Significant efforts have gone into the development of statistical models for analyzing data in the form of networks, such as social networks. Most existing work has focused on modeling static networks, which represent either a single time snapshot or an aggregate view over time. There has been recent interest in statistical modeling of dynamic networks, which are observed at multiple points in time and offer a richer representation of many complex phenomena. In this paper, we present a state-space model for dynamic networks that extends the well-known stochastic blockmodel for static networks to the dynamic setting. We fit the model in a near-optimal manner using an extended Kalman filter (EKF) augmented with a local search. We demonstrate that the EKF-based algorithm performs competitively with a state-of-the-art algorithm based on Markov chain Monte Carlo sampling but is significantly less computationally demanding.
Hoff @cite_14 proposed a dynamic latent factor model analogous to an eigenvalue decomposition with time-invariant eigenvectors and time-varying eigenvalues. The model is applicable to many types of data in the form of multi-way arrays, including dynamic social networks, and is fit using MCMC sampling. In @cite_38 , Lee and Priebe proposed a latent process model for attributed (multi-relational) dynamic networks using random dot product spaces. The authors fit mathematically tractable first- and second-order approximations of the random dot process model, for which individual network snapshots are drawn from attributed versions of the Erd o s-R ' e nyi and latent space models, respectively. Perry and Wolfe @cite_20 proposed a point process model for dynamic networks of directed interactions and a partial likelihood inference procedure to fit their model. The authors model interactions using a multivariate counting process that accounts for effects including homophily. Their model operates in continuous time, unlike the proposed model in this paper, which operates on discrete-time snapshots.
@cite_38 @cite_14 @cite_20
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We introduce a latent process model for time series of attributed random graphs for characterizing multiple modes of association among a collection of actors over time. Two mathematically tractable approximations are derived, and we examine the performance of a class of test statistics for an illustrative change-point detection problem and demonstrate that the analysis through approximation can provide valuable information regarding inference properties. Reduced-rank decompositions provide descriptions of the variation among the elements of a matrix or array. In such decompositions, the elements of an array are expressed as products of low-dimensional latent factors. This article presents a model-based version of such a decomposition, extending the scope of reduced-rank methods to accommodate a variety of data types such as longitudinal social networks and continuous multivariate data that are cross-classified by categorical variables. The proposed model-based approach is hierarchical, in that the latent factors corresponding to a given dimension of the array are not a priori independent, but exchangeable. Such a hierarchical approach allows more flexibility in the types of patterns that can be represented. Abstract : Network data often take the form of repeated interactions between senders and receivers tabulated over time. A primary question to ask of such data is which traits and behaviors are predictive of interaction. To answer this question, a model is introduced for treating directed interactions as a multivariate point process: a Cox multiplicative intensity model using covariates that depend on the history of the process. Consistency and asymptotic normality are proved for the resulting partial-likelihood-based estimators under suitable regularity conditions, and an efficient fitting procedure is described. Multicast interactions--those involving a single sender but multiple receivers--are treated explicitly. The resulting inferential framework is then employed to model message sending behavior in a corporate e-mail network. The analysis gives a precise quantification of which static shared traits and dynamic network effects are predictive of message recipient selection.