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## A Survey of Statistical Network Models

Citations: | 72 - 8 self |

### Citations

6594 |
Neural Networks for Pattern Recognition
- Bishop
- 1995
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Citation Context ... [258; 305]. • Neural networks. Neural networks originated as simple models for connections in the brain but have more recently been used as a computational tool for pattern recognition (e.g., Bishop =-=[38]-=-), machine learning (e.g., Neal [228]), and models of cognition (e.g., Rogers and McClelland [257]). • Networks and economic theory. A relatively new area of study is the link between network problems... |

4349 | Latent Dirichlet Allocation
- BLEI, NG, et al.
- 2003
(Show Context)
Citation Context ...ve models that scale in reasonable ways to substantial-sized networks. The class of mixed membership models resembles a form of soft clustering [95] and includes the latent Dirichlet allocation model =-=[41]-=- from machine learning as a special case. This class of models offers much promise for the kinds of network dynamical processes we discuss here. 1.2 What This Survey Does Not Cover This survey focuses... |

2380 | On generalized graphs
- Bollobas
- 1965
(Show Context)
Citation Context ...y unconnected with the present exposition. For excellent introductions to this literature, see Chung and Lu [69] and Durrett [91]. For related results on the mathematics of graph theory, see Bollobás =-=[43]-=-. • Efficient computation on networks. There is a substantial computer science literature dealing with efficient calculation of quantities associated with network structures, such as shortest paths, n... |

2137 | Statistical mechanics of complex networks
- Albert, Barabási
- 2002
(Show Context)
Citation Context ...320] interpolates between an ordered finitedimensional lattice and an Erdös-Rényi-Gilbert random graph in order to produce local clustering and triadic closures (see section 4.2). Albert and Barabási =-=[12]-=- describe a number of variants on these themes. Many of the investigators exploring the use of such models often focus on the empirical degree distribution, claiming for example that it follows a powe... |

1660 | On power-law relationships of the internet topology
- Faloutsos, Faloutsos, et al.
- 1999
(Show Context)
Citation Context ... the protein-protein interaction data in Drosophila melanogaster species best. Machine learning approaches emerged in several forms over the past decade with the empirical studies of Faloutsos et al. =-=[97]-=- and Kleinberg [173, 172, 174], who introduced a model for which the underlying graph is a grid—the graphs generated do not have a power law degree distribution, and each vertex has the same expected ... |

1629 |
Spatial interaction and the statistical analysis of lattice systems (with discussion
- Besag
- 1974
(Show Context)
Citation Context ...Park and Newman [240] formally characterized sensitivity issues. Snijders et al. [280] recently proposed a variant of 6 This is the definition of Markov property for spatial processes on a lattice in =-=[33]-=-. 30these models where the major problem of double-counting is mitigated but not overcome. Hunter and Handcock [155] estimate likelihood ratios for nearby {θi} using a MCMC procedure related to the w... |

946 | A novel genetic system to detect protein–protein interactions. Nature - Fields, Song - 1989 |

869 |
Network biology: understanding the cell’s functional organization, Nature Rev. Genet 5
- Barabási, Oltvai
- 2004
(Show Context)
Citation Context ...ed to be between 18,000 [328] and 30,000 [307]. Figure 2.4 shows a popular image of the interaction network among proteins in the budding yeast, produced as part of an analysis by Barabási and Oltvai =-=[27]-=-. Statistical methods have been developed for analyzing many aspects of this large protein interaction network, including de-noising [32; 8], function prediction [227], and identification of binding m... |

651 | Linked: the New Science of Networks - Barabási - 2002 |

606 | Powerlaw distributions in empirical data
- Clauset, Shalizi, et al.
- 2009
(Show Context)
Citation Context ... empirical data and used Bayes factors to show that the proposed model is not representative of e-mail communication patterns. See a related discussion of the poor fit of power laws in Clauset et al. =-=[74]-=-. There are several works, however, that try to address model fitting and model comparison. For example, the work of Williams and Martinez [323] showed how a simple two-parameter model predicted “key ... |

506 |
Classes of small-world networks
- Amaral, Scala, et al.
- 2000
(Show Context)
Citation Context ...ks. Durrett [91] discusses links between small-world models and stochastic processes. Typical usage of small-world models include empirical analyses involving aggregate summary statistics (see, e.g., =-=[18; 231]-=-). There are as yet no formal statistical methods for examining the evolution of small-world network models and for assessing their fit to network data measured over time. 4.3 Duplication-Attachment M... |

489 | Group formation in large social networks: Membership, growth, and evolution
- Backstrom, Huttenlocher, et al.
- 2006
(Show Context)
Citation Context ...ction by Newman et al. [231]. More recently this style of statistical physics models have been used to detect community structure in networks, e.g., see Girvan and Newman [122] and 5Backstrom et al. =-=[20]-=-, a phenomenon which has its counterpart description in the social science network modeling literature. The probabilistic literature on random graph models from the 1990s made the link with epidemics ... |

371 |
Network motifs: theory and experimental approaches
- Alon
- 2007
(Show Context)
Citation Context ...d to locate subgraphs that are common among species, thus advancing our understanding of evolution [105]. Motif finding, or more generally the search for subgraph patterns, also has many applications =-=[17]-=-. Combining networks from heterogeneous data sources helps to improve the accuracy of predicted genetic interactions [327]. Heterogeneity of network data sources in biology introduces a lot of noise i... |

366 | Mixed membership stochastic blockmodels
- Airoldi, Blei, et al.
(Show Context)
Citation Context ...del as well. More recently, a number of authors have looked to combine the stochastic blockmodel ideas from the 1980s with latent space models, model-based clustering [137] or mixed-membership models =-=[9]-=-, to provide generative models that scale in reasonable ways to substantial-sized networks. The class of mixed membership models resembles a form of soft clustering [95] and includes the latent Dirich... |

