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23
ON TENSORS, SPARSITY, AND NONNEGATIVE FACTORIZATIONS
, 2012
"... Tensors have found application in a variety of fields, ranging from chemometrics to signal processing and beyond. In this paper, we consider the problem of multilinear modeling of sparse count data. Our goal is to develop a descriptive tensor factorization model of such data, along with appropriat ..."
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Cited by 17 (1 self)
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Tensors have found application in a variety of fields, ranging from chemometrics to signal processing and beyond. In this paper, we consider the problem of multilinear modeling of sparse count data. Our goal is to develop a descriptive tensor factorization model of such data, along with appropriate algorithms and theory. To do so, we propose that the random variation is best described via a Poisson distribution, which better describes the zeros observed in the data as compared to the typical assumption of a Gaussian distribution. Under a Poisson assumption, we fit a model to observed data using the negative loglikelihood score. We present a new algorithm for Poisson tensor factorization called CANDECOMP–PARAFAC alternating Poisson regression (CPAPR) that is based on a majorizationminimization approach. It can be shown that CPAPR is a generalization of the Lee–Seung multiplicative updates. We show how to prevent the algorithm from converging to nonKKT points and prove convergence of CPAPR under mild conditions. We also explain how to implement CPAPR for largescale sparse tensors and present results on several data sets, both real and simulated.
Discovering latent network structure in point process data.
 In ThirtyFirst International Conference on Machine Learning (ICML).
, 2014
"... Abstract Networks play a central role in modern data analysis, enabling us to reason about systems by studying the relationships between their parts. Most often in network analysis, the edges are given. However, in many systems it is difficult or impossible to measure the network directly. Examples ..."
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Abstract Networks play a central role in modern data analysis, enabling us to reason about systems by studying the relationships between their parts. Most often in network analysis, the edges are given. However, in many systems it is difficult or impossible to measure the network directly. Examples of latent networks include economic interactions linking financial instruments and patterns of reciprocity in gang violence. In these cases, we are limited to noisy observations of events associated with each node. To enable analysis of these implicit networks, we develop a probabilistic model that combines mutuallyexciting point processes with random graph models. We show how the Poisson superposition principle enables an elegant auxiliary variable formulation and a fullyBayesian, parallel inference algorithm. We evaluate this new model empirically on several datasets.
ContinuousTime Regression Models for Longitudinal Networks
"... The development of statistical models for continuoustime longitudinal network data is of increasing interest in machine learning and social science. Leveraging ideas from survival and event history analysis, we introduce a continuoustime regression modeling framework for network event data that ca ..."
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Cited by 11 (2 self)
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The development of statistical models for continuoustime longitudinal network data is of increasing interest in machine learning and social science. Leveraging ideas from survival and event history analysis, we introduce a continuoustime regression modeling framework for network event data that can incorporate both timedependent network statistics and timevarying regression coefficients. We also develop an efficient inference scheme that allows our approach to scale to large networks. On synthetic and realworld data, empirical results demonstrate that the proposed inference approach can accurately estimate the coefficients of the regression model, which is useful for interpreting the evolution of the network; furthermore, the learned model has systematically better predictive performance compared to standard baseline methods. 1
Latent point process models for spatialtemporal networks
, 2013
"... Social network data is generally incomplete with missing information about nodes and their interactions. Here we propose a spatialtemporal latent point process model that describes geographically distributed interactions between pairs of entities. In contrast to most existing approaches, we assume ..."
