Time varying undirected graphs

Zhou, Shengxi; Lafferty, John; Wasserman, Larry

doi:10.1007/s10994-010-5180-0

Cited by 196 publications

(253 citation statements)

References 9 publications

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“…6, a time interval-dependent kernel was applied to weight every sample in D with respect to t*, which are subsequently treated as reweighed iid samples from G t* for estimating G t* . It can be shown that if {X t } are continuous valued and follow a time-varying graphical Gaussian model (GGM), and when the precision matrix ⌰ of the GGM is assumed to be smoothly evolving, this scheme can consistently recover the (value of) ⌰ t* corresponding to every G t* in the limit (6). However, another important type of consistency known as model-selection consistency, or pattern consistency, which concerns the identification of nonzero elements of ⌰ t* , and hence directly leads to recovery of the topology E t* of graph G t* , is not available.…”

Section: Problem Formulationmentioning

confidence: 99%

“…It is noteworthy that in ref. 6, the smooth evolution assumption is used as a precondition to guarantee value consistency of the ⌰ t* estimator, rather than being treated as an explicitly tunable constraint that can be used to accommodate real data. Therefore, in cases where more turbulent dynamics (e.g., sudden jumps) drives graph evolution, this method may run into difficulties.…”

Section: Problem Formulationmentioning

confidence: 99%

“…Importantly, TESLA can be cast as a convex optimization problem for which a globally optimal solution exists and can be efficiently computed for networks with thousands of nodes. Recently, Zhou et al (6) proposed a nonparametric local kernel-weighting technique for learning smoothly evolving graphical Gaussian models by using the method in ref. 12 and showed interesting asymptotic consistency results of their estimator.…”

mentioning

confidence: 99%

“…Our ongoing theoretical analysis of TESLA suggests that it can detect blockiness and jumps in graph evolution, and possibly enjoys graph-structure consistency rather than parameterestimation consistency as shown in ref. 6 for their method.…”

mentioning

confidence: 99%

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Recovering time-varying networks of dependencies in social and biological studies

Ahmed

Xing

2009

Proc. Natl. Acad. Sci. U.S.A.

220

224

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A plausible representation of the relational information among entities in dynamic systems such as a living cell or a social community is a stochastic network that is topologically rewiring and semantically evolving over time. Although there is a rich literature in modeling static or temporally invariant networks, little has been done toward recovering the network structure when the networks are not observable in a dynamic context. In this article, we present a machine learning method called TESLA, which builds on a temporally smoothed l1-regularized logistic regression formalism that can be cast as a standard convex-optimization problem and solved efficiently by using generic solvers scalable to large networks. We report promising results on recovering simulated timevarying networks and on reverse engineering the latent sequence of temporally rewiring political and academic social networks from longitudinal data, and the evolving gene networks over >4,000 genes during the life cycle of Drosophila melanogaster from a microarray time course at a resolution limited only by sample frequency.evolving network ͉ social network ͉ gene network ͉ lasso ͉ Markov random field I n many problems arising in social, biological, and other fields, it is often necessary to analyze populations of entities (e.g., individuals, genes) interconnected by a set of relationships (e.g., friendship, communication, influence) represented as a network. Real-time analysis of network data is important for detecting anomalies, predicting vulnerability, and assessing the potential impact of interventions in various social, biological, or engineering systems. It is not unusual for network data to be large, dynamic, heterogeneous, noisy, and incomplete. Each of these characteristics adds a degree of complexity to the interpretation and analysis of networks.Classical network analyses mostly assume that the networks in question are fully observable, static, and isotropic. Given the heterogeneity and complexity of network data in many domains, these assumptions are limiting. For example, a majority of current investigations of biological regulatory circuitry focus on networks with invariant topology over a given set of molecules, such as a protein-protein interaction network over all proteins of an organism regardless of the conditions under which individual interactions may take place or a static gene network inferred from microarray data even though the samples may be collected over a time course or multiple conditions. In reality, over the course of a cellular process, such as a cell cycle or an immune response, there may exist multiple underlying ''themes'' that determine the functionalities of each molecule and their relationships to each other, and such themes are dynamic and stochastic. As a result, the molecular networks at each time point are context dependent and can undergo systematic rewiring, rather than being invariant over time. Indeed, in a seminal study by Luscombe et al. (1), it was shown that the ''active regulatory paths'' in a ge...

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Section: Problem Formulationmentioning

confidence: 99%

Section: Problem Formulationmentioning

confidence: 99%

mentioning

confidence: 99%

mentioning

confidence: 99%

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Recovering time-varying networks of dependencies in social and biological studies

Ahmed

Xing

2009

Proc. Natl. Acad. Sci. U.S.A.

220

224

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“…b) Learning time-varying graphical models: Several methods have focussed on inferring time-varying interactions based on the assumption that interaction networks change slowly over time [40], [22], [23]. Song et.…”

Section: Introductionmentioning

confidence: 99%

DLOREAN: Dynamic Location-Aware Reconstruction of Multiway Networks

Johansson

Jethava

Dubhashi

2013

2013 IEEE 13th International Conference on Data Mining Workshops

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Abstract-This paper presents a method for learning timevarying higher-order interactions based on node observations, with application to short-term traffic forecasting based on traffic flow sensor measurements. We incorporate domain knowledge into the design of a new damped periodic kernel which leverages traffic flow patterns towards better structure learning. We introduce location-based regularization for learning models with desirable geographical properties (short-range or long-range interactions). We show using experiments on synthetic and real data, that our approach performs better than static methods for reconstruction of multiway interactions, as well as time-varying methods which recover only pair-wise interactions. Further, we show on real traffic data that our model is useful for short-term traffic forecasting, improving over state-of-the-art.

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Bayesian varying‐effects vector autoregressive models for inference of brain connectivity networks and covariate effects in pediatric traumatic brain injury

Ren,

Osborne,

Peterson

et al. 2024

Human Brain Mapping

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In this article, we develop an analytical approach for estimating brain connectivity networks that accounts for subject heterogeneity. More specifically, we consider a novel extension of a multi‐subject Bayesian vector autoregressive model that estimates group‐specific directed brain connectivity networks and accounts for the effects of covariates on the network edges. We adopt a flexible approach, allowing for (possibly) nonlinear effects of the covariates on edge strength via a novel Bayesian nonparametric prior that employs a weighted mixture of Gaussian processes. For posterior inference, we achieve computational scalability by implementing a variational Bayes scheme. Our approach enables simultaneous estimation of group‐specific networks and selection of relevant covariate effects. We show improved performance over competing two‐stage approaches on simulated data. We apply our method on resting‐state functional magnetic resonance imaging data from children with a history of traumatic brain injury (TBI) and healthy controls to estimate the effects of age and sex on the group‐level connectivities. Our results highlight differences in the distribution of parent nodes. They also suggest alteration in the relation of age, with peak edge strength in children with TBI, and differences in effective connectivity strength between males and females.

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Time varying undirected graphs

Cited by 196 publications

References 9 publications

Recovering time-varying networks of dependencies in social and biological studies

Recovering time-varying networks of dependencies in social and biological studies

DLOREAN: Dynamic Location-Aware Reconstruction of Multiway Networks

Bayesian varying‐effects vector autoregressive models for inference of brain connectivity networks and covariate effects in pediatric traumatic brain injury

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