Each vertex is either excitatory (probability p) or inhibitory (probability 1 − p). If p = 1 2 , we take the mean-field limit of Z N , leading to a multivariate point process Z. We rescale the interaction intensity by N and find that the limit intensity process solves a deterministic convolution equation and all components of Z are independent. The fluctuations around the mean field limit converge to the solution of a stochastic convolution equation. In the critical case, p = 1 2 , we rescale by N 1/2 and discuss difficulties, both heuristically and numerically.

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Mutually Exciting Point Process Graphs for Modeling Dynamic Networks

Cited by 8 publications

References 30 publications

A source separation approach to temporal graph modelling for computer networks

A source separation approach to temporal graph modelling for computer networks

A Comparative Study of Some Point Process Models for Dynamic Networks

Mean-field limits for non-linear Hawkes processes with inhibition on a Erdős-Rényi-graph

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