353 | Evolution of the social network of scientific collaborations. Physica A: Statistical Mechanics and its Applications
- Barabási, Jeong, et al.
- 2002
(Show Context)
Citation Context ...etwork properties and testing hypotheses about network structure, see, e.g., [280]. Physicists, on the other hand, tend to be interested in understanding parsimonious mechanisms for network formation =-=[28; 235]-=-. For example, a common modeling goal is to explain how a given network comes to have its particular degree distribution or diameter at time t. Several network analysis concepts have found niches in c... |

353 |
Agent-based modeling: Methods and techniques for simulating human systems,”
- Bonabeau
- 2002
(Show Context)
Citation Context ...ain of research has been linked with network ideas. With the recent advances in high-performance computing, simulations of large-scale social systems have become an active area of research, e.g., see =-=[46]-=-. In particular, there is a strong interest in areas that revolve around national security and the military, with studies on the effects of catastrophic events and biological warfare, as well as compu... |

347 |
Markov graphs
- Frank, Strauss
- 1986
(Show Context)
Citation Context ...s [103] and stochastic blockmodels. This approach to modeling network data quickly evolved into the class of p ∗ or exponential random graph models (ERGM) originating in the work of Frank and Strauss =-=[110]-=- and Strauss and Ikeda [287]. A trio of papers demonstrating procedures for using ERGMs [316; 241; 254] led to the wide-spread use of ERGMs in a descriptive form for cross sectional network structures... |

269 |
The Origin of Bursts and Heavy Tails in Human Dynamics.” Nature 435:207–11
- Barabási
- 2005
(Show Context)
Citation Context ...y or sufficient as descriptors for the actual network data. Moreover, these summary quantities can often be highly misleading as the critique by Stouffer et al. [285, 286] of methods used by Barabási =-=[25]-=- and Vázquez et al. [304] suggest. Barabási claimed that the dynamics of a number of human activities are scale-free, i.e., he specifically reported that the probability distribution of time intervals... |

267 | Algebraic algorithms for sampling from conditional distributions, Annals of Statistics 26
- Diaconis, Sturmfels
- 1998
(Show Context)
Citation Context ...n. Generating such exact distributions is a very tricky matter in discrete exponential families because of the need to utilize appropriate Markov bases, either explicitly as in Diaconis and Sturmfels =-=[85]-=- or implicitly. It is unclear whether the proposals in this literature are in fact reaching all possible tables associated with the distribution. Blitzstein and Diaconis [42] explore different efficie... |

256 |
JH (2008) The collective dynamics of smoking in a large social network
- NA, Fowler
(Show Context)
Citation Context ...attributions of the individuals via longitudinal logistic-regression models with lagged effects. Subsequently, they have published similar papers focused on the dynamics of smoking behavior over time =-=[66]-=- and on happiness [67], both using the structure of Framingham “offspring” cohort. This work has come under criticism by others. For example Cohen-Cole and Fletcher note that there are plausible alter... |

252 |
The analysis of crossclassified categorical data, 2nd
- Fienberg
- 1980
(Show Context)
Citation Context ...eraction corresponds to p1 with constant reciprocation, and the standard iterative proportional fitting algorithm 4 can be used to compute the maximum 4 For details on IPF for contingency tables, see =-=[39; 99]-=- j ij 28likelihood estimates. Fienberg et al. [103] show that same type of contingency table representation also works for the correlated p1 model for multiple relations, and Meyer [213] provides a t... |

245 |
M: Hierarchical structure and the prediction of missing links in networks
- Clauset, Moore, et al.
(Show Context)
Citation Context ... connectivity [122; 232; 234; 266]. In the machine learning community, networks are often used to predict missing information, which can be edge related, e.g., predicting missing links in the network =-=[238; 73; 198]-=-, or attribute related, e.g., predicting how likely a movie is to be a box office hit [229]. Other applications include locating the crucial missing link in a business or a terrorist network, or calcu... |

244 | R-mat: A recursive model for graph mining
- Chakrabarti, Zhan, et al.
(Show Context)
Citation Context ...< 1. Barabási et al. [28] and Durrett [91] provide an account of this and other extensions to the original model of Albert and Barabási. Alternative graph generation mechanisms appear every day—R–MAT =-=[60]-=-,‘winners don’t take all’ [242],‘forest fire’ [194],‘butterfly’ [212] and RTG [10], to name a few. The latest, RTG model, proves conformance to 11 empirical laws observed in real networks. The main go... |

239 | Inferring friendship network structure by using mobile phone data. - Eagle, Pentland, et al. - 2009 |

216 | Diameter of the world wide web
- Albert, Jeong, et al.
- 1999
(Show Context)
Citation Context ...ks [158], functional and co-expression gene similarity networks and gene regulatory networks [111; 309], computer science applications revolve around e-mail [207], the internet [97; 63; 151], the web =-=[152; 13]-=-, academic paper co-authorship [127] and citation networks [204; 216]. Citation networks have a long history 10of modeling in different areas of research starting with the seminal paper of de Solla P... |

199 |
Exchangeability and related topics
- Aldous
- 1985
(Show Context)
Citation Context ...graph model, the latent binary strings do not carry semantic meaning, rather they are mathematical artifacts that help to represent a graph and induce an expressive parametric family of distributions =-=[15; 165; 5]-=-. Most importantly, the exchangeable graph model is meant to be a tool to represent and explore the space of connectivity patterns in a smooth, principled semi-parametric fashion. In this regard, exch... |

