A review of dynamic network models with latent variables

Kim, Bomin; Lee, Kevin H.; Xue, Lingzhou; Niu, Xiaoyue

doi:10.1214/18-ss121

Cited by 111 publications

(83 citation statements)

References 79 publications

(111 reference statements)

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“…Extensions to the model with link persistence, where connections/disconnections can also be copied from the previous to the next snapshot [49,50], would allow additional control over the rate of dynamics, i.e., on how fast the topology changes from snapshot to snapshot. The dynamic-S 1 or extensions of it may apply to other types of timevarying networks, such as the ones considered in [51,52], and constitute the basis of maximum likelihood estimation methods that infer the node coordinates and their evolution in the latent spaces of real systems [53]. Taken altogether, our results pave the way towards generative modeling of temporal networks that simultaneously satisfies simplicity, realism, and mathematical tractability.…”

Section: Discussionmentioning

confidence: 83%

Latent geometry and dynamics of proximity networks

Papadopoulos

Flores

2019

Phys. Rev. E

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Proximity networks are time-varying graphs representing the closeness among humans moving in a physical space. Their properties have been extensively studied in the past decade as they critically affect the behavior of spreading phenomena and the performance of routing algorithms. Yet, the mechanisms responsible for their observed characteristics remain elusive. Here, we show that many of the observed properties of proximity networks emerge naturally and simultaneously in a simple latent space network model, called dynamic-S 1 . The dynamic-S 1 does not model node mobility directly, but captures the connectivity in each snapshot-each snapshot in the model is a realization of the S 1 model of traditional complex networks, which is isomorphic to hyperbolic geometric graphs. By forgoing the motion component the model facilitates mathematical analysis, allowing us to prove the contact, inter-contact and weight distributions. We show that these distributions are power laws in the thermodynamic limit with exponents lying within the ranges observed in real systems. Interestingly, we find that network temperature plays a central role in network dynamics, dictating the exponents of these distributions, the time-aggregated agent degrees, and the formation of unique and recurrent components. Further, we show that paradigmatic epidemic and rumor spreading processes perform similarly in real and modeled networks. The dynamic-S 1 or extensions of it may apply to other types of time-varying networks and constitute the basis of maximum likelihood estimation methods that infer the node coordinates and their evolution in the latent spaces of real systems.

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Section: Discussionmentioning

confidence: 83%

Latent geometry and dynamics of proximity networks

Papadopoulos

Flores

2019

Phys. Rev. E

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“…However, this first kind of approach has been criticized because it can not fully capture the timevarying patterns of the network structure. This opens to a second stream of literature which aims to describe these patterns with models having time-varying (latent) parameters that capture how network topology changes in time, see [10] for a review. A milestone work is represented by the study of Sarkar and Moore [11] that generalized the latent space model introduced in [12] to dynamic networks.…”

Section: Introductionmentioning

confidence: 99%

A dynamic network model with persistent links and node-specific latent variables, with an application to the interbank market

Mazzarisi

Barucca

Lillo

et al. 2020

European Journal of Operational Research

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We propose a dynamic network model where two mechanisms control the probability of a link between two nodes: (i) the existence or absence of this link in the past, and (ii) node-specific latent variables (dynamic fitnesses) describing the propensity of each node to create links. Assuming a Markov dynamics for both mechanisms, we propose an Expectation-Maximization algorithm for model estimation and inference of the latent variables. The estimated parameters and fitnesses can be used to forecast the presence of a link in the future. We apply our methodology to the e-MID interbank network for which the two linkage mechanisms are associated with two different trading behaviors in the process of network formation, namely preferential trading and trading driven by node-specific characteristics. The empirical results allow to recognise preferential lending in the interbank market and indicate how a method that does not account for time-varying network topologies tends to overestimate preferential linkage.

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“…Various Bayesian statistical models have also been developed for dynamic network studies with state-space models (Kim et al, 2018). State-space models represent data with coupled observation (noise, natural random variation) components and latent process (underlying state variables with stochastic but sustained patterns over time).…”

Section: Related Workmentioning

confidence: 99%

Bayesian dynamic modeling and monitoring of network flows

Chen¹,

Banks

West

2019

Net Sci

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In the context of a motivating study of dynamic network flow data on a large-scale ecommerce web site, we develop Bayesian models for on-line/sequential analysis for monitoring and adapting to changes reflected in node-node traffic. For large-scale networks, we customize core Bayesian time series analysis methods using dynamic generalized linear models (DGLMs). These are integrated into the context of multivariate networks using the concept of decouple/recouple that was recently introduced in multivariate time series. This method enables flexible dynamic modeling of flows on large-scale networks and exploitation of partial parallelization of analysis while maintaining coherence with an over-arching multivariate dynamic flow model. This approach is anchored in a case-study on internet data, with flows of visitors to a commercial news web site defining a long time series of nodenode counts on over 56,000 node pairs. Central questions include characterizing inherent stochasticity in traffic patterns, understanding node-node interactions, adapting to dynamic changes in flows and allowing for sensitive monitoring to flag anomalies. The methodology of dynamic network DGLMs applies to many dynamic network flow studies.

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A review of dynamic network models with latent variables

Cited by 111 publications

References 79 publications

Latent geometry and dynamics of proximity networks

Latent geometry and dynamics of proximity networks

A dynamic network model with persistent links and node-specific latent variables, with an application to the interbank market

Bayesian dynamic modeling and monitoring of network flows

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