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This research proposes a flexible Bayesian extension of the composite Gaussian process (CGP) model of Ba and Joseph (2012) for predicting (stationary or) non-stationary $y(\mathbf{x})$. The CGP generalizes the regression plus stationary…

Methodology · Statistics 2019-06-27 Casey B. Davis , Christopher M. Hans , Thomas J. Santner

Random geometric graphs (RGGs) are commonly used to model networked systems that depend on the underlying spatial embedding. We concern ourselves with the probability distribution of an RGG, which is crucial for studying its random…

Information Theory · Computer Science 2018-01-16 Mihai-Alin Badiu , Justin P. Coon

Graphical Gaussian models have proven to be useful tools for exploring network structures based on multivariate data. Applications to studies of gene expression have generated substantial interest in these models, and resulting recent…

Methodology · Statistics 2011-08-10 Michael Finegold , Mathias Drton

We derive representation theorems for exchangeable distributions on finite and infinite graphs using elementary arguments based on geometric and graph-theoretic concepts. Our results elucidate some of the key differences, and their…

Statistics Theory · Mathematics 2018-09-18 Steffen L. Lauritzen , Alessandro Rinaldo , Kayvan Sadeghi

This article studies the asymptotic properties of Bayesian or frequentist estimators of a vector of parameters related to structural properties of sequences of graphs. The estimators studied originate from a particular class of graphex…

Statistics Theory · Mathematics 2025-02-06 Zacharie Naulet , Judith Rousseau , François Caron

We consider the problem of determining the proportion of edges that are discovered in an Erdos-Renyi graph when one constructs all shortest paths from a given source node to all other nodes. This problem is equivalent to the one of…

Statistical Mechanics · Physics 2009-11-13 Vincent D. Blondel , Jean-Loup Guillaume , Julien M. Hendrickx , Raphael M. Jungers

Exponential random graph models are an important tool in the statistical analysis of data. However, Bayesian parameter estimation for these models is extremely challenging, since evaluation of the posterior distribution typically involves…

Computation · Statistics 2017-05-05 Lampros Bouranis , Nial Friel , Florian Maire

We perform a detailed computational study of the recently introduced Sombor indices on random graphs. Specifically, we apply Sombor indices on three models of random graphs: Erd\"os-R\'enyi graphs, random geometric graphs, and bipartite…

Combinatorics · Mathematics 2021-08-11 R. Aguilar-Sanchez , J. A. Mendez-Bermudez , Jose M. Rodriguez , Jose M. Sigarreta

Graph-theoretic methods have seen wide use throughout the literature on multi-agent control and optimization. When communications are intermittent and unpredictable, such networks have been modeled using random communication graphs. When…

Optimization and Control · Mathematics 2020-08-12 Beth Bjorkman , Matthew Hale , Thomas Lamkin , Benjamin Robinson , Craig Thompson

Mixed-effects regression models represent a useful subclass of regression models for grouped data; the introduction of random effects allows for the correlation between observations within each group to be conveniently captured when…

Methodology · Statistics 2024-09-25 Jackson Zhou , John T. Ormerod , Clara Grazian

Some practical results are derived for population inference based on a sample, under the two qualitative conditions of 'ignorability' and exchangeability. These are the 'Histogram Theorem', for predicting the outcome of a non-sampled member…

Statistics Theory · Mathematics 2015-11-12 Jonathan Rougier

A growing set of on-line applications are generating data that can be viewed as very large collections of small, dense social graphs -- these range from sets of social groups, events, or collaboration projects to the vast collection of…

Social and Information Networks · Computer Science 2013-05-15 Johan Ugander , Lars Backstrom , Jon Kleinberg

Random graph models are frequently used as a controllable and versatile data source for experimental campaigns in various research fields. Generating such data-sets at scale is a non-trivial task as it requires design decisions typically…

Data Structures and Algorithms · Computer Science 2020-03-03 Manuel Penschuck , Ulrik Brandes , Michael Hamann , Sebastian Lamm , Ulrich Meyer , Ilya Safro , Peter Sanders , Christian Schulz

Exchangeable models for countable vertex-labeled graphs cannot replicate the large sample behaviors of sparsity and power law degree distribution observed in many network datasets. Out of this mathematical impossibility emerges the question…

Statistics Theory · Mathematics 2016-10-24 Harry Crane , Walter Dempsey

This paper establishes new concentration inequalities for random matrices constructed from independent random variables. These results are analogous with the generalized Efron-Stein inequalities developed by Boucheron et al. The proofs rely…

Probability · Mathematics 2014-08-18 Daniel Paulin , Lester Mackey , Joel A. Tropp

We extend the well-known and widely used Exponential Random Graph Model (ERGM) by including nodal random effects to compensate for heterogeneity in the nodes of a network. The Bayesian framework for ERGMs proposed by Caimo and Friel (2011)…

Applications · Statistics 2015-01-13 Stephanie Thiemichen , Nial Friel , Alberto Caimo , Göran Kauermann

We study properties of some standard network models when the population is split into two types and the connection pattern between the types is varied. The studied models are generalizations of the Erd\H{o}s-R\'{e}nyi graph, the…

Probability · Mathematics 2017-07-17 Maria Deijfen , Robert Fitzner

Experimental reproducibility and replicability are critical topics in machine learning. Authors have often raised concerns about their lack in scientific publications to improve the quality of the field. Recently, the graph representation…

Machine Learning · Computer Science 2022-02-21 Federico Errica , Marco Podda , Davide Bacciu , Alessio Micheli

Exponential random graph models (ERGMs) are flexible probability models allowing edge dependency. However, it is known that, to a first-order approximation, many ERGMs behave like Erd\"os-R\'enyi random graphs, where edges are independent.…

Probability · Mathematics 2024-01-04 Wen-Yi Ding , Xiao Fang

We investigate first passage percolation on inhomogeneous random graphs. The random graph model G(n,kappa) we study is the model introduced by Bollob\'as, Janson and Riordan, where each vertex has a type from a type space S and edge…

Probability · Mathematics 2016-11-14 István Kolossváry , Júlia Komjáthy