199 | Random Graph Dynamics
- Durrett
- 2007
(Show Context)
Citation Context ...ic phenomena. Picking up on this idea, Watts and Strogatz [320] and others used epidemic models to capture general characteristics of the evolution of these new variations on random networks. Durrett =-=[91]-=- has provided us with a book-length treatment on the topic with a number of interesting variations on the theme. The appeal of stochastic processes as descriptions of dynamic network models comes from... |

180 | The spectra of random graphs with given expected degrees
- Chung, Lu, et al.
(Show Context)
Citation Context ..., 239], and they either fix the degree-distribution parameters or compute distributions that are conditional on some function of the degree distributions or sequences, such as their expectations (cf. =-=[235; 70]-=-). Software is available to sample from the space of random graphs with a given degree distribution based on Monte Carlo Markov chain methods [42; 138]. There would appear to be a direct link between ... |

177 | The phase transition in inhomogeneous random graphs.
- Bollobas, Janson, et al.
- 2007
(Show Context)
Citation Context ...s of random graphs with such a property has been recently rediscovered and further explored in the mathematics literature, where the class of such graphs is referred to as inhomogeneous random graphs =-=[45]-=-. An alternative and arguably more interesting set of specifications can be obtained by imposing dependence among the bits at each node. This can be accomplished by sampling sets of dependent probabil... |

165 | An experimental study of search in global social networks. Science 301(5634
- Dodds, Muhamad, et al.
- 2003
(Show Context)
Citation Context ...s data were gathered in batches of transmission, and thus these models can be thought of as representing early examples of generative descriptions of dynamic network evolution. Recently, Dodds et al. =-=[86]-=- studied a global “replication” variation on the Milgram study in which more than 60,000 e-mail users attempted to reach one of 18 target persons in 13 countries by forwarding messages to acquaintance... |

159 |
4). Dynamic Spread of Happiness in a Large Social Network: Longitudinal Analysis Over 20 Years in the Farmingham Heart Study.
- Fowler, Christakis
- 2008
(Show Context)
Citation Context ...dividuals via longitudinal logistic-regression models with lagged effects. Subsequently, they have published similar papers focused on the dynamics of smoking behavior over time [66] and on happiness =-=[67]-=-, both using the structure of Framingham “offspring” cohort. This work has come under criticism by others. For example Cohen-Cole and Fletcher note that there are plausible alternative explanations to... |

146 | Collective entity resolution in relational data
- Bhattacharya, Getoor
(Show Context)
Citation Context ...ant in analyzing communication networks, e.g., in detecting possible latent terrorist cells [30]. The related task of discovering the “roles” of individual nodes is useful for identity disambiguation =-=[36]-=- and for business organization analysis [207]. These applications often take the machine learning approach of graph partitioning, a topic previously known in social science and statistics literature a... |

141 |
Complex Graphs and Networks
- CHUNG, LU
- 2006
(Show Context)
Citation Context ...dels comes from being able to exploit the extensive literature already developed, including the existence and the form of stationary distributions and other model features or properties. Chung and Lu =-=[69]-=- provide a complementary treatment of these models and their probabilistic properties. One of the principal problems with this diverse network literature that we see is that, with some notable excepti... |

132 | Mixed-membership models of scientific publications
- Erosheva, Fienberg, et al.
(Show Context)
Citation Context ...137] or mixed-membership models [9], to provide generative models that scale in reasonable ways to substantial-sized networks. The class of mixed membership models resembles a form of soft clustering =-=[95]-=- and includes the latent Dirichlet allocation model [41] from machine learning as a special case. This class of models offers much promise for the kinds of network dynamical processes we discuss here.... |

130 |
editors. Network Analysis: Methodological Foundations
- Brandes, Erlebach
- 2005
(Show Context)
Citation Context ... of quantities associated with network structures, such as shortest paths, network diameter, and other measures of connectivity, centrality, clustering, etc. The edited volume by Brandes and Erlebach =-=[48]-=- contains good overviews of a number of these topics as well as other computational issues associated with the study of graphs. • Use of the network as a tool for sampling. Adaptive sampling strategie... |

121 | Chains of affection: The structure of adolescent romantic and sexual networks
- Bearman, Moody, et al.
- 2004
(Show Context)
Citation Context ...hs after Wave I in 1996 and followed up on the in-home interviews. The dataset covered 14,738 adolescents and 128 school administrators. Based on the data collected from Wave I and II, Bearman et al. =-=[31]-=- constructed the timed sequence of relationship networks amongst students from the two large schools with saturated sampling. The resulting sexual relationship network bears strong resemblance to a sp... |

119 | Finding local community structure in networks - Clauset - 2005 |

113 |
A nonparametric view of network models and Newman-Girvan and other modularities
- Bickel, Chen
- 2009
(Show Context)
Citation Context ...rategy to approximate the posterior distribution on the latent variables, (Π, Z). (Variational methods scale to large problems without loosing much in terms of accuracy [3; 49; 308].) Bickel and Chen =-=[37]-=-, the most recent contribution to this literature, brings new twists to the model-based approach of community discovery. They use a blockmodel to formalize a given network in terms of its community st... |

113 |
Genetic and physical maps of Saccharomyces cerevisiae
- Cherry
- 1997
(Show Context)
Citation Context ...llular organism that has become a de-facto model organism for the study of molecular and cellular biology [47]. There are about 6,000 proteins in the budding yeast, which interact in a number of ways =-=[64]-=-. For instance, proteins bind together to form protein complexes, the physical units that carry out most functions in the cell [184]. In recent years, a large amount of resources has been directed to ... |

110 | Relational topic models for document networks
- Chang, Blei
- 2009
(Show Context)
Citation Context ...ribed here, especially the mixed membership stochastic blockmodels of section 3.8, since the text could naturally be modeled by mixed-membership topic models. McCallum et al. [208] and Chang and Blei =-=[61]-=- suggest different ways to approach this kind of combination model. Dynamic models that combine evolving block and topic structures would be of special interest for such applications. 60Chapter 6 Sum... |

