scholarly journals On the interpretation of inflated correlation path weights in concentration graphs

2021 ◽  
Author(s):  
Alberto Roverato
Keyword(s):  
Graphical Models ◽  
Statistical Models ◽  
Centrality Measures ◽  
Full Description ◽  
Theoretical Interest ◽  
Association Measure ◽  
Association Structure ◽  
Concentration Graphs ◽  
Order Structures ◽  
Insight Into

AbstractStatistical models associated with graphs, called graphical models, have become a popular tool for representing network structures in many modern applications. Relevant features of the model are represented by vertices, edges and other higher order structures. A fundamental structural component of the network is represented by paths, which are a sequence of distinct vertices joined by a sequence of edges. The collection of all the paths joining two vertices provides a full description of the association structure between the corresponding variables. In this context, it has been shown that certain pairwise association measures can be decomposed into a sum of weights associated with each of the paths connecting the two variables. We consider a pairwise measure called an inflated correlation coefficient and investigate the properties of the corresponding path weights. We show that every inflated correlation weight can be factorized into terms, each of which is associated either to a vertex or to an edge of the path. This factorization allows one to gain insight into the role played by a path in the network by highlighting the contribution to the weight of each of the elementary units forming the path. This is of theoretical interest because, by establishing a similarity between the weights and the association measure they decompose, it provides a justification for the use of these weights. Furthermore we show how this factorization can be exploited in the computation of centrality measures and describe their use with an application to the analysis of a dietary pattern.

scholarly journals Modeling In-Match Sports Dynamics Using the Evolving Probability Method

2021 ◽  
Vol 11 (10) ◽  
pp. 4429
Author(s):  
Ana Šarčević ◽  
Damir Pintar ◽  
Mihaela Vranić ◽  
Ante Gojsalić
Keyword(s):  
Monte Carlo Simulation ◽  
Statistical Models ◽  
Empirical Bayes ◽  
Hybrid Approach ◽  
Real Life ◽  
Bayes Estimation ◽  
Probability Method ◽  
Specific Nature ◽  
Sport Event ◽  
Insight Into

The prediction of sport event results has always drawn attention from a vast variety of different groups of people, such as club managers, coaches, betting companies, and the general population. The specific nature of each sport has an important role in the adaption of various predictive techniques founded on different mathematical and statistical models. In this paper, a common approach of modeling sports with a strongly defined structure and a rigid scoring system that relies on an assumption of independent and identical point distributions is challenged. It is demonstrated that such models can be improved by introducing dynamics into the match models in the form of sport momentums. Formal mathematical models for implementing these momentums based on conditional probability and empirical Bayes estimation are proposed, which are ultimately combined through a unifying hybrid approach based on the Monte Carlo simulation. Finally, the method is applied to real-life volleyball data demonstrating noticeable improvements over the previous approaches when it comes to predicting match outcomes. The method can be implemented into an expert system to obtain insight into the performance of players at different stages of the match or to study field scenarios that may arise under different circumstances.

scholarly journals Bayesian Uncertainty Estimation for Gaussian Graphical Models and Centrality Indices

2021 ◽  
Author(s):  
Joran Jongerling ◽  
Sacha Epskamp ◽  
Donald Ray Williams
Keyword(s):  
Bayesian Estimation ◽  
Graphical Models ◽  
Estimation Methods ◽  
Centrality Measures ◽  
Gaussian Graphical Models ◽  
Graphical Lasso ◽  
Study Results ◽  
Partial Correlations ◽  
Good Coverage ◽  
Better Than

Gaussian Graphical Models (GGMs) are often estimated using regularized estimation and the graphical LASSO (GLASSO). However, the GLASSO has difficulty estimating(uncertainty in) centrality indices of nodes. Regularized Bayesian estimation might provide a solution, as it is better suited to deal with bias in the sampling distribution ofcentrality indices. This study therefore compares estimation of GGMs with a Bayesian GLASSO- and a Horseshoe prior to estimation using the frequentist GLASSO in an extensive simulation study. Results showed that out of the two Bayesian estimation methods, the Bayesian GLASSO performed best. In addition, the Bayesian GLASSOperformed better than the frequentist GLASSO with respect to bias in edge weights, centrality measures, correlation between estimated and true partial correlations, andspecificity. With respect to sensitivity the frequentist GLASSO performs better.However, sensitivity of the Bayesian GLASSO is close to that of the frequentist GLASSO (except for the smallest N used in the simulations) and tends to be favored over the frequentist GLASSO in terms of F1. With respect to uncertainty in the centrality measures, the Bayesian GLASSO shows good coverage for strength andcloseness centrality. Uncertainty in betweenness centrality is estimated less well, and typically overestimated by the Bayesian GLASSO.

