In the context of a motivating study of dynamic network flow data on a large-scale e-commerce web site, we develop Bayesian models for on-line sequential analysis for monitoring and adapting to changes reflected in node-node traffic. For large-scale networks, we customize core Bayesian time series analysis methods using dynamic generalized linear models (DGLMs) integrated into the multivariate network context using the concept of decouple recouple recently introduced in multivariate time series. This enables flexible dynamic modeling of flows on large-scale networks and exploitation of partial parallelization of analysis while critically maintaining coherence with an over-arching multivariate dynamic flow model. Development is anchored in a case-study on internet data, with flows of visitors to a commercial news web site defining a long time series of node-node counts on over 56,000 node pairs. Characterizing inherent stochasticity in traffic patterns, understanding node-node interactions, adapting to dynamic changes in flows and allowing for sensitive monitoring to flag anomalies are central questions. The methodology of dynamic network DGLMs will be of interest and utility in broad ranges of dynamic network flow studies.
Various Bayesian statistical models have also been developed for dynamic network studies with state-space models . State-space models represent data with coupled observation (noise, natural random variation) components and latent process (underlying state variables with stochastic but sustained patterns over time). Conditionally linear, Gaussian models are amenable to analytic computation using Kalman filtering-style analysis, and more extensive analysis using broader classes of Bayesian state-state space models [e.g.][] WestHarrison1997 . However, many most problems of network inference in dynamic contexts involve non-Gaussian data structures and non-linear effects, so one needs stronger computational methods such as Markov chain Monte Carlo . For example, @cite_3 map the dynamic co-occurrence data to dynamic embeddings in low-dimension Euclidean space, while @cite_2 and @cite_4 extend well-known stochastic block models to study dynamic network tomography. More closely allied to some of our main interests here are past works on the so-called network tomography problem [e.g.][] Tebaldi1998 and state-space models for physical traffic flow forecasting [e.g.][] Tebaldi2002,Queen2009, AnacletoEtAl2013a, AnacletoEtAl2013b . Our work presents a broader approach to such studies by exploiting rich classes of Bayesian state-space models to characterize and analyse complex, time-varying flows on networks.
@cite_4 @cite_3 @cite_2
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Computational advertising uses information on web-browsing activity and additional covariates to select advertisements for display to the user. The statistical challenge is to develop methodology that matches ads to users who are likely to purchase the advertised product. These methods not only involve text mining, but also may draw upon additional modeling related to both the user and the advertisement. This paper reviews various aspects of text mining, including n-grams, topic modeling, and text networks, and discusses different strategies in the context of specific business models. © 2013 Wiley Periodicals, Inc. Statistical Analysis and Data Mining, 2013 In a dynamic social or biological environment, the interactions between the actors can undergo large and systematic changes. In this paper we propose a model-based approach to analyze what we will refer to as the dynamic tomography of such time-evolving networks. Our approach offers an intuitive but powerful tool to infer the semantic underpinnings of each actor, such as its social roles or biological functions, underlying the observed network topologies. Our model builds on earlier work on a mixed membership stochastic blockmodel for static networks, and the state-space model for tracking object trajectory. It overcomes a major limitation of many current network inference techniques, which assume that each actor plays a unique and invariant role that accounts for all its interactions with other actors; instead, our method models the role of each actor as a time-evolving mixed membership vector that allows actors to behave differently over time and carry out different roles functions when interacting with different peers, which is closer to reality. We present an efficient algorithm for approximate inference and learning using our model; and we applied our model to analyze a social network between monks (i.e., the Sampson's network), a dynamic email communication network between the Enron employees, and a rewiring gene interaction network of fruit fly collected during its full life cycle. In all cases, our model reveals interesting patterns of the dynamic roles of the actors.