110 | Connected: The surprising power of our social networks and how they shape our lives—how your friends’ friends’ friends affect everything you feel, think, and do. - Christakis, Fowler - 2011 |

109 | The origin of power laws in Internet topologies revisited
- Chen, Chang, et al.
- 2002
(Show Context)
Citation Context ... 328], metabolic networks [158], functional and co-expression gene similarity networks and gene regulatory networks [111; 309], computer science applications revolve around e-mail [207], the internet =-=[97; 63; 151]-=-, the web [152; 13], academic paper co-authorship [127] and citation networks [204; 216]. Citation networks have a long history 10of modeling in different areas of research starting with the seminal ... |

101 | Nexus: Small Worlds and the Groundbreaking Science of Networks. - Buchanan - 2002 |

94 |
Finetti. Theory of Probability.
- De
- 1974
(Show Context)
Citation Context ... the vertex set of the Khypercube, i.e., the unit hypercube in K dimensions. 23pendent given the binary string representations of the incident nodes. They are exchangeable in the sense of De Finetti =-=[82]-=-. From a statistical perspective, the exchangeable graph model we survey here [1; 5] provides perhaps the simplest step-up in complexity from the random graph model [93; 119]. In the data generation p... |

82 | The diameter of a cycle plus random matching.
- Bollobás, Chung
- 1988
(Show Context)
Citation Context ...er “small-world” model interpolates between an ordered finite-dimensional lattice and an Erdös-Rényi-Gilbert random graph in order to produce local clustering and triadic closures. Bollobás and Chung =-=[44]-=- had previously noted that adding random edges to a ring of N nodes drastically reduces the diameter of the network. The Watts-Strogatz model begins with a ring lattice with N nodes and k edges per no... |

82 |
The nature of the social agent
- Carley, Newell
- 1994
(Show Context)
Citation Context ...al explorations of possible recovery strategies [57; 59]. These works are the contemporary counterparts of more classical work at the interface between artificial intelligence and the social sciences =-=[54; 56; 55]-=-. 8Chapter 2 Motivation and Dataset Examples 2.1 Motivations for Network Analysis Why do we analyze networks? The motivation behind network analysis is as diverse as the origin of network problems wi... |

77 | Statistical analysis of multiple sociometric relations
- Fienberg, Meyer, et al.
- 1985
(Show Context)
Citation Context ... for easy computation of maximum likelihood estimates using a contingency table formulation of the model [101; 102]. It also allowed for various generalizations to multidimensional network structures =-=[103]-=- and stochastic blockmodels. This approach to modeling network data quickly evolved into the class of p ∗ or exponential random graph models (ERGM) originating in the work of Frank and Strauss [110] a... |

70 |
Categorical data analysis of single sociometric relations
- Fienberg, Wasserman
- 1981
(Show Context)
Citation Context ...s an additional effect due to reciprocation. The p1 model was log-linear in form, which allowed for easy computation of maximum likelihood estimates using a contingency table formulation of the model =-=[101; 102]-=-. It also allowed for various generalizations to multidimensional network structures [103] and stochastic blockmodels. This approach to modeling network data quickly evolved into the class of p ∗ or e... |

69 |
Group stability: A socio-cognitive approach,
- Carley
- 1990
(Show Context)
Citation Context ...al explorations of possible recovery strategies [57; 59]. These works are the contemporary counterparts of more classical work at the interface between artificial intelligence and the social sciences =-=[54; 56; 55]-=-. 8Chapter 2 Motivation and Dataset Examples 2.1 Motivations for Network Analysis Why do we analyze networks? The motivation behind network analysis is as diverse as the origin of network problems wi... |

60 | Mining social networks for viral marketing,”
- Domingos
- 2005
(Show Context)
Citation Context ...he concept of information propagation also finds many applications in the network domain, such as virus propagation in computer networks [310], HIV infection networks [222; 163; 164], viral marketing =-=[87]-=- and more generally gossiping [170]. Here some work focuses on finding network configurations optimal for routing, while other research assumes that the network structure is given and focus on suitabl... |

60 | A Geometric Preferential Attachment Model of Networks
- Flaxman, Frieze, et al.
(Show Context)
Citation Context ...ide at least one possible way to assess whether a graph corresponding to a network is in fact scale-free. For more informal discussions related to this theoretical work, see [14; 324]. Flaxman et al. =-=[106; 107]-=- describe a class of network models linked to the preferential attachment model that also yield a power-law degree distribution. Most descriptions of generative models fall short of studying the full ... |

55 | Markov random fields in statistics.
- Clifford
- 1990
(Show Context)
Citation Context ... the parameters in ERGMs. Remark. It is possible to express the current formulation of exponential random graphs using the formalism of undirected graphical models and the Hammersley-Clifford theorem =-=[76; 33]-=-. We can write the likelihood of an arbitrary undirected graph as ∏ c∈C Pr(y|θ) = ψ(yc|θc) , (3.8) z where yc denotes the nodes in clique c, θc denotes the corresponding set of parameters, ψ are ∑ ∏ n... |

53 |
Is obesity contagious?: social networks vs. environmental factors in the obesity epidemic’,
- Cohen-Cole, Fletcher
- 2008
(Show Context)
Citation Context ...” cohort. This work has come under criticism by others. For example Cohen-Cole and Fletcher note that there are plausible alternative explanations to the network structure based on contextual factors =-=[77]-=-, and in a separate paper demonstrate that the same methodology detects “implausible” social network effects for such medical conditions as acne and headaches as well as for physical height [78]. The ... |

