Spatial autoregression with repeated measurements for social networks

Spatial autoregressive model (SAR) is found useful to estimate the social autocorrelation in social networks recently. However, the rapid development of information technology enables researchers to collect repeated measurements for a given social network. The SAR model for social networks is designed for cross-sectional data and is thus not feasible. In this article, we propose a new model which is referred to as SAR with random effects (SARRE) for social networks. It could be considered as a natural combination of two types of models, the SAR model for social networks and a particular type of mixed model. To solve the problem of high computational complexity in large social networks, a pseudo-maximum likelihood estimate (PMLE) is proposed. The asymptotic properties of the estimate are established. We demonstrate the performance of the proposed method by extensive numerical studies and a real data example.     

Bayesian inference for dynamic social network data

We consider a continuous-time model for the evolution of social networks. A social network is here conceived as a (di-) graph on a set of vertices, representing actors, and the changes of interest are creation and disappearance over time of (arcs) edges in the graph. Hence we model a collection of random edge indicators that are not, in general, independent. We explicitly model the interdependencies between edge indicators that arise from interaction between social entities. A Markov chain is defined in terms of an embedded chain with holding times and transition probabilities. Data are observed at fixed points in time and hence we are not able to observe the embedded chain directly. Introducing a prior distribution for the parameters we may implement an MCMC algorithm for exploring the posterior distribution of the parameters by simulating the evolution of the embedded process between observations.     

The stochastic topic block model for the clustering of vertices in networks with textual edges

Due to the significant increase of communications between individuals via social media (Facebook, Twitter, Linkedin) or electronic formats (email, web, e-publication) in the past two decades, network analysis has become an unavoidable discipline. Many random graph models have been proposed to extract information from networks based on person-to-person links only, without taking into account information on the contents. This paper introduces the stochastic topic block model, a probabilistic model for networks with textual edges. We address here the problem of discovering meaningful clusters of vertices that are coherent from both the network interactions and the text contents. A classification variational expectation-maximization algorithm is proposed to perform inference. Simulated datasets are considered in order to assess the proposed approach and to highlight its main features. Finally, we demonstrate the effectiveness of our methodology on two real-word datasets: a directed communication network and an undirected co-authorship network.     

Degree-based goodness-of-fit tests for heterogeneous random graph models: Independent and exchangeable cases

The degrees are a classical and relevant way to study the topology of a network. They can be used to assess the goodness of fit for a given random graph model. In this paper, we introduce goodness-of-fit tests for two classes of models. First, we consider the case of independent graph models such as the heterogeneous Erdös-Rényi model in which the edges have different connection probabilities. Second, we consider a generic model for exchangeable random graphs called the W-graph. The stochastic block model and the expected degree distribution model fall within this framework. We prove the asymptotic normality of the degree mean square under these independent and exchangeable models and derive formal tests. We study the power of the proposed tests and we prove the asymptotic normality under specific sparsity regimes. The tests are illustrated on real networks from social sciences and ecology, and their performances are assessed via a simulation study.     

Phase I monitoring of social network with baseline periods using poisson regression

Social network analysis is an important analytic tool to forecast social trends by modeling and monitoring the interactions between network members. This paper proposes an extension of a statistical process control method to monitor social networks by determining the baseline periods when the reference network set is collected. We consider probability density profile (PDP) to identify baseline periods using Poisson regression to model the communications between members. Also, Hotelling T² and likelihood ratio test (LRT) statistics are developed to monitor the network in Phase I. The results based on signal probability indicate a satisfactory performance for the proposed method.     

PCA likelihood ratio test approach for attributed social networks monitoring

Abstract

One of the most important factors in building and changing communication mechanisms in social networks is considering features of the members of social networks. Most of the existing methods in network monitoring don’t consider effects of features in network formation mechanisms and others don’t lead to reliable results when the features abound or when there are correlations among them. In this article, we combined two methods principal component analysis (PCA) and likelihood method to monitor the underlying network model when the features of individuals abound and when some of them have high correlations with each other.     

Adjusting for Network Size and Composition Effects in Exponential-Family Random Graph Models

Exponential-family random graph models (ERGMs) provide a principled way to model and simulate features common in human social networks, such as propensities for homophily and friend-of-a-friend triad closure. We show that, without adjustment, ERGMs preserve density as network size increases. Density invariance is often not appropriate for social networks. We suggest a simple modification based on an offset which instead preserves the mean degree and accommodates changes in network composition asymptotically. We demonstrate that this approach allows ERGMs to be applied to the important situation of egocentrically sampled data. We analyze data from the National Health and Social Life Survey (NHSLS).     

On Uniformly Optimal Networks: A Reversal of Fortune?

