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The Nonparametric Metadata Dependent Relational Model
"... We introduce the nonparametric metadata dependent relational (NMDR) model, a Bayesian nonparametric stochastic block model for network data. The NMDR allows the entities associated with each node to have mixed membership in an unbounded collection of latent communities. Learned regression models all ..."
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We introduce the nonparametric metadata dependent relational (NMDR) model, a Bayesian nonparametric stochastic block model for network data. The NMDR allows the entities associated with each node to have mixed membership in an unbounded collection of latent communities. Learned regression models allow these memberships to depend on, and be predicted from, arbitrary node metadata. We develop efficient MCMC algorithms for learning NMDR models from partially observed node relationships. Retrospective MCMC methods allow our sampler to work directly with the infinite stickbreaking representation of the NMDR, avoiding the need for finite truncations. Our results demonstrate recovery of useful latent communities from realworld social and ecological networks, and the usefulness of metadata in link prediction tasks. 1.
Nonparametric Multigroup Membership Model for Dynamic Networks
"... Relational data—like graphs, networks, and matrices—is often dynamic, where the relational structure evolves over time. A fundamental problem in the analysis of timevarying network data is to extract a summary of the common structure and the dynamics of the underlying relations between the entitie ..."
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Relational data—like graphs, networks, and matrices—is often dynamic, where the relational structure evolves over time. A fundamental problem in the analysis of timevarying network data is to extract a summary of the common structure and the dynamics of the underlying relations between the entities. Here we build on the intuition that changes in the network structure are driven by the dynamics at the level of groups of nodes. We propose a nonparametric multigroup membership model for dynamic networks. Our model contains three main components: We model the birth and death of individual groups with respect to the dynamics of the network structure via a distance dependent Indian Buffet Process. We capture the evolution of individual node group memberships via a Factorial Hidden Markov model. And, we explain the dynamics of the network structure by explicitly modeling the connectivity structure of groups. We demonstrate our model’s capability of identifying the dynamics of latent groups in a number of different types of network data. Experimental results show that our model provides improved predictive performance over existing dynamic network models on future network forecasting and missing link prediction. 1
CoEvolution of MultiTyped Objects in Dynamic Star Networks
"... Abstract—Mining network evolution has emerged as an intriguing research topic in many domains such as data mining, social networks, and machine learning. While a bulk of research has focused on mining the evolutionary pattern of homogeneous networks (e.g., networks of friends), however, most realwo ..."
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Abstract—Mining network evolution has emerged as an intriguing research topic in many domains such as data mining, social networks, and machine learning. While a bulk of research has focused on mining the evolutionary pattern of homogeneous networks (e.g., networks of friends), however, most realworld networks are heterogeneous, containing objects of different types, such as authors, papers, venues, and terms in a bibliographic network. Modeling coevolution of multityped objects can capture richer information than that on singletyped objects alone. For example, studying coevolution of authors, venues, and terms in a bibliographic network can tell better the evolution of research areas than just examining coauthor network or term network alone. In this paper, we study mining coevolution of multityped objects in a special type of heterogeneous networks, called star networks, and examine how the multityped objects influence each other in the network evolution. A Hierarchical Dirichlet Process Mixture Modelbased evolution model is proposed, which detects the coevolution of multityped objects in the form of multityped cluster evolution in dynamic star networks. An efficient inference algorithm is provided to learn the proposed model. Experiments on several real networks (DBLP, Twitter, and Delicious) validate the effectiveness of the model and the scalability of the algorithm. Index Terms—Information network analysis, data mining, coevolution, clustering, dynamic star networks F 1
Subset Infinite Relational Models
"... We propose a new probabilistic generative model for analyzing sparse and noisy pairwise relational data, such as friendlinks on social network services and customer records in online shops. Realworld relational data often include a large portion of noninformative pairwise data entries. Many exist ..."
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We propose a new probabilistic generative model for analyzing sparse and noisy pairwise relational data, such as friendlinks on social network services and customer records in online shops. Realworld relational data often include a large portion of noninformative pairwise data entries. Many existing stochastic blockmodels suffer from these irrelevant data entries because of their rather simpler forms of priors. The proposed model incorporates a latent variable that explicitly indicates whether each data entry is relevant or not to diminish bad effects associated with such irrelevant data. Through experiments using synthetic and real data sets, we show that the proposed model can extract clusters with stronger relations among data within the cluster than clusters obtained by the conventional model. 1
Nonparametric Network Models for Link Prediction
, 2016
"... Abstract Many data sets can be represented as a sequence of interactions between entitiesfor example communications between individuals in a social network, proteinprotein interactions or DNAprotein interactions in a biological context, or vehicles' journeys between cities. In these context ..."