52 |
Agents and Organizations of the Future
- Carley, Smart
(Show Context)
Citation Context ...al explorations of possible recovery strategies [57; 59]. These works are the contemporary counterparts of more classical work at the interface between artificial intelligence and the social sciences =-=[54; 56; 55]-=-. 8Chapter 2 Motivation and Dataset Examples 2.1 Motivations for Network Analysis Why do we analyze networks? The motivation behind network analysis is as diverse as the origin of network problems wi... |

51 |
On random graphs. Publicationes Mathematicae 6:290–297
- Erdös, Rényi
- 1959
(Show Context)
Citation Context ...this model as a description of a neural network. But the formal properties of simple random graph network models are usually traced back to Gilbert [119], who examined G(N, p), and to Erdös and Rényi =-=[93]-=-. The Erdös-Rényi-Gilbert random graph model, G(N, E), describes an undirected graph involving N nodes and a fixed number of edges, E, chosen randomly from the ( ) N possible edges in the graph; an eq... |

49 |
Deep South: A social anthropological study of caste and class. Chicago:
- Davis, Gardner, et al.
- 1941
(Show Context)
Citation Context ...ork data repositories are available on public websites and as part of packages. For example, UCINet 1 includes a lot of well known smaller scale datasets such as the Davis Southern Club Women dataset =-=[80]-=-, Zachary’s karate club dataset [330], and Sampson’s monk data [259] described below. Pajek 2 contains a larger set of small and large networks from domains such as biology, linguistics, and food-web.... |

49 | Graph limits and exchangeable random graphs.
- Diaconis, Janson
- 2008
(Show Context)
Citation Context ...) unbiased and lead to the discovery of the correct community structure. The proof relies on the exchangeability results developed in the statistics community [15; 165] applied to paired measurements =-=[84]-=-. 3.9 Latent Space Models The intuition at the core of latent space models is that each node i ∈ N can be represented as a point zi in a “low dimensional” space, say R k . The existence of an edge in ... |

48 | A Sequential Importance Sampling Algorithm for Generating RandomGraphs with Prescribed Degrees. Internet Mathematics. 2011; 6(4):489–522. doi
- Blitzstein, Diaconis
(Show Context)
Citation Context ...ns or sequences, such as their expectations (cf. [235; 70]). Software is available to sample from the space of random graphs with a given degree distribution based on Monte Carlo Markov chain methods =-=[42; 138]-=-. There would appear to be a direct link between these ideas and the representation of degree distributions in the family of p1 models. In the latter, the αi and βi parameters represent the out-degree... |

40 |
Yeast as a model organism,”
- Botstein, Chervitz, et al.
- 1997
(Show Context)
Citation Context ... see [58]. 2.2.3 The Protein Interaction Network in Budding Yeast The budding yeast is a unicellular organism that has become a de-facto model organism for the study of molecular and cellular biology =-=[47]-=-. There are about 6,000 proteins in the budding yeast, which interact in a number of ways [64]. For instance, proteins bind together to form protein complexes, the physical units that carry out most f... |

39 | Estimating Peer Effects on Health in Social Networks: A Response to Cohen-Cole and Fletcher;
- Fowler, Christakis
- 2008
(Show Context)
Citation Context ... methodology detects “implausible” social network effects for such medical conditions as acne and headaches as well as for physical height [78]. The authors answer to these criticisms can be found in =-=[108]-=-. The question of the magnitude and significance of social network effects is still a subject of an ongoing debate. 2.2.6 The NIPS Paper Co-Authorship Dataset The NIPS dataset contains information on ... |

37 | Discovering hidden groups in communication networks
- Baumes, Goldberg, et al.
- 2004
(Show Context)
Citation Context ... 9of biological applications of networks, please see [332]. The task of finding hidden groups is also relevant in analyzing communication networks, e.g., in detecting possible latent terrorist cells =-=[30]-=-. The related task of discovering the “roles” of individual nodes is useful for identity disambiguation [36] and for business organization analysis [207]. These applications often take the machine lea... |

36 |
Metric inference for social networks
- Banks, Carley
- 1994
(Show Context)
Citation Context ...ons of this ERGM model that involve directed edges are natural generalizations of the p1 model. Alternative parameterizations that go beyond Markov graph models have been recently proposed, e.g., see =-=[280; 317; 21]-=-. Frank and Strauss [110] worked mainly with the three parameter model where θ3, . . . , θn−1 = 0. They proposed a pseudo-likelihood parameter estimation method [287] that maximizes ℓ(θ) = ∑ ( log i<j... |

35 |
Variational inference for large-scale models of discrete choice
- Braun, McAuliffe
- 2010
(Show Context)
Citation Context ...nested variational inference strategy to approximate the posterior distribution on the latent variables, (Π, Z). (Variational methods scale to large problems without loosing much in terms of accuracy =-=[3; 49; 308]-=-.) Bickel and Chen [37], the most recent contribution to this literature, brings new twists to the model-based approach of community discovery. They use a blockmodel to formalize a given network in te... |

31 | Models for Network Evolution
- Banks, Carley
- 1996
(Show Context)
Citation Context ...ease refer to Koskinen and Snijders [179]. 4.5 Discrete Time Markov Models In this section, we outline three recent proposals of dynamic network models operating in the discrete time domain (see also =-=[22]-=-). All three models have the Markov property and represent the likelihood as a sequence of factored conditional probabilities Pr(Y 1 , Y 2 , . . . , Y T ) = Pr(Y T | Y T −1 ) Pr(Y T −1 | Y T −2 ) · · ... |

28 |
BioWar: Scalable Agentbased Model of Bioattacks,”
- Carley
- 2006
(Show Context)
Citation Context ...hat revolve around national security and the military, with studies on the effects of catastrophic events and biological warfare, as well as computational explorations of possible recovery strategies =-=[57; 59]-=-. These works are the contemporary counterparts of more classical work at the interface between artificial intelligence and the social sciences [54; 56; 55]. 8Chapter 2 Motivation and Dataset Example... |