In this article, the general problem of comparing the performance of two communication networks is examined. The standard approach, using stochastic ordering as a metric, is reviewed, as are the mixed results on the existence of uniformly optimal networks (UONs) which have emerged from this approach. While UONs have been shown to exist for certain classes of networks, it has also been shown that no UON network exists for other classes. Results to date beg the question: Is the problem of identifying a Uniformly Optimal Network (UON) of a given size dead or alive? We reframe the investigation into UONs in terms of network signatures and the alternative metric of stochastic precedence. While the endeavor has been dead, or at least dormant, for some 20 years, the findings in the present article suggest that the question above is by no means settled. Specifically, we examine a class of networks of a particular size for which it was shown that no individual network was uniformly optimal relative to the standard metric (the uniform ordering of reliability polynomials), and we show, using the aforementioned alternative metric, that this class is totally ordered and that a uniformly optimal network exists after all. Optimality with respect to “performance per unit cost” type metrics is also discussed.     

Affiliation discrete weighted networks with an increasing degree sequence

Affiliation network is one kind of two-mode social network with two different sets of nodes (namely, a set of actors and a set of social events) and edges representing the affiliation of the actors with the social events. The connections in many affiliation networks are only binary weighted between actors and social events that can not reveal the affiliation strength relationship. Although a number of statistical models are proposed to analyze affiliation binary weighted networks, the asymptotic behaviors of the maximum likelihood estimator (MLE) are still unknown or have not been properly explored in affiliation weighted networks. In this paper, we study an affiliation model with the degree sequence as the exclusively natural sufficient statistic in the exponential family distributions. We derive the consistency and asymptotic normality of the maximum likelihood estimator in affiliation finite discrete weighted networks when the numbers of actors and events both go to infinity. Simulation studies and a real data example demonstrate our theoretical results.     

Identification and Efficient Estimation of Simultaneous Equations Network Models

This article considers identification and estimation of social network models in a system of simultaneous equations. We show that, with or without row-normalization of the social adjacency matrix, the network model has different equilibrium implications, needs different identification conditions, and requires different estimation strategies. When the adjacency matrix is not row-normalized, the variation in the Bonacich centrality across nodes in a network can be used as an IV to identify social interaction effects and improve estimation efficiency. The number of such IVs depends on the number of networks. When there are many networks in the data, the proposed estimators may have an asymptotic bias due to the presence of many IVs. We propose a bias-correction procedure for the many-instrument bias. Simulation experiments show that the bias-corrected estimators perform well in finite samples. We also provide an empirical example to illustrate the proposed estimation procedure.     

大数据背景下基于社交网络的聚类随机游走抽样算法研究

数字经济时代,社交网络作为数字化平台经济的重要载体,受到了国内外学者的广泛关注。大数据背景下,社交网络的商业应用价值巨大,但由于其网络规模空前庞大,传统的网络分析方法 因计算成本过高而不再适用。而通过网络抽样算法获取样本网络,再推断整体网络,可节约计算资源, 因此抽样算法的好坏将直接影响社交网络分析结论的准确性。现有社交网络抽样算法存在忽略网络内部拓扑结构、容易陷入局部网络、抽样效率过低等缺陷。为了弥补现有社交网络抽样算法的缺陷,本文结合大数据社交网络的社区特征,提出了一种聚类随机游走抽样算法。该方法首先使用社区聚类算法将原始网络节点进行社区划分,得到多个社区网络,然后分别对每个社区进行随机游走抽样获取样本网 络。数值模拟和案例应用的结果均表明,聚类随机游走抽样算法克服了传统网络抽样算法的缺点,能够在降低网络规模的同时较好地保留原始网络的结构特征。此外,该抽样算法还可以并行运算,有效提升抽样效率,对于大数据背景下大规模社交网络的抽样实践具有重大现实意义。     

A LINEAR PROGRAMMING APPROACH TO THE STEADY-STATE ANALYSIS OF REFLECTED BROWNIAN MOTION

Abstract

We consider a flow of data packets from one source to many destinations in a communication network represented by a random oriented tree. Multicast transmission is characterized by the ability of some tree vertices to replicate received packets depending on the number of destinations downstream. We are interested in characteristics of multicast flows on Galton–Watson trees and trees generated by point aggregates of a Poisson process. Such stochastic settings are intended to represent tree shapes arising in the Internet and in some ad hoc networks. The main result in the branching process case is a functional equation for the joint probability generating function of flow volumes through a given vertex and in the whole tree. We provide conditions for the existence and uniqueness of solution and a method to compute it using Picard iterations. In the point process case, we provide bounds on flow volumes using the technique of stochastic comparison from the theory of continuous percolation. We use these results to derive a number of random trees' characteristics and discuss their applications to analytical evaluation of the load induced on a network by a multicast session.     

Multiple change points detection and clustering in dynamic networks

The increasing amount of data stored in the form of dynamic interactions between actors necessitates the use of methodologies to automatically extract relevant information. The interactions can be represented by dynamic networks in which most existing methods look for clusters of vertices to summarize the data. In this paper, a new framework is proposed in order to cluster the vertices while detecting change points in the intensities of the interactions. These change points are key in the understanding of the temporal interactions. The model used involves non-homogeneous Poisson point processes with cluster-dependent piecewise constant intensity functions and common discontinuity points. A variational expectation maximization algorithm is derived for inference. We show that the pruned exact linear time method, originally developed for change points detection in univariate time series, can be considered for the maximization step. This allows the detection of both the number of change points and their location. Experiments on artificial and real datasets are carried out, and the proposed approach is compared with related methods.     

