Consider data consisting of pairwise measurements, such as presence or absence of links between pairs of objects. These data arise, for instance, in the analysis of protein interactions and gene regulatory networks, collections of author-recipient email, and social networks. Analyzing pairwise measurements with probabilistic models requires special assumptions, since the usual independence or exchangeability assumptions no longer hold. Here we introduce a class of variance allocation models for pairwise measurements: mixed membership stochastic blockmodels. These models combine global parameters that instantiate dense patches of connectivity (blockmodel) with local parameters that instantiate node-specific variability in the connections (mixed membership). We develop a general variational inference algorithm for fast approximate posterior inference. We demonstrate the advantages of mixed membership stochastic blockmodels with applications to social networks and protein interaction networks.

/pdf/mixed-membership-stochastic-blockmodels-2a6y107lg8.pdf

Mixed Membership Stochastic Blockmodels

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.

Mixed membership stochastic blockmodels

This article reviews the state-of-the-art in overlapping community detection algorithms, quality measures, and benchmarks. A thorough comparison of different algorithms (a total of fourteen) is provided. In addition to community-level evaluation, we propose a framework for evaluating algorithms' ability to detect overlapping nodes, which helps to assess overdetection and underdetection. After considering community-level detection performance measured by normalized mutual information, the Omega index, and node-level detection performance measured by F-score, we reached the following conclusions. For low overlapping density networks, SLPA, OSLOM, Game, and COPRA offer better performance than the other tested algorithms. For networks with high overlapping density and high overlapping diversity, both SLPA and Game provide relatively stable performance. However, test results also suggest that the detection in such networks is still not yet fully resolved. A common feature observed by various algorithms in real-world networks is the relatively small fraction of overlapping nodes (typically less than 30p), each of which belongs to only 2 or 3 communities.

Overlapping community detection in networks: The state-of-the-art and comparative study

Networks are ubiquitous in science and have become a focal point for discussion in everyday life. Formal statistical models for the analysis of network data have emerged as a major topic of interest in diverse areas of study, and most of these involve a form of graphical representation. Probability models on graphs date back to 1959. Along with empirical studies in social psychology and sociology from the 1960s, these early works generated an active "network community" and a substantial literature in the 1970s. This effort moved into the statistical literature in the late 1970s and 1980s, and the past decade has seen a burgeoning network literature in statistical physics and computer science. The growth of the World Wide Web and the emergence of online "networking communities" such as Facebook, MySpace, and LinkedIn, and a host of more specialized professional network communities has intensified interest in the study of networks and network data.

Our goal in this review is to provide the reader with an entry point to this burgeoning literature. We begin with an overview of the historical development of statistical network modeling and then we introduce a number of examples that have been studied in the network literature. Our subsequent discussion focuses on a number of prominent static and dynamic network models and their interconnections. We emphasize formal model descriptions, and pay special attention to the interpretation of parameters and their estimation. We end with a description of some open problems and challenges for machine learning and statistics.

https://dash.harvard.edu/bitstream/handle/1/4645865/Goldenberg_NetSurvey.pdf?sequence=1