27 |
Detecting implausible social network effects in acne, height, and headaches: longitudinal analysis’,
- Cohen-Cole, Fletcher
- 2008
(Show Context)
Citation Context ...ctors [77], and in a separate paper demonstrate that the same methodology detects “implausible” social network effects for such medical conditions as acne and headaches as well as for physical height =-=[78]-=-. The authors answer to these criticisms can be found in [108]. The question of the magnitude and significance of social network effects is still a subject of an ongoing debate. 2.2.6 The NIPS Paper C... |

24 | A.: Mixing time of exponential random graphs
- Bhamidi, Bresler, et al.
- 2011
(Show Context)
Citation Context ...rical investigation rooted in the theory of discrete exponential families [136; 251]. For a discussion of mixing times of MCMC methods for ERGMs and the relevance to convergence and degeneracies, see =-=[35]-=-. There are two carefully constructed packages of routines that are available for analyzing network data using ERGMs: statnet7 and SIENA8 . These packages focus on the use of MCMC methods for estimati... |

23 | Sampling algorithms for pure network topologies
- Airoldi, Carley
- 2005
(Show Context)
Citation Context ...e [135], who adapt MCMC algorithms for exponential random graph models to account for sampling designs. To date, these are the only works to seriously explore this important topic. Airoldi and Carley =-=[6]-=- quantify the sensitivity of alternative sampling algorithms to generate graphs that share similar topological properties, as well as the divergence of topological properties of algorithms for samplin... |

23 |
A general model for food web structure.
- Allesina, Alonso, et al.
- 2008
(Show Context)
Citation Context ...nication networks have come under similar scrutiny, especially since the events of September 11, 2001 (e.g., see [182; 250; 249; 62]). There has also been work on ecological networks such as foodwebs =-=[323; 16]-=-, neuronal networks [188], network epidemiology [306], economic trading networks [123], transportation networks (roads, railways, airplanes; e.g., [113]), resource distribution networks, mobile phone ... |

22 |
Constructing blockmodels: How and why
- Arabie, Boorman, et al.
- 1978
(Show Context)
Citation Context ...ir paper and the discussion of structural equivalence gave rise to innumerable papers in mathematical sociology, (see, e.g., [53]) and algorithmic search strategies for determining blocks (see, e.g., =-=[19; 88; 89]-=-). By embedding these ideas within a framework of random graphs, Holland et al. [150] explained how a special version of p1 could be used to describe a random graph model with predefined blocks. (See ... |

21 | Generalized blockmodeling of two-mode network data..
- Doreian, Batagelj, et al.
- 2004
(Show Context)
Citation Context ...ir paper and the discussion of structural equivalence gave rise to innumerable papers in mathematical sociology, (see, e.g., [53]) and algorithmic search strategies for determining blocks (see, e.g., =-=[19; 88; 89]-=-). By embedding these ideas within a framework of random graphs, Holland et al. [150] explained how a special version of p1 could be used to describe a random graph model with predefined blocks. (See ... |

19 | Catching the ‘network science’ bug: Insight and opportunity for the operations researcher
- Alderson
- 2008
(Show Context)
Citation Context ...ale-free graphs. They provide at least one possible way to assess whether a graph corresponding to a network is in fact scale-free. For more informal discussions related to this theoretical work, see =-=[14; 324]-=-. Flaxman et al. [106; 107] describe a class of network models linked to the preferential attachment model that also yield a power-law degree distribution. Most descriptions of generative models fall ... |

18 |
Græmlin: General and robust alignment of multiple large interaction networks. Genome Res
- Flannick, Novak, et al.
- 2006
(Show Context)
Citation Context ...n networks can be harnessed to help with functional gene annotation [226]. Graph alignment can be used to locate subgraphs that are common among species, thus advancing our understanding of evolution =-=[105]-=-. Motif finding, or more generally the search for subgraph patterns, also has many applications [17]. Combining networks from heterogeneous data sources helps to improve the accuracy of predicted gene... |

17 |
Getting started in probabilistic graphical models
- AIROLDI
- 2007
(Show Context)
Citation Context ...nested variational inference strategy to approximate the posterior distribution on the latent variables, (Π, Z). (Variational methods scale to large problems without loosing much in terms of accuracy =-=[3; 49; 308]-=-.) Bickel and Chen [37], the most recent contribution to this literature, brings new twists to the model-based approach of community discovery. They use a blockmodel to formalize a given network in te... |

16 |
S.E.: A latent mixed-membership model for relational data. In:
- Airoldi, Blei, et al.
- 2005
(Show Context)
Citation Context ...nalysis concepts have found niches in computational biology. For example, work on protein function classification can be thought of as finding hidden groups in the protein-protein interaction network =-=[7; 8]-=- to gain better understanding of underlying biological processes. Label propagation (node similarity) in networks can be harnessed to help with functional gene annotation [226]. Graph alignment can be... |

15 | Counting and locating the solutions of polynomial systems of maximum likelihood equations, II: The Behrens-Fisher problem
- Buot, Hosten, et al.
(Show Context)
Citation Context ...ents of points to mixture components to obtain an equivalent solution. There are a number of papers that describe the issue in various models (e.g., [283; 132]) and from different perspectives (e.g., =-=[51; 52]-=- from the algebraic perspective). A few solutions to address this issue have been proposed recently. Some consider inference on equivalence classes in a blockmodel for network data [236]. Others pre-p... |

