Convex Risk Minimization to Infer Networks from probabilistic diffusion data at multiple scales

Sefer, Emre; Kingsford, Carl

doi:10.1109/icde.2015.7113323

Cited by 22 publications

(24 citation statements)

References 19 publications

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“…To overcome this shortage of available information for the network reconstruction for SI and SIR models, a commonly employed setting is the observation of multiple, independent outbreaks or cascades [2]. The state-of-the-art network reconstruction methods for SI and SIR models confine to a maximum-likelihood formulation in discrete time [3], [4], [5], [6], [7], [8]. Besides network reconstruction methods based on observing viral dynamics, current research also focusses on other dynamical processes on networks.…”

Section: Related Workmentioning

confidence: 99%

“…Only recently, attention has been drawn to establishing accuracy bounds on estimators for discrete parameter settings [25]. Motivated by translating the estimation into an optimisation problem and the strength for completely continuous parameter estimation, the vast majority of approaches to network reconstruction rely on maximum-likelihood or MAP estimation methods [3], [4], [5], [6], [7], [8].…”

Section: Maximum-a-posteriori Formulationmentioning

confidence: 99%

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Exact Network Reconstruction from Complete SIS Nodal State Infection Information Seems Infeasible

Prasse

Mieghem

2019

IEEE Trans. Netw. Sci. Eng.

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The SIS dynamics of the spread of a virus crucially depend on both the network topology and the spreading parameters. Since neither the topology nor the spreading parameters are known for the majority of applications, they have to be inferred from observations of the viral spread. We propose an inference method for both topology and spreading parameters based on a maximum-a-posteriori estimation approach for the sampled-time Markov chain of an SIS process. The resulting estimation problem, given by a mixed-integer optimisation problem, results in exponential computational time if a brute-force approach is employed. By introducing an efficient and accurate, polynomial-time heuristic, the topology of the network can almost always be exactly reconstructed. Notwithstanding, reconstructing the network with a reasonably high accuracy requires a subexponentially increasing number of observations and an exponentially increasing computation time with respect to the number of nodes N. Such long observation periods are hardly realistic, which justifies the claim in the title.

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Section: Related Workmentioning

confidence: 99%

Section: Maximum-a-posteriori Formulationmentioning

confidence: 99%

Exact Network Reconstruction from Complete SIS Nodal State Infection Information Seems Infeasible

Prasse

Mieghem

2019

IEEE Trans. Netw. Sci. Eng.

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“…[6], [7]), and the outbreak of a contagious disease in different geographic regions (e.g. [8]). What qualifies all of these inherently different phenomena to be studied as a diffusion process is the commonality of three main components: Nodes, i.e., the set of separate agents; Infection, i.e., the change in the state of a node that can be transferred from one node to the other; and Causality, i.e., the underlying structure based on which the infection is transferred between nodes.…”

Section: Introductionmentioning

confidence: 99%

Online Bayesian Inference of Diffusion Networks

Shaghaghian

Coates

2017

IEEE Trans. on Signal and Inf. Process. over Networks

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Abstract-Understanding the process by which a contagion disseminates throughout a network is of great importance in many real world applications. The required sophistication of the inference approach depends on the type of information we want to extract as well as the number of observations that are available to us. We analyze scenarios in which not only the underlying network structure (parental relationships and link strengths) needs to be detected, but also the infection times must be estimated. We assume that our only observation of the diffusion process is a set of time series, one for each node of the network, which exhibit changepoints when an infection occurs. After formulating a model to describe the contagion, and selecting appropriate prior distributions, we seek to find the set of model parameters that best explains our observations. Modeling the problem in a Bayesian framework, we exploit Monte Carlo Markov Chain, Sequential Monte Carlo, and time series analysis techniques to develop batch and online inference algorithms. We evaluate the performance of our proposed algorithms via numerical simulations of synthetic network contagions and analysis of real-world datasets.

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“…Another related problem is Graph Inference where we want to reconstruct the unknown graph from observed multiple diffusion traces over it. This problem is fundamentally different than the history reconstruction problem as graph inference methods (Gomez-Rodriguez, Leskovec and Schölkopf, 2013; Holme, 2013; Sefer and Kingsford, 2015) search in the graph space assuming full observability of multiple traces whereas our methods search in temporal diffusion progression space as they try to complete the missing history of a single trace.…”

Section: Introductionmentioning

confidence: 99%

Diffusion archeology for diffusion progression history reconstruction

Sefer

Kingsford

2015

Knowl Inf Syst

Self Cite

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Diffusion through graphs can be used to model many real-world processes, such as the spread of diseases, social network memes, computer viruses, or water contaminants. Often, a real-world diffusion cannot be directly observed while it is occurring — perhaps it is not noticed until some time has passed, continuous monitoring is too costly, or privacy concerns limit data access. This leads to the need to reconstruct how the present state of the diffusion came to be from partial diffusion data. Here, we tackle the problem of reconstructing a diffusion history from one or more snapshots of the diffusion state. This ability can be invaluable to learn when certain computer nodes are infected or which people are the initial disease spreaders to control future diffusions. We formulate this problem over discrete-time SEIRS-type diffusion models in terms of maximum likelihood. We design methods that are based on submodularity and a novel prize-collecting dominating-set vertex cover (PCDSVC) relaxation that can identify likely diffusion steps with some provable performance guarantees. Our methods are the first to be able to reconstruct complete diffusion histories accurately in real and simulated situations. As a special case, they can also identify the initial spreaders better than the existing methods for that problem. Our results for both meme and contaminant diffusion show that the partial diffusion data problem can be overcome with proper modeling and methods, and that hidden temporal characteristics of diffusion can be predicted from limited data.

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Convex Risk Minimization to Infer Networks from probabilistic diffusion data at multiple scales

Cited by 22 publications

References 19 publications

Exact Network Reconstruction from Complete SIS Nodal State Infection Information Seems Infeasible

Exact Network Reconstruction from Complete SIS Nodal State Infection Information Seems Infeasible

Online Bayesian Inference of Diffusion Networks

Diffusion archeology for diffusion progression history reconstruction

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