Comparison of large networks with sub-sampling strategies

Ali, Waqar; Wegner, Anatol E.; Gaunt, Robert E.; Deane, Charlotte M.; Reinert, Gesine

doi:10.1038/srep28955

Cited by 16 publications

(21 citation statements)

References 33 publications

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“…where d min > 0 is a cutoff determining where the tail of the degree distribution starts. Most of empirical graphs are reported to haveγ Hill ∈ [2, 3], while graphex processes have almost-surely index γ = 1 + σ ∈ [1,2], at least if we rely on the definition of equation (4.3). So one might think graphex processes are unrealistic to model graphs withγ Hill ∈ [2,3].…”

Section: Relation To Hill Estimatormentioning

confidence: 99%

Bootstrap estimators for the tail-index and for the count statistics of graphex processes

Naulet¹,

Roy²,

Sharma³

et al. 2021

Electron. J. Statist.

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Graphex processes resolve some pathologies in traditional random graph models, notably, providing models that are both projective and allow sparsity. Most of the literature on graphex processes study them from a probabilistic point of view. Techniques for inferring the parameter of these processes -the so-called graphon -are still marginal; exceptions are a few papers considering parametric families of graphons. Nonparametric estimation remains unconsidered. In this paper, we propose estimators for a selected choice of functionals of the graphon. Our estimators originate from the subsampling theory for graphex processes, hence can be seen as a form of bootstrap procedure.

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Section: Relation To Hill Estimatormentioning

confidence: 99%

Bootstrap estimators for the tail-index and for the count statistics of graphex processes

Naulet¹,

Roy²,

Sharma³

et al. 2021

Electron. J. Statist.

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show abstract

“…The subsampling procedure of Bhattacharyya and Bickel (2015) focuses on assessment of uncertainty in motif, or subgraph counts in dense exchangeable networks and is not feasible for inference on degree distribution. The method of Ali et al (2016) also targets inference on counts of small sub-graphs and is based on the notion of dependency graphs under the network exchangeability framework. The vertex bootstrap approach of Snijders and Borgatti (1999), implemented in our R package snowboot, does not impose density limitations but assumes availability of the whole network upfront and is applicable to only small networks.…”

Section: Assumptionsmentioning

confidence: 99%

Snowboot: Bootstrap Methods for Network Inference

Chen¹,

Gel²,

Lyubchich³

et al. 2019

The R Journal

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Complex networks are used to describe a broad range of disparate social systems and natural phenomena, from power grids to customer segmentation to human brain connectome. Challenges of parametric model specification and validation inspire a search for more data-driven and flexible nonparametric approaches for inference of complex networks. In this paper we discuss methodology and R implementation of two bootstrap procedures on random networks, that is, patchwork bootstrap of Thompson et al. (2016) and Gel et al. (2017) and vertex bootstrap of Snijders and Borgatti (1999). To our knowledge, the new R package snowboot is the first implementation of the vertex and patchwork bootstrap inference on networks in R. Our new package is accompanied with a detailed user's manual, and is compatible with the popular R package on network studies igraph. We evaluate the patchwork bootstrap and vertex bootstrap with extensive simulation studies and illustrate their utility in application to analysis of real world networks. The accepted manuscript is published in the R Journal. This is an open access article under the CC BY 4.0 license (https://creativecommons.org/licenses/by/4.0/). (The R Journal (2018) 10:2, pages 95-113; doi: https://doi.The new R package snowboot (Ramirez-Ramirez et al., 2018) is the first to offer vertex and patchwork bootstrap in R. Moreover, to our knowledge, there currently exist only two more R packages implementing bootstrap analysis of networks, bootnet and sna. The package bootnet assesses uncertainty in estimation of edge-weights and centrality indices but does not account for network dependence structure among vertices. The package sna implements parametric bootstrapping of edges to generate new random graphs that can be further used for hypothesis testing of matching between the observed network and randomized baseline network as well as canonical correlation coefficients. This paper aims to further fill the gap and showcase utility of nonparametric resampling for network inference, with a particular focus on vertex and patchwork bootstraps. snowboot imports The R Journal Vol. XX/YY, AAAA 20ZZ

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“…This opens the door for comparing very large networks which are outside the reach of current methods while still retaining state of the art performance. Furthermore, the NetEmd measures perform well under sub-sampling of nodes [Ali et al, 2016] (see Appendix D) which can be leveraged to further improve computational efficiency.…”

Section: Netemd Based On Different Sets Of Inputsmentioning

confidence: 99%

Identifying networks with common organizational principles

Wegner

Ospina-Forero

Gaunt

et al. 2018

Journal of Complex Networks

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Many complex systems can be represented as networks, and the problem of network comparison is becoming increasingly relevant. There are many techniques for network comparison, from simply comparing network summary statistics to sophisticated but computationally costly alignment-based approaches. Yet it remains challenging to accurately cluster networks that are of a different size and density, but hypothesized to be structurally similar. In this paper, we address this problem by introducing a new network comparison methodology that is aimed at identifying common organizational principles in networks. The methodology is simple, intuitive and applicable in a wide variety of settings ranging from the functional classification of proteins to tracking the evolution of a world trade network.

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Comparison of large networks with sub-sampling strategies

Cited by 16 publications

References 33 publications

Bootstrap estimators for the tail-index and for the count statistics of graphex processes

Bootstrap estimators for the tail-index and for the count statistics of graphex processes

Snowboot: Bootstrap Methods for Network Inference

Identifying networks with common organizational principles

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