14 |
Networks of scientific papers: The pattern of bibliographic references indicates the nature of the scientific research front
- Price
- 1965
(Show Context)
Citation Context ...demic paper co-authorship [127] and citation networks [204; 216]. Citation networks have a long history 10of modeling in different areas of research starting with the seminal paper of de Solla Price =-=[83]-=- and more recently in physics [190]. With the recent rise of online networks, computer science and social science researchers are also starting to examine blogger networks such as LiveJournal, social ... |

13 | RTG: a recursive realistic graph generator using random typing
- Akoglu, Faloutsos
(Show Context)
Citation Context ...tensions to the original model of Albert and Barabási. Alternative graph generation mechanisms appear every day—R–MAT [60],‘winners don’t take all’ [242],‘forest fire’ [194],‘butterfly’ [212] and RTG =-=[10]-=-, to name a few. The latest, RTG model, proves conformance to 11 empirical laws observed in real networks. The main goal of these random graph models is to describe a process that could generate netwo... |

13 | Graph model selection using maximum likelihood
- Bezáková, Kalai, et al.
- 2006
(Show Context)
Citation Context ...ot propose procedures for fitting the proposed methods to real data, though there are a few works that suggest maximum likelihood, MCMC and other frameworks for fitting these models to data (for e.g. =-=[34; 75; 214; 323]-=-). One of the notable exceptions is work based on Kronecker graph multiplication. What started as yet another generative procedure [192] 43Figure 4.1: Log-log plots of degree distributions for a quer... |

13 |
Scaling behavior of developing and decaying networks.
- Dorogovtsev, Mendes
- 2000
(Show Context)
Citation Context ...ions of the model have been proposed that allow for flexible power-law exponents, edge modifications, non-uniform dependence on the node degree distributions, etc. For example, Dorogovtsev and Mendes =-=[90]-=- proposed that creating an edge to node i should be proportional not just to its degree ki but also to its age, decaying as (t − ti) −ν , where ν is a tunable parameter. This leads to a power law degr... |

13 |
an exponential family of probability distributions for directed graphs
- Fienberg, Wasserman, et al.
- 1981
(Show Context)
Citation Context ...s an additional effect due to reciprocation. The p1 model was log-linear in form, which allowed for easy computation of maximum likelihood estimates using a contingency table formulation of the model =-=[101; 102]-=-. It also allowed for various generalizations to multidimensional network structures [103] and stochastic blockmodels. This approach to modeling network data quickly evolved into the class of p ∗ or e... |

12 | Reconstructing the topology of protein complexes
- Bernard
- 2007
(Show Context)
Citation Context ... yeast, produced as part of an analysis by Barabási and Oltvai [27]. Statistical methods have been developed for analyzing many aspects of this large protein interaction network, including de-noising =-=[32; 8]-=-, function prediction [227], and identification of binding motifs [23]. 2.2.4 The Add Health Adolescent Relationship and HIV Transmission Study The National Longitudinal Study of Adolescent Health (Ad... |

12 | Clearing the FOG: Fuzzy, Overlapping Groups for Social Networks
- Carley
- 2008
(Show Context)
Citation Context ...or the past four decades. Researchers typically consider the faction labels assigned by Sampson to the novices as the anthropological ground truth in their analysis. For example analyses, we refer to =-=[103; 137; 81; 9]-=-. 2.2.2 The Enron Email Corpus The Enron email corpus has been widely studied in recent machine learning network literature. Enron Corporation was an energy and trading company specializing in the mar... |

12 | A small world threshold for economic network formation
- Even-Dar, Kearns
- 2007
(Show Context)
Citation Context .... • Networks and economic theory. A relatively new area of study is the link between network problems, economic theory, and game theory. Some useful entrees to this literature are Even-Dar and Kearns =-=[96]-=-, Goyal [131], Kearns et al. [169], and Jackson 7[160], whose book contains an excellent semi-technical introduction to network concepts and structures. • Relational networks. This is a very popular ... |

10 | NetGrep: fast network schema searches in interactomes.
- Banks, Nabieva, et al.
- 2008
(Show Context)
Citation Context ...istical methods have been developed for analyzing many aspects of this large protein interaction network, including de-noising [32; 8], function prediction [227], and identification of binding motifs =-=[23]-=-. 2.2.4 The Add Health Adolescent Relationship and HIV Transmission Study The National Longitudinal Study of Adolescent Health (Add Health) is a study of adolescents in the United States drawn from a ... |

10 |
Generalized Blockmodeling (Structural Analysis
- Doreian, Batagelj, et al.
- 2004
(Show Context)
Citation Context ...s organization analysis [207]. These applications often take the machine learning approach of graph partitioning, a topic previously known in social science and statistics literature as blockmodeling =-=[199; 89]-=-. A related question is functional clustering, where the goal is not to statistically cluster the network, but to discover members of dynamic communities with similar functions based on existing netwo... |

8 |
Network sampling and model fitting
- Frank
- 2005
(Show Context)
Citation Context ... links are certain to be complete are not included in the boundary – the condition that is hard to satisfy in real world networks. 58selected subgraphs. For details, see the many papers by Ove Frank =-=[109; 295]-=- and others [125; 135; 258]. Wiuf and Stumpf [325] and Stumpf and Thorne [288] recently adopted a related but different approach focusing on properties such as degree distributions using binomial rand... |

6 | Mixed membership analysis of high-throughput interaction studies: Relational data. Available at ArXiv e-prints
- Airoldi, Blei, et al.
- 2007
(Show Context)
Citation Context ...nalysis concepts have found niches in computational biology. For example, work on protein function classification can be thought of as finding hidden groups in the protein-protein interaction network =-=[7; 8]-=- to gain better understanding of underlying biological processes. Label propagation (node similarity) in networks can be harnessed to help with functional gene annotation [226]. Graph alignment can be... |

