Latent Space Modeling of Hypergraph Data Turnbull, Kathryn; Lunagómez, Simón; Nemeth, Christopher ...
Journal of the American Statistical Association,
12/2023
Journal Article
Observations consisting of measurements on relationships for pairs of objects arise in many settings, such as protein interaction and gene regulatory networks, collections of author-recipient email, ...and social networks. Analyzing such data with probabilisic models can be delicate because the simple exchangeability assumptions underlying many boilerplate models no longer hold. In this paper, we describe a latent variable model of such data called the mixed membership stochastic blockmodel. This model extends blockmodels for relational data to ones which capture mixed membership latent relational structure, thus providing an object-specific low-dimensional representation. We develop a general variational inference algorithm for fast approximate posterior inference. We explore applications to social and protein interaction networks.
Dynamic network data describe interactions among a fixed population through time. This data type can be modelled using the latent space framework, where the probability of a connection forming is ...expressed as a function of low-dimensional latent coordinates associated with the nodes, and sequential estimation of model parameters can be achieved via Sequential Monte Carlo (SMC) methods. In this setting, SMC is a natural candidate for estimation which offers greater scalability than existing approaches commonly considered in the literature, allows for estimates to be conveniently updated given additional observations and facilitates both online and offline inference. A novel approach to sequentially infer parameters of dynamic latent space network models is proposed by building on techniques from the high-dimensional SMC literature. The scalability and performance of the proposed approach is explored via simulation, and the flexibility under model variants is demonstrated. Finally, a real-world dataset describing classroom contacts is analysed using the proposed methodology.
Modeling Network Populations via Graph Distances Lunagómez, Simón; Olhede, Sofia C.; Wolfe, Patrick J.
Journal of the American Statistical Association,
10/2021, Letnik:
116, Številka:
536
Journal Article
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This article introduces a new class of models for multiple networks. The core idea is to parameterize a distribution on labeled graphs in terms of a Fréchet mean graph (which depends on a ...user-specified choice of metric or graph distance) and a parameter that controls the concentration of this distribution about its mean. Entropy is the natural parameter for such control, varying from a point mass concentrated on the Fréchet mean itself to a uniform distribution over all graphs on a given vertex set. We provide a hierarchical Bayesian approach for exploiting this construction, along with straightforward strategies for sampling from the resultant posterior distribution. We conclude by demonstrating the efficacy of our approach via simulation studies and two multiple-network data analysis examples: one drawn from systems biology and the other from neuroscience. This article has online
supplementary materials
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The application of statistical network analysis, such as Exponential Random Graph Models (ERGM) and Simulation Investigation for Empirical Network Analysis (Siena), has been widespread in social ...network analysis. In this article, the characteristics of these methods were reviewed, following which their usefulness was discussed. The advantages of statistical network analysis methods are multivariate modeling of the effects of the features of nodes or node pairs in networks upon the connections of nodes and the statistical significance tests of these effects. The recent development of statistical packages for these methods made it easy to apply them to real data; however, some research suggested that the usefulness of these methods is restrictive for the purpose of social network analysis, which investigates social structures. This article demonstrated that statistical network analysis methods mainly focus on the micro features of networks, which makes it difficult to model the macro features of networks, and that these methods assume that the effects upon the node pairs are uniform. Finally, the application of these methods to the analysis of network processes such as formation, development, and declination was proposed.
Mixture models are probabilistic models aimed at uncovering and representing latent subgroups within a population. In the realm of network data analysis, the latent subgroups of nodes are typically ...identified by their connectivity behaviour, with nodes behaving similarly belonging to the same community. In this context, mixture modelling is pursued through stochastic blockmodelling. We consider stochastic blockmodels and some of their variants and extensions from a mixture modelling perspective. We also explore some of the main classes of estimation methods available and propose an alternative approach based on the reformulation of the blockmodel as a graphon. In addition to the discussion of inferential properties and estimating procedures, we focus on the application of the models to several real-world network datasets, showcasing the advantages and pitfalls of different approaches.
Performance bounds are given for exploratory co-clustering/block-modeling of bipartite graph data, where we assume the rows and columns of the data matrix are samples from an arbitrary population. ...This is equivalent to assuming that the data is generated from a nonsmooth graphon. It is shown that co-clusters found by any method can be extended to the row and column populations, or equivalently that the estimated blockmodel approximates a blocked version of the generative graphon, with estimation error bounded by OP(n−1/2). Analogous performance bounds are also given for degree-corrected blockmodels and random dot product graphs, with error rates depending on the dimensionality of the latent variable space.
Product architecture knowledge is typically embedded in the communication patterns of established development organizations. While this enables the development of products using the existing ...architecture, it hinders the organization's ability to implement novel architectures, especially for complex products. Structured methods addressing this issue are lacking, as previous research has studied complex product development from two separate perspectives: product architecture and organizational structure. Our research integrates these viewpoints with a structured approach to study how design interfaces in the product architecture map onto communication patterns within the development organization. We investigate how organizational and system boundaries, design interface strength, indirect interactions, and system modularity impact the alignment of design interfaces and team interactions. We hypothesize and test how these factors explain the existence of the following cases: (1) known design interfaces not addressed by team interactions, and (2) observed team interactions not predicted by design interfaces. Our results offer important insights to managers dealing with interdependences across organizational and functional boundaries. In particular, we show how boundary effects moderate the impact of design interface strength and indirect team interactions, and are contingent on system modularity. The research uses data collected from a large commercial aircraft engine development process.
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