Semiparametric Analysis of Network Formation

ABSTRACT

We consider a statistical model for directed network formation that features both node-specific parameters that capture degree heterogeneity and common parameters that reflect homophily among nodes. The goal is to perform statistical inference on the homophily parameters while treating the node-specific parameters as fixed effects. Jointly estimating all parameters leads to incidental-parameter bias and incorrect inference. As an alternative, we develop an approach based on a sufficient statistic that separates inference on the homophily parameters from estimation of the fixed effects. The estimator is easy to compute and can be applied to both dense and sparse networks, and is shown to have desirable asymptotic properties under sequences of growing networks. We illustrate the improvements of this estimator over maximum likelihood and bias-corrected estimation in a series of numerical experiments. The technique is applied to explain the import and export patterns in a dense network of countries and to estimate a more sparse advice network among attorneys in a corporate law firm.     

A statistical social network model for consumption data in trophic food webs

We adapt existing statistical modeling techniques for social networks to study consumption data observed in trophic food webs. These data describe the feeding volume (non-negative) among organisms grouped into nodes, called trophic species, that form the food web. Model complexity arises due to the extensive amount of zeros in the data, as each node in the web is predator/prey to only a small number of other trophic species. Many of the zeros are regarded as structural (non-random) in the context of feeding behavior. The presence of basal prey and top predator nodes (those who never consume and those who are never consumed, with probability 1) creates additional complexity to the statistical modeling. We develop a special statistical social network model to account for such network features. The model is applied to two empirical food webs; focus is on the web for which the population size of seals is of concern to various commercial fisheries.     

Model-based clustering for social networks

Summary.  Network models are widely used to represent relations between interacting units or actors. Network data often exhibit transitivity, meaning that two actors that have ties to a third actor are more likely to be tied than actors that do not, homophily by attributes of the actors or dyads, and clustering. Interest often focuses on finding clusters of actors or ties, and the number of groups in the data is typically unknown. We propose a new model, the latent position cluster model , under which the probability of a tie between two actors depends on the distance between them in an unobserved Euclidean 'social space', and the actors' locations in the latent social space arise from a mixture of distributions, each corresponding to a cluster. We propose two estimation methods: a two-stage maximum likelihood method and a fully Bayesian method that uses Markov chain Monte Carlo sampling. The former is quicker and simpler, but the latter performs better. We also propose a Bayesian way of determining the number of clusters that are present by using approximate conditional Bayes factors. Our model represents transitivity, homophily by attributes and clustering simultaneously and does not require the number of clusters to be known. The model makes it easy to simulate realistic networks with clustering, which are potentially useful as inputs to models of more complex systems of which the network is part, such as epidemic models of infectious disease. We apply the model to two networks of social relations. A free software package in the R statistical language, latentnet, is available to analyse data by using the model.     

城市群经济网络与经济增长——基于大数据与网络分析方法的研究

借助大数据时代下获得的海量数据,本文分析了长三角城市群的经济网络特征,重点研究了城市群经济网络的增长效应。首先,构建了长三角城市群的人口流动网络、企业组织网络与电子商务网络,对其各自的网络结构特征进行了对比。其次,将网络分析方法与空间计量模型结合起来,使用扩展的J检验方法对不同网络结构下的模型设定方法进行了识别,考察了经济网络带来的溢出效应对于城市群经济增长的影响。分析结果显示,三种经济网络下长三角城市群均呈现出了“中心-外围”的网络结构,其中上海、杭州、苏州、南京及无锡位于城市群经济网络的核心圈层。对网络结构的模型识别结果显示,中心城市在长三角城市群经济网络的溢出效应中扮演着重要角色。具体而言,在人口流动网络下,资本、政府行为存在显著为负的网络溢出效应;在企业组织网络下,人口规模、对外开放呈现出显著为正的网络溢出效应;在电子商务网络下,政府行为存在显著为负的网络溢出效应,对外开放呈现出显著为正的网络溢出效应。     

Affiliation networks with an increasing degree sequence

Affiliation network is one kind of two-mode social network with two different sets of nodes (namely, a set of actors and a set of social events) and edges representing the affiliation of the actors with the social events. Although a number of statistical models are proposed to analyze affiliation networks, the asymptotic behaviors of the estimator are still unknown or have not been properly explored. In this article, we study an affiliation model with the degree sequence as the exclusively natural sufficient statistic in the exponential family distributions. We establish the uniform consistency and asymptotic normality of the maximum likelihood estimator when the numbers of actors and events both go to infinity. Simulation studies and a real data example demonstrate our theoretical results.