scholarly journals On using centrality to understand importance of entities in the Panama Papers

PLoS ONE ◽  
2021 ◽  
Vol 16 (3) ◽  
pp. e0248573
Author(s):  
Mayank Kejriwal
Keyword(s):  
Social Science ◽  
Network Science ◽  
Computational Social Science ◽  
Centrality Measures ◽  
Law Firms ◽  
Tax Havens ◽  
The Past ◽  
Past Half Century ◽  
Past Half ◽  
Insight Into

The Panama Papers comprise one of the most recent influential leaks containing detailed information on intermediary companies (such as law firms), offshore entities and company officers, and serve as a valuable source of insight into the operations of (approximately) 214,000 shell companies incorporated in tax havens around the globe over the past half century. Entities and relations in the papers can be used to construct a network that permits, in principle, a systematic and scientific study at scale using techniques developed in the computational social science and network science communities. In this paper, we propose such a study by attempting to quantify and profile the importance of entities. In particular, our research explores whether intermediaries are significantly more influential than offshore entities, and whether different centrality measures lead to varying, or even incompatible, conclusions. Some findings yield conclusions that resemble Simpson’s paradox. We also explore the role that jurisdictions play in determining entity importance.

scholarly journals A Trypanosoma brucei orphan kinesin employs a convergent microtubule organization strategy to complete cytokinesis

2021 ◽  
Author(s):  
Thomas E Sladewski ◽  
Paul C Campbell ◽  
Neil Billington ◽  
Alexandra D'Ordine ◽  
Christopher L de Graffenried
Keyword(s):  
Trypanosoma Brucei ◽  
Biophysical Properties ◽  
Microtubule Organization ◽  
Division Plane ◽  
Mechanistic Insight ◽  
Organization Strategy ◽  
Cytoskeletal Elements ◽  
Order Structures ◽  
Insight Into

Many single-celled eukaryotes have complex cell morphologies defined by cytoskeletal elements comprising microtubules arranged into higher-order structures. Trypanosoma brucei (T. brucei) cell polarity is mediated by a parallel array of microtubules that underlie the plasma membrane and define the auger-like shape of the parasite. The subpellicular array must be partitioned and segregated using a microtubule-based mechanism during cell division. We previously identified an orphan kinesin, KLIF, that localizes to the division plane and is essential for the completion of cytokinesis. To gain mechanistic insight into how this novel kinesin functions to complete cleavage furrow ingression, we characterized the biophysical properties of the KLIF motor domain in vitro. We found that KLIF is a non-processive dimeric kinesin that dynamically crosslinks microtubules. Microtubules crosslinked in an antiparallel orientation are translocated relative to one another by KLIF, while microtubules crosslinked parallel to one another remain static, resulting in the formation of organized parallel bundles. In addition, we found that KLIF stabilizes the alignment of microtubule plus ends. These features provide a mechanistic understanding for how KLIF functions to form a new pole of aligned microtubule plus ends that defines the shape of the new posterior, which is a unique requirement for the completion of cytokinesis in T. brucei.

scholarly journals A tensor-based framework for studying eigenvector multicentrality in multilayer networks

2019 ◽  
Vol 116 (31) ◽  
pp. 15407-15413 ◽  
Author(s):  
Mincheng Wu ◽  
Shibo He ◽  
Yongtao Zhang ◽  
Jiming Chen ◽  
Youxian Sun ◽  
...  
Keyword(s):  
Complex Networks ◽  
Prior Knowledge ◽  
General Framework ◽  
Single Layer ◽  
Structure And Function ◽  
Centrality Measures ◽  
Multilayer Networks ◽  
And Function ◽  
The Impact ◽  
Insight Into

Centrality is widely recognized as one of the most critical measures to provide insight into the structure and function of complex networks. While various centrality measures have been proposed for single-layer networks, a general framework for studying centrality in multilayer networks (i.e., multicentrality) is still lacking. In this study, a tensor-based framework is introduced to study eigenvector multicentrality, which enables the quantification of the impact of interlayer influence on multicentrality, providing a systematic way to describe how multicentrality propagates across different layers. This framework can leverage prior knowledge about the interplay among layers to better characterize multicentrality for varying scenarios. Two interesting cases are presented to illustrate how to model multilayer influence by choosing appropriate functions of interlayer influence and design algorithms to calculate eigenvector multicentrality. This framework is applied to analyze several empirical multilayer networks, and the results corroborate that it can quantify the influence among layers and multicentrality of nodes effectively.

