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16
Modelling Reciprocating Relationships with Hawkes Processes
"... We present a Bayesian nonparametric model that discovers implicit social structure from interaction time-series 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 time-series 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 co-dependent through time. Our model outperforms general, unstructured Hawkes processes as well as structured Poisson process-based models at predicting verbal and email turn-taking, and military conflicts among nations. 1
Modeling Events with Cascades of Poisson Processes
"... We present a probabilistic model of events in continuous time in which each event triggers a Poisson process of successor events. The ensemble of observed events is thereby modeled as a superposition of Poisson processes. Efficient inference is feasible under this model with an EM algorithm. Moreove ..."
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Cited by 18 (0 self)
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We present a probabilistic model of events in continuous time in which each event triggers a Poisson process of successor events. The ensemble of observed events is thereby modeled as a superposition of Poisson processes. Efficient inference is feasible under this model with an EM algorithm. Moreover, the EM algorithm can be implemented as a distributed algorithm, permitting the model to be applied to very large datasets. We apply these techniques to the modeling of Twitter messages and the revision history of Wikipedia. 1
Bayesian inference for sparse generalized linear models
- In Machine Learning: ECML
, 2007
"... Abstract. We present a framework for efficient, accurate approximate Bayesian inference in generalized linear models (GLMs), based on the expectation propagation (EP) technique. The parameters can be endowed with a factorizing prior distribution, encoding properties such as sparsity or non-negativit ..."
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Cited by 11 (4 self)
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Abstract. We present a framework for efficient, accurate approximate Bayesian inference in generalized linear models (GLMs), based on the expectation propagation (EP) technique. The parameters can be endowed with a factorizing prior distribution, encoding properties such as sparsity or non-negativity. The central role of posterior log-concavity in Bayesian GLMs is emphasized and related to stability issues in EP. In particular, we use our technique to infer the parameters of a point process model for neuronal spiking data from multiple electrodes, demonstrating significantly superior predictive performance when a sparsity assumption is enforced via a Laplace prior distribution. 1
CT-NOR: representing and reasoning about events in continuous time
- In International Conference on Uncertainty in Artificial Intelligence
, 2008
"... We present a generative model for representing and reasoning about the relationships among events in continuous time. We apply the model to the domain of networked and distributed computing environments where we fit the parameters of the model from timestamp observations, and then use hypothesis tes ..."
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Cited by 10 (3 self)
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We present a generative model for representing and reasoning about the relationships among events in continuous time. We apply the model to the domain of networked and distributed computing environments where we fit the parameters of the model from timestamp observations, and then use hypothesis testing to discover dependencies between the events and changes in behavior for monitoring and diagnosis. After introducing the model, we present an EM algorithm for fitting the parameters and then present the hypothesis testing approach for both dependence discovery and change-point detection. We validate the approach for both tasks using real data from a trace of network events at Microsoft Research Cambridge. Finally, we formalize the relationship between the proposed model and the noisy-or gate for cases when time can be discretized. 1
Multiplicative Forests for Continuous-Time Processes
"... Learning temporal dependencies between variables over continuous time is an important and challenging task. Continuous-time Bayesian networks effectively model such processes but are limited by the number of conditional intensity matrices, which grows exponentially in the number of parents per varia ..."
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Cited by 5 (4 self)
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Learning temporal dependencies between variables over continuous time is an important and challenging task. Continuous-time Bayesian networks effectively model such processes but are limited by the number of conditional intensity matrices, which grows exponentially in the number of parents per variable. We develop a partition-based representation using regression trees and forests whose parameter spaces grow linearly in the number of node splits. Using a multiplicative assumption we show how to update the forest likelihood in closed form, producing efficient model updates. Our results show multiplicative forests can be learned from few temporal trajectories with large gains in performance and scalability. 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 spatial-temporal latent point process model that describes geographically distributed interac-tions 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 spatial-temporal latent point process model that describes geographically distributed interac-tions 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 obser-vations. We develop an efficient approximate algorithm based on variational expectation-maximization to infer unknown participants in an event given the location and the time of the event. We validate the model on syn-thetic as well as real–world data, and ob-tain very promising results on the identity-inference task. We also use our model to predict the timing and participants of future events, and demonstrate that it compares fa-vorably with a baseline approach. 1
A Multitask Point Process Predictive Model
"... Point process data are commonly observed in fields like healthcare and the social sciences. De-signing predictive models for such event streams is an under-explored problem, due to often scarce training data. In this work we propose a multi-task point process model, leveraging information from all t ..."
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Cited by 4 (0 self)
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Point process data are commonly observed in fields like healthcare and the social sciences. De-signing predictive models for such event streams is an under-explored problem, due to often scarce training data. In this work we propose a multi-task point process model, leveraging information from all tasks via a hierarchical Gaussian pro-cess (GP). Nonparametric learning functions im-plemented by a GP, which map from past events to future rates, allow analysis of flexible arrival patterns. To facilitate efficient inference, we pro-pose a sparse construction for this hierarchical model, and derive a variational Bayes method for learning and inference. Experimental results are shown on both synthetic data and as well as real electronic health-records data. 1.
Forest-Based Point Process for Event Prediction from Electronic Health Records
"... Abstract. Accuratepredictionoffutureonsetofdisease fromElectronic Health Records (EHRs) has important clinical and economic implications. In this domain the arrival of data comes at semi-irregular intervals and makes the prediction task challenging. We propose a method called multiplicative-forest p ..."
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Cited by 4 (1 self)
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Abstract. Accuratepredictionoffutureonsetofdisease fromElectronic Health Records (EHRs) has important clinical and economic implications. In this domain the arrival of data comes at semi-irregular intervals and makes the prediction task challenging. We propose a method called multiplicative-forest point processes (MFPPs) that learns the rate of future events based on an event history. MFPPs join previous theory in multiplicative forest continuous-time Bayesian networks and piecewisecontinuous conditional intensity models. We analyze the advantages of using MFPPs over previous methods and show that on synthetic and real EHR forecasting of heart attacks, MFPPs outperform earlier methods and augment off-the-shelf machine learning algorithms. 1
Auxiliary gibbs sampling for inference in piecewiseconstant conditional intensity models
- In UAI
, 2015
"... A piecewise-constant conditional intensity model (PCIM) is a non-Markovian model of temporal stochastic dependencies in continuous-time 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 piecewise-constant conditional intensity model (PCIM) is a non-Markovian model of temporal stochastic dependencies in continuous-time 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 forward-backward pass at discrete times to generate samples. We show that our sampler can successfully perform inference tasks in both Markovian and non-Markovian models, and can be employed in Expectation-Maximization PCIM parameter estimation and structural learning with partially observed data. 1
AMultitask Point Process Predictive Model
"... Point process data are commonly observed in fields like healthcare and the social sciences. De-signing predictive models for such event streams is an under-explored problem, due to often scarce training data. In this work we propose a multi-task point process model, leveraging information from all t ..."
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Point process data are commonly observed in fields like healthcare and the social sciences. De-signing predictive models for such event streams is an under-explored problem, due to often scarce training data. In this work we propose a multi-task point process model, leveraging information from all tasks via a hierarchical Gaussian pro-cess (GP). Nonparametric learning functions im-plemented by a GP, which map from past events to future rates, allow analysis of flexible arrival patterns. To facilitate efficient inference, we pro-pose a sparse construction for this hierarchical model, and derive a variational Bayes method for learning and inference. Experimental results are shown on both synthetic data and as well as real electronic health-records data. 1.
