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18
Modelling Reciprocating Relationships with Hawkes Processes
"... We present a Bayesian nonparametric model that discovers implicit social structure from interaction timeseries data. Social groups are often formed implicitly, through actions among members of groups. Yet many models of social networks use explicitly declared relationships to infer social structure ..."
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Cited by 27 (3 self)
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We present a Bayesian nonparametric model that discovers implicit social structure from interaction timeseries data. Social groups are often formed implicitly, through actions among members of groups. Yet many models of social networks use explicitly declared relationships to infer social structure. We consider a particular class of Hawkes processes, a doubly stochastic point process, that is able to model reciprocity between groups of individuals. We then extend the Infinite Relational Model by using these reciprocating Hawkes processes to parameterise its edges, making events associated with edges codependent through time. Our model outperforms general, unstructured Hawkes processes as well as structured Poisson processbased models at predicting verbal and email turntaking, and military conflicts among nations. 1
Conjoint Modeling of Temporal Dependencies in Event Streams
"... Many real world applications depend on modeling the temporal dynamics of streams of diverse events, many of which are rare. We introduce a novel model class, Conjoint PiecewiseConstant Conditional Intensity Models, and a learning algorithm that together yield a datadriven approach to parameter sha ..."
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Cited by 21 (2 self)
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Many real world applications depend on modeling the temporal dynamics of streams of diverse events, many of which are rare. We introduce a novel model class, Conjoint PiecewiseConstant Conditional Intensity Models, and a learning algorithm that together yield a datadriven approach to parameter sharing with the aim of better modeling such event streams. We empirically demonstrate that our approach yields more accurate models of two real world data sets: search query logs and data center system logs. 1
Learning Social Infectivity in Sparse Lowrank Networks Using Multidimensional Hawkes Processes
"... How will the behaviors of individuals in a social network be influenced by their neighbors, the authorities and the communities in a quantitative way? Such critical and valuable knowledge is unfortunately not readily accessible and we tend to only observe its manifestation in the form of recurrent ..."
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Cited by 18 (8 self)
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How will the behaviors of individuals in a social network be influenced by their neighbors, the authorities and the communities in a quantitative way? Such critical and valuable knowledge is unfortunately not readily accessible and we tend to only observe its manifestation in the form of recurrent and timestamped events occurring at the individuals involved in the social network. It is an important yet challenging problem to infer the underlying network of social inference based on the temporal patterns of those historical events that we can observe. In this paper, we propose a convex optimization approach to discover the hidden network of social influence by modeling the recurrent events at different individuals as multidimensional Hawkes processes, emphasizing the mutualexcitation nature of the dynamics of event occurrence. Furthermore, our estimation procedure, using nuclear and!1 norm regularization simultaneously on the parameters, is able to take into account the prior knowledge of the presence of neighbor interaction, authority influence, and community coordination in the social network. To efficiently solve the resulting optimization problem, we also design an algorithm ADM4 which combines techniques of alternating direction method of multipliers and majorization minimization. We experimented with both synthetic and real world data sets, and showed that the proposed method can discover the hidden network more accurately and produce a better predictive model than several baselines.
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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Cited by 13 (0 self)
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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.
Learning Triggering Kernels for Multidimensional Hawkes Processes
"... How does the activity of one person affect that of another person? Does the strength of influence remain periodic or decay exponentially over time? In this paper, we study these critical questions in social networkanalysisquantitativelyundertheframework of multidimensional Hawkes processes. In part ..."