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Social network data is generally incomplete with missing information about nodes and their interactions. Here we propose a spatialtemporal latent point process model that describes geographically distributed interactions between pairs of entities. In contrast to most existing approaches, we assume that interactions are not fully observable, and certain interaction events lack information about participants. Instead, this information needs to be inferred from the available observations. We develop an efficient approximate algorithm based on variational expectationmaximization to infer unknown participants in an event given the location and the time of the event. We validate the model on synthetic as well as real–world data, and obtain very promising results on the identityinference task. We also use our model to predict the timing and participants of future events, and demonstrate that it compares favorably with a baseline approach. 1
A scalable signal processing architecture for massive graph analysis
 in Proc. ICASSP
, 2012
"... In many applications, it is convenient to represent data as a graph, and often these datasets will be quite large. This paper presents an architecture for analyzing massive graphs, with a focus on signal processing applications such as modeling, filtering, and signal detection. We describe the arch ..."
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In many applications, it is convenient to represent data as a graph, and often these datasets will be quite large. This paper presents an architecture for analyzing massive graphs, with a focus on signal processing applications such as modeling, filtering, and signal detection. We describe the architecture, which covers the entire processing chain, from data storage to graph construction to graph analysis and subgraph detection. The data are stored in a new format that allows easy extraction of graphs representing any relationship existing in the data. The principal analysis algorithm is the partial eigendecomposition of the modularity matrix, whose running time is discussed. A large document dataset is analyzed, and we present subgraphs that stand out in the principal eigenspace of the timevarying graphs, including behavior we regard as clutter as well as small, tightlyconnected clusters that emerge over time. Index Terms — Graph theory, large data analysis, processing architectures, residuals analysis, emergent behavior
Predictability of User Behavior in Social Media: BottomUp v. TopDown Modeling
"... Abstract—Recent work has attempted to capture the behavior of users on social media by modeling them as computational units processing information. We propose to extend this perspective by explicitly examining the predictive power of such a view. We consider a network of fifteen thousand users on Tw ..."
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Abstract—Recent work has attempted to capture the behavior of users on social media by modeling them as computational units processing information. We propose to extend this perspective by explicitly examining the predictive power of such a view. We consider a network of fifteen thousand users on Twitter over a seven week period. To evaluate the predictability of the users, we apply two contrasting modeling paradigms: computational mechanics and echo state networks. Computational mechanics seeks to construct the simplest model with the maximal predictive capability, while echo state networks relax from very complicated dynamics until predictive capability is reached. We demonstrate that the behavior of users on Twitter can be wellmodeled as processes with selffeedback and compare the performance of models built with both the statistical and neural paradigms. I.
Understanding the Predictive Power of Computational Mechanics and Echo State Networks in Social Media
"... There is a large amount of interest in understanding users of social media in order to predict their behavior in this space. Despite this interest, user predictability in social media is not wellunderstood. To examine this question, we consider a network of fifteen thousand users on Twitter over a ..."
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There is a large amount of interest in understanding users of social media in order to predict their behavior in this space. Despite this interest, user predictability in social media is not wellunderstood. To examine this question, we consider a network of fifteen thousand users on Twitter over a seven week period. We apply two contrasting modeling paradigms: computational mechanics and echo state networks. Both methods attempt to model the behavior of users on the basis of their past behavior. We demonstrate that the behavior of users on Twitter can be wellmodeled as processes with selffeedback. We find that the two modeling approaches perform very similarly for most users, but that they differ in performance on a small subset of the users. By exploring the properties of these performancedifferentiated users, we highlight the challenges faced in applying predictive models to dynamic social data. I
Network Discovery with Multiintelligence Sources
"... Analysts can glean much useful intelligence information from identifying relationships between individuals and groups, and tracking their activities. However, detecting networks of people and then investigating their activities are difficult tasks, especially in this era of information overload. Gra ..."
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Analysts can glean much useful intelligence information from identifying relationships between individuals and groups, and tracking their activities. However, detecting networks of people and then investigating their activities are difficult tasks, especially in this era of information overload. Graph analysis has proven to be a useful tool for addressing these tasks, but it can be laborintensive. To aid in this analysis, Lincoln Laboratory researchers developed a diffusionbased analytic that helps solve the problems of network discovery and prioritized exploration. This analytic, called threat propagation, has been demonstrated to effectively handle network detection and