A Survey of Statistical Network Models

Networks beyond pairwise interactions: Structure and dynamics

Clearing the FOG: Fuzzy, overlapping groups for social networks

We address the problem of homology identification in complex multidomain families with varied domain architectures. The challenge is to distinguish sequence pairs that share common ancestry from pairs that share an inserted domain but are otherwise unrelated. This distinction is essential for accuracy in gene annotation, function prediction, and comparative genomics. There are two major obstacles to multidomain homology identification: lack of a formal definition and lack of curated benchmarks for evaluating the performance of new methods. We offer preliminary solutions to both problems: 1) an extension of the traditional model of homology to include domain insertions; and 2) a manually curated benchmark of well-studied families in mouse and human. We further present Neighborhood Correlation, a novel method that exploits the local structure of the sequence similarity network to identify homologs with great accuracy based on the observation that gene duplication and domain shuffling leave distinct patterns in the sequence similarity network. In a rigorous, empirical comparison using our curated data, Neighborhood Correlation outperforms sequence similarity, alignment length, and domain architecture comparison. Neighborhood Correlation is well suited for automated, genome-scale analyses. It is easy to compute, does not require explicit knowledge of domain architecture, and classifies both single and multidomain homologs with high accuracy. Homolog predictions obtained with our method, as well as our manually curated benchmark and a web-based visualization tool for exploratory analysis of the network neighborhood structure, are available at http://www.neighborhoodcorrelation.org. Our work represents a departure from the prevailing view that the concept of homology cannot be applied to genes that have undergone domain shuffling. In contrast to current approaches that either focus on the homology of individual domains or consider only families with identical domain architectures, we show that homology can be rationally defined for multidomain families with diverse architectures by considering the genomic context of the genes that encode them. Our study demonstrates the utility of mining network structure for evolutionary information, suggesting this is a fertile approach for investigating evolutionary processes in the post-genomic era.

/pdf/sequence-similarity-network-reveals-common-ancestry-of-231050golz.pdf

Sequence Similarity Network Reveals Common Ancestry of Multidomain Proteins

We study properties of multidomain proteins from a graph theoretical perspective. In particular, we demonstrate connections between properties of the domain overlap graph and certain variants of Dollo parsimony models. We apply our graph theoretical results to address several interrelated questions: do proteins acquire new domains infrequently, or often enough that the same combinations of domains will be created repeatedly through independent events? Once domain architectures are created, do they persist? In other words, is the existence of ancestral proteins with domain compositions not observed in contemporary proteins unlikely? Our experimental results indicate that independent merges of domain pairs are not uncommon in large superfamilies.

/pdf/graph-theoretical-insights-into-evolution-of-multidomain-v9z0iqkypl.pdf

Graph theoretical insights into evolution of multidomain proteins.

Our work explores the convergence between participatory sensing, political activism and public expressions Unlike prior research, which focuses on personal sensing, we present low-cost, networked air quality sensors, designed to be repositioned across public landscapes by communities of citizen stakeholders Our GPS-enabled sensors report dust, exhaust, or VOC's (volatile organic compounds), along with temperature, humidity and light levels to a website that visualizes this data in real time The sensors can be attached to a variety of surfaces serving as research probes to demarcate ('tag') public spaces with environmental concerns We deploy our fully functional system with four urban communities - parents, bicyclists, homeless and activists, positioning our system as a tool for studying and supporting community togetherness and public activism Our findings highlight community sharing of the physical sensors and dialogues surrounding the collected data

Ceci n'est pas une pipe bombe: authoring urban landscapes with air quality sensors

Significant work has been done on computational aspects of solving games under various solution concepts, such as Nash equilibrium, subgame perfect Nash equilibrium, correlated equilibrium, and (iterated) dominance However, the fundamental concepts of rationalizability and CURB (Closed Under Rational Behavior sets have not, to our knowledge, been studied from a computational perspective First, for rationalizability we describe an LP-based polynomial algorithm that finds all strategies that are rationalizable against a mixture over a given set of opponent strategies Then, we describe a series of increasingly sophisticated polynomial algorithms for finding all minimal CURB sets, one minimal CURB set, and the smallest minimal CURB set Finally, we give theoretical results regarding the relationships between CURB sets and Nash equilibria, showing that finding a Nash equilibrium can be exponential only in the size of the smallest CURB set We show that this can lead to an arbitrarily large reduction in the complexity of finding a Nash equilibrium On the downside, we also show that the smallest CURB set can be arbitrarily larger than the supports of the enclosed Nash equilibrium

/pdf/algorithms-for-rationalizability-and-curb-sets-37sxq4b1si.pdf

George B. Davis

Papers

Clearing the FOG: Fuzzy, overlapping groups for social networks

Sequence Similarity Network Reveals Common Ancestry of Multidomain Proteins

Graph theoretical insights into evolution of multidomain proteins.

Ceci n'est pas une pipe bombe: authoring urban landscapes with air quality sensors

Algorithms for rationalizability and CURB sets