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Cited by 13 (4 self)
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How does the activity of one person affect that of another person? Does the strength of influence remain periodic or decay exponentially over time? In this paper, we study these critical questions in social networkanalysisquantitativelyundertheframework of multidimensional Hawkes processes. In particular, we focus on the nonparametric learning of the triggering kernels, and propose an algorithm MMEL that combines the idea of decoupling the parameters through constructing a tight upperbound of the objective function and application of EulerLagrange equations for optimization in infinite dimensional functional space. We show that the proposed method performs significantly better than alternatives in experiments on both synthetic and real world datasets. 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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Cited by 4 (0 self)
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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
Continuous time Bayesian network classifiers
 Journal of Biomedical Informatics
, 2012
"... Continuous time Bayesian network classifiers are designed for temporal classification of multivariate streaming data when time duration of events matters and the class does not change over time. This paper introduces the CTBNCToolkit: an open source Java toolkit which provides a standalone applicat ..."
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Cited by 3 (1 self)
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Continuous time Bayesian network classifiers are designed for temporal classification of multivariate streaming data when time duration of events matters and the class does not change over time. This paper introduces the CTBNCToolkit: an open source Java toolkit which provides a standalone application for temporal classification and a library for continuous time Bayesian network classifiers. CTBNCToolkit implements the inference algorithm, the parameter learning algorithm, and the structural learning algorithm for continuous time Bayesian network classifiers. The structural learning algorithm is based on scoring functions: the marginal loglikelihood score and the conditional loglikelihood score are provided. CTBNCToolkit provides also an implementation of the expectation maximization algorithm for clustering purpose. The paper introduces continuous time Bayesian network classifiers. How to use the CTBNToolkit from the command line is described in a specific section. Tutorial examples are included to facilitate users to understand how the toolkit must be used. A section dedicate to the Java library is proposed to help further code extensions. ‡ Authors ’ contributions The toolkit was developed by Daniele Codecasa, who also wrote the paper. Fabio Stella read the paper and made valuable suggestions. A former MATLAB implementation of the CTBNC inference algorithm was made available by Fabio Stella in order to test the correctness of the inference using the CTBNCToolkit1. 1CTBNCToolkit website and the repository will be updated soon. 1 ar
Auxiliary gibbs sampling for inference in piecewiseconstant conditional intensity models
 In UAI
, 2015
"... A piecewiseconstant conditional intensity model (PCIM) is a nonMarkovian model of temporal stochastic dependencies in continuoustime event streams. It allows efficient learning and forecasting given complete trajectories. However, no general inference algorithm has been developed for PCIMs. We pr ..."
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Cited by 2 (1 self)
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A piecewiseconstant conditional intensity model (PCIM) is a nonMarkovian model of temporal stochastic dependencies in continuoustime event streams. It allows efficient learning and forecasting given complete trajectories. However, no general inference algorithm has been developed for PCIMs. We propose an effective and efficient auxiliary Gibbs sampler for inference in PCIM, based on the idea of thinning for inhomogeneous Poisson processes. The sampler alternates between sampling a finite set of auxiliary virtual events with adaptive rates, and performing an efficient forwardbackward pass at discrete times to generate samples. We show that our sampler can successfully perform inference tasks in both Markovian and nonMarkovian models, and can be employed in ExpectationMaximization PCIM parameter estimation and structural learning with partially observed data. 1
Hawkes Processes with Stochastic Excitations
"... Abstract We propose an extension to Hawkes processes by treating the levels of selfexcitation as a stochastic differential equation. Our new point process allows better approximation in application domains where events and intensities accelerate each other with correlated levels of contagion. We g ..."
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Abstract We propose an extension to Hawkes processes by treating the levels of selfexcitation as a stochastic differential equation. Our new point process allows better approximation in application domains where events and intensities accelerate each other with correlated levels of contagion. We generalize a recent algorithm for simulating draws from Hawkes processes whose levels of excitation are stochastic processes, and propose a hybrid Markov chain Monte Carlo approach for model fitting. Our sampling procedure scales linearly with the number of required events and does not require stationarity of the point process. A modular inference procedure consisting of a combination between Gibbs and Metropolis Hastings steps is put forward. We recover expectation maximization as a special case. Our general approach is illustrated for contagion following geometric Brownian motion and exponential Langevin dynamics.