6 |
Special Issue on Analyzing Large Scale Networks
- Carley, Skillicorn
- 2005
(Show Context)
Citation Context ...53]. 13network analysis to visualization. A collection of papers working with the Enron corpus were gathered together in a special 2005 issue of Computational & Mathematical Organization Theory, see =-=[58]-=-. 2.2.3 The Protein Interaction Network in Budding Yeast The budding yeast is a unicellular organism that has become a de-facto model organism for the study of molecular and cellular biology [47]. The... |

4 |
Evaluating and optimising models of network growth
- Clegg, Landa, et al.
- 2009
(Show Context)
Citation Context ...ot propose procedures for fitting the proposed methods to real data, though there are a few works that suggest maximum likelihood, MCMC and other frameworks for fitting these models to data (for e.g. =-=[34; 75; 214; 323]-=-). One of the notable exceptions is work based on Kronecker graph multiplication. What started as yet another generative procedure [192] 43Figure 4.1: Log-log plots of degree distributions for a quer... |

4 | Algebraic statistics for p1 random graph models: Markov bases and their uses, vol - Fienberg, Petrović, et al. - 2010 |

3 |
Bayesian Mixed Membership Models of Complex and Evolving Networks
- Airoldi
- 2006
(Show Context)
Citation Context ... node-specific binary strings. This extension helps focus the analysis, whether empirical or theoretical, on the interplay between connectivity of a graph and its node-specific sources of variability =-=[1; 5]-=-. Consider the following data generating process for an exchangeable graph model, which generates binary observations on pairs of nodes. 1. Sample node-specific K-bit binary strings for each node n ∈ ... |

3 | Exchangeable random networks
- Bassetti, Lagomarsino, et al.
(Show Context)
Citation Context ...the true populations have comparable sizes. Recent work on exchangeable Rasch matrices is related to to this topic and potentially relevant for network analysis. Lauritzen [186, 187]; Bassetti et al. =-=[29]-=- suggest applications to bipartite graphs. • Agent-based modeling. Building on older ideas such as cellular automata, agent-based modeling attempts to simulate the simultaneous operations of multiple ... |

3 |
How do networks become navigable? http://arXiv.org/ abs/cond-mat/0309415
- Clauset, Moore
- 2003
(Show Context)
Citation Context ... Several follow-up works have made adjustments to Kleinberg’s rewiring procedure in attempt to improve the understanding and efficiency of the navigability of networks. For example, Clauset and Moore =-=[72]-=- suggested to rewire a long distance edge from node x, if while performing a greedy walk over to y, the original topology of the network did not allow to reach y within Tthresh steps. The edge was rew... |

3 | On small world statistics
- Fienberg, Lee
- 1975
(Show Context)
Citation Context ...s were never completed! (His studies provided the title for the play and movie Six Degrees of Separation, ignoring the compleity of his results due to the censoring.) White [321] and Fienberg and Lee =-=[100]-=- gave a formal Markov-chain like model and analysis of the Milgram experimental data, including information on the uncompleted chains. Milgram’s data were gathered in batches of transmission, and thus... |

2 |
Model-based clustering for social networks: Discussion
- Airoldi
(Show Context)
Citation Context ...ph model is simple to write, ∫ ℓ(Y |θ) = d ⃗ ( ∏ b1:N Pr (Yn,m| ⃗bn, ⃗bm, q) ∏ Pr ( ⃗bn|θ) ) , n,m where θ = (⃗µ, σ, α) or an appropriate set of parameters. We can apply standard inference techniques =-=[2; 9]-=-. Fitting an exchangeable graph model allows us to assess the complexity of an observed graph, leveraging notions from information theory. For instance, we can use the minimum description length (MDL)... |

2 |
A family of distributions on the unit hypercube
- Airoldi
- 2009
(Show Context)
Citation Context ..., Σ), where u ∈ R k and Σii = α, Σij = β for i ̸= j. Then define pi = (1 + e −ui ) −1 for i = 1 . . . k. The resulting density for ⃗p, where ⃗p ∈ [0, 1] k is fP (⃗p | ⃗µ, α, β) = For more details see =-=[4]-=-. 1 − |2πΣ| 2 ∏ d j=1 pj(1 − pj) exp ( − 1 2 (log(⃗p/(1 − ⃗p)) − ⃗µ)′ Σ −1 ) (log(⃗p/(1 − ⃗p)) − ⃗µ) . 24giant component emerges because a number of smaller components must intersect with high probab... |

2 |
The exchangeable graph model
- Airoldi
- 2009
(Show Context)
Citation Context ... node-specific binary strings. This extension helps focus the analysis, whether empirical or theoretical, on the interplay between connectivity of a graph and its node-specific sources of variability =-=[1; 5]-=-. Consider the following data generating process for an exchangeable graph model, which generates binary observations on pairs of nodes. 1. Sample node-specific K-bit binary strings for each node n ∈ ... |

2 |
Model-based clustering for social networks: Discussion
- Blei, Fienberg
(Show Context)
Citation Context ... It would be interesting to explore computational tradeoffs for the latent space cluster model [137] as the sample size grows and when large numbers of covariates are added. Remark. Blei and Fienberg =-=[40]-=- argue that a stochastic blockmodel and node-specific mixed membership vectors are two sets of parameters that are directly interpretable in terms of notions and concepts relevant to social scientists... |

2 |
ORA: Organizational Risk Analyzer. http://www. casos.cs.cmu.edu/projects/ora
- Carley, Reminga
- 2004
(Show Context)
Citation Context ...hat revolve around national security and the military, with studies on the effects of catastrophic events and biological warfare, as well as computational explorations of possible recovery strategies =-=[57; 59]-=-. These works are the contemporary counterparts of more classical work at the interface between artificial intelligence and the social sciences [54; 56; 55]. 8Chapter 2 Motivation and Dataset Example... |