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Abstract Many data sets can be represented as a sequence of interactions between entitiesfor example communications between individuals in a social network, proteinprotein interactions or DNAprotein interactions in a biological context, or vehicles' journeys between cities. In these contexts, there is often interest in making predictions about future interactions, such as who will message whom. A popular approach to network modeling in a Bayesian context is to assume that the observed interactions can be explained in terms of some latent structure. For example, traffic patterns might be explained by the size and importance of cities, and social network interactions might be explained by the social groups and interests of individuals. Unfortunately, while elucidating this structure can be useful, it often does not directly translate into an effective predictive tool. Further, many existing approaches are not appropriate for sparse networks, a class that includes many interesting realworld situations. In this paper, we develop models for sparse networks that combine structure elucidation with predictive performance. We use a Bayesian nonparametric approach, which allows us to predict interactions with entities outside our training set, and allows the both the latent dimensionality of the model and the number of nodes in the network to grow in expectation as we see more data. We demonstrate that we can capture latent structure while maintaining predictive power, and discuss possible extensions.
Online Community Detection in Social Sensing
"... The proliferation of location and GPS data streams which are collected in a wide variety of participatory sensing applications has created numerous possibilities for analysis of the underlying patterns of activity. Typically, the spatiotemporal patterns arising from such activity can be analyzed in ..."
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The proliferation of location and GPS data streams which are collected in a wide variety of participatory sensing applications has created numerous possibilities for analysis of the underlying patterns of activity. Typically, the spatiotemporal patterns arising from such activity can be analyzed in order to determine the latent community structure in the underlying data. In this paper, we will examine the problem of online community detection from the location data collected from such social sensing applications in real time. Such data brings numerous challenges associated with it, in that they can be of a relatively large scale, and can be extremely noisy from the perspective of both data representation and analysis. Furthermore, the community structure in the underlying data cannot be directly inferred from the shape of the underlying trajectories, since a considerable amount of variation may exist in terms of trajectories of individuals belonging to the same community. In this paper, we will design online algorithms for community detection in social sensing applications. Our algorithm uses a robust and efficiently updateable model with the use of Gibbs sampling, and we will show its effectiveness and efficiency for social sensing applications.
Stochastic Block Transition Models for Dynamic Networks
, 2014
"... There has been great interest in recent years in the development of statistical models for dynamic networks. This paper targets networks evolving in discrete time in which both nodes and edges can appear and disappear over time, such as dynamic networks of social interactions. We propose a stochasti ..."
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There has been great interest in recent years in the development of statistical models for dynamic networks. This paper targets networks evolving in discrete time in which both nodes and edges can appear and disappear over time, such as dynamic networks of social interactions. We propose a stochastic block transition model (SBTM) for dynamic networks that is inspired by the wellknown stochastic block model (SBM) for static networks and several recent dynamic extensions of the SBM. Unlike most existing dynamic models, it does not make a hidden Markov assumption on the edgelevel dynamics, allowing the presence or absence of edges to directly influence future edge probabilities. We demonstrate that the proposed SBTM is significantly better at reproducing durations of edges in real social network data between edges while retaining the interpretability of the SBM. 1
Bayesian Logistic Gaussian Process Models for Dynamic Networks
"... Timevarying adjacency matrices encoding the presence or absence of a relation among entities are available in many research fields. Motivated by an application to studying dynamic networks among sports teams, we propose a Bayesian nonparametric model. The proposed approach uses a logistic mapping ..."
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Timevarying adjacency matrices encoding the presence or absence of a relation among entities are available in many research fields. Motivated by an application to studying dynamic networks among sports teams, we propose a Bayesian nonparametric model. The proposed approach uses a logistic mapping from the probability matrix, encoding link probabilities between each team, to an embedded latent relational space. Within this latent space, we incorporate a dictionary of Gaussian process (GP) latent trajectories characterizing changes over time in each team, while allowing learning of the number of latent dimensions through a specially tailored prior for the GP covariance. The model is provably flexible and borrows strength across the network and over time. We provide simulation experiments and an application to the Italian soccer Championship. 1
Metadata Dependent Mondrian Processes
"... Stochastic partition processes in a product space play an important role in modeling relational data. Recent studies on the Mondrian process have introduced more flexibility into the block structure in relational models. A sideeffect of such high flexibility is that, in data sparsity scenarios, t ..."
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Stochastic partition processes in a product space play an important role in modeling relational data. Recent studies on the Mondrian process have introduced more flexibility into the block structure in relational models. A sideeffect of such high flexibility is that, in data sparsity scenarios, the model is prone to overfit. In reality, relational entities are always associated with meta information, such as user profiles in a social network. In this paper, we propose a metadata dependent Mondrian process (MDMP) to incorporate meta information into the stochastic partition process in the product space and the entity allocation process on the resulting block structure. MDMP can not only encourage homogeneous relational interactions within blocks but also discourage metalabel diversity within blocks. Regularized by meta information, MDMP becomes more robust in data sparsity scenarios and easier to converge in posterior inference. We apply MDMP to link prediction and rating prediction and demonstrate that MDMP is more effective than the baseline models in prediction accuracy with a more parsimonious model structure. 1.