Analysis of co-occurrence networks with clique occurrence information

2014 ◽  
Vol 25 (05) ◽  
pp. 1440015 ◽  
Author(s):  
Bin Shen ◽  
Yixiao Li
Keyword(s):  
Occurrence Frequency ◽  
Occurrence Rate ◽  
Centrality Measures ◽  
Average Size ◽  
Insight Into

Most of co-occurrence networks only record co-occurrence relationships between two entities, and ignore the weights of co-occurrence cliques whose size is bigger than two. However, this ignored information may help us to gain insight into the co-occurrence phenomena of systems. In this paper, we analyze co-occurrence networks with clique occurrence information (CNCI) thoroughly. First, we describe the components of CNCIs and discuss the generation of clique occurrence information. And then, to illustrate the importance and usefulness of clique occurrence information, several metrics, i.e. single occurrence rate, average size of maximal co-occurrence cliques and four types of co-occurrence coefficients etc., are given. Moreover, some applications, such as combining co-occurrence frequency with structure-oriented centrality measures, are also discussed.

scholarly journals Growing scale-free simplices

2021 ◽  
Vol 4 (1) ◽  
Author(s):  
Kiriil Kovalenko ◽  
Irene Sendiña-Nadal ◽  
Nagi Khalil ◽  
Alex Dainiak ◽  
Daniil Musatov ◽  
...  
Keyword(s):  
Degree Distribution ◽  
General Scheme ◽  
Simplicial Complexes ◽  
Generative Models ◽  
Analytical Control ◽  
Scaling Exponents ◽  
Scale Free ◽  
Pairwise Interactions ◽  
Order Structures ◽  
Insight Into

AbstractThe past two decades have seen significant successes in our understanding of networked systems, from the mapping of real-world networks to the establishment of generative models recovering their observed macroscopic patterns. These advances, however, are restricted to pairwise interactions and provide limited insight into higher-order structures. Such multi-component interactions can only be grasped through simplicial complexes, which have recently found applications in social, technological, and biological contexts. Here we introduce a model to grow simplicial complexes of order two, i.e., nodes, links, and triangles, that can be straightforwardly extended to structures containing hyperedges of larger order. Specifically, through a combination of preferential and/or nonpreferential attachment mechanisms, the model constructs networks with a scale-free degree distribution and an either bounded or scale-free generalized degree distribution. We arrive at a highly general scheme with analytical control of the scaling exponents to construct ensembles of synthetic complexes displaying desired statistical properties.

scholarly journals Growing Scale-Free Simplices

2020 ◽  
Author(s):  
Kiriil Kovalenko ◽  
Irene Sendina-Nadal ◽  
Nagi Khalil ◽  
Alex Dainak ◽  
Daniil Musatov ◽  
...  
Keyword(s):  
Degree Distribution ◽  
Preferential Attachment ◽  
General Scheme ◽  
Simplicial Complexes ◽  
Generative Models ◽  
Scaling Exponents ◽  
Scale Free ◽  
Pairwise Interactions ◽  
Order Structures ◽  
Insight Into

Abstract The past two decades have seen significant successes in our understanding of networked systems, from the mapping of real-world networks to the establishment of generative models recovering their observed macroscopic patterns. These advances, however, are restricted to pairwise interactions and provide limited insight into higher-order structures. Such multi-component interactions can only be grasped through simplicial complexes, which have recently found applications in social, technological and biological contexts. Here we introduce, study, and characterize a model to grow simplicial complexes of order two, i.e. nodes, links and triangles. Specifically, through a combination of preferential and/or non preferential attachment mechanisms, the model constructs networks with a scale-free degree distribution and an either bounded or scale-free generalized degree distribution. Allowing to analytically control the scaling exponents we arrive at a highly general scheme by which one is able to construct ensembles of synthetic complexes displaying desired statistical properties.

scholarly journals Mixtures and products in two graphical models

2018 ◽  
Vol 9 (1) ◽  
pp. 1-20 ◽  
Author(s):  
Anna Seigal ◽  
Guido Montufar
Keyword(s):  
Maximum Likelihood ◽  
Closed Form ◽  
Graphical Models ◽  
Statistical Models ◽  
The Other ◽  
Maximum Likelihood Estimates ◽  
Boltzmann Machine ◽  
Algebraic Description ◽  
Binary Random Variables ◽  
Probability Simplex

We compare two statistical models of three binary random variables. One is a mixture model and the other is a product of mixtures model called a restricted Boltzmann machine. Although the two models we study look different from their parametrizations, we show that they represent the same set of distributions on the interior of the probability simplex, and are equal up to closure. We give a semi-algebraic description of the model in terms of six binomial inequalities and obtain closed form expressions for the maximum likelihood estimates. We briefly discuss extensions to larger models.

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