Online estimation and community detection of network point processes for event streams

Published in

Statistics and computing(2020)

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TL;DR

This work proposes a fast online variational inference algorithm for estimating the latent structure underlying dynamic event arrivals on a network, using continuous-time point process latent network models, and investigates the theoretical properties of such an inference scheme.

Abstract

A common goal in network modeling is to uncover the latent community structure present among nodes. For many real-world networks, the true connections consist of events arriving as streams, which are then aggregated to form edges, ignoring the dynamic temporal component. A natural way to take account of these temporal dynamics of interactions is to use point processes as the foundation of network models for community detection. Computational complexity hampers the scalability of such approaches to large sparse networks. To circumvent this challenge, we propose a fast online variational inference algorithm for estimating the latent structure underlying dynamic event arrivals on a network, using continuous-time point process latent network models. We describe this procedure for network models capturing community structure. This structure can be learned as new events are observed on the network, updating the inferred community assignments. We investigate the theoretical properties of such an inference scheme, and provide regret bounds on the loss function of this procedure. The proposed inference procedure is then thoroughly compared, using both simulation studies and real data, to non-online variants. We demonstrate that online inference can obtain comparable performance, in terms of community recovery, to non-online variants, while realising computational gains. Our proposed inference framework can also be readily modified to incorporate other popular network structures.

Authors

Guanhua Fang

1 papers

Owen G. Ward

1 papers

T. Zheng

1 papers

References52 items

A Mutually Exciting Latent Space Hawkes Process Model for Continuous-time Networks

Group Network Hawkes Process

Anomaly Detection in Large-Scale Networks With Latent Space Models

A Generalization Bound for Online Variational Inference

Solving the Sparsity Problem in Recommendations via Cross-Domain Item Embedding Based on Co-Clustering

Online estimation and community detection of network point processes for event streams

Published in

Statistics and computing(2020)

External Links:

Generate Graph

TL;DR

Abstract

Authors

Guanhua Fang

1 papers

Owen G. Ward

1 papers

T. Zheng

1 papers

References52 items

A Mutually Exciting Latent Space Hawkes Process Model for Continuous-time Networks

Group Network Hawkes Process

Anomaly Detection in Large-Scale Networks With Latent Space Models

A Generalization Bound for Online Variational Inference

Solving the Sparsity Problem in Recommendations via Cross-Domain Item Embedding Based on Co-Clustering

Change Point Estimation in a Dynamic Stochastic Block Model

Modelling sparsity, heterogeneity, reciprocity and community structure in temporal interaction data

A block model for node popularity in networks with community structure

Temporal Exponential Random Graph Models with btergm: Estimation and Bootstrap Confidence Intervals

Hawkes processes and their applications to finance: a review

A Tutorial on Hawkes Processes for Events in Social Media

Community Discovery in Dynamic Networks

Concentration of tempered posteriors and of their variational approximations

Spectral clustering in the dynamic stochastic block model

An Initial Condition

Varying-coefficient models for dynamic networks

Community detection in networks: A user guide

Variational Inference: A Review for Statisticians

A semiparametric extension of the stochastic block model for longitudinal networks

Latent Space Models for Dynamic Networks

Biclustering on expression data: A review

Statistical clustering of temporal networks through a dynamic stochastic block model

Achieving Optimal Misclassification Proportion in Stochastic Block Models

On comparing partitions

Predicting Taxi–Passenger Demand Using Streaming Data

An Introduction to the Theory of Point Processes

Streaming Variational Bayes

Pseudo-likelihood methods for community detection in large sparse networks

Stochastic variational inference

Online Learning and Online Convex Optimization

Consistency of community detection in networks under degree-corrected stochastic block models

Consistency of maximum-likelihood and variational estimators in the Stochastic Block Model

Online Learning for Latent Dirichlet Allocation

Sentiment Knowledge Discovery in Twitter Streaming Data

Bayesian anomaly detection methods for social networks

A scalable collaborative filtering framework based on co-clustering

Estimation and Prediction for Stochastic Blockstructures

On Spectral Clustering: Analysis and an algorithm

Biclustering of Expression Data

Statistical Models for Earthquake Occurrences and Residual Analysis for Point Processes

A cluster process representation of a self-exciting process

Mean Field for the Stochastic Blockmodel: Optimization Landscape and Convergence Issues

Online Learning for Multivariate Hawkes Processes

Markov chain Monte Carlo in Practice

Theory of point estimation

C5 [ Boundedness ] For simplicity, we assume the functions λ ij ( t | z ), log λ ij ( t | z ) and their derivatives are continuous bounded function of parameter θ for all z and t

We take out ﬁrst m 0 nodes such that d i m 0 ≥

Temporal exponential con-ﬁdence

NetworkgroupHawkesprocessmodel (2020)

Let d i be the number nodes that individual i connects to. We assume that d i (cid:17) d n for all with d n = n r d (0 < r d < 1)

We perform K -means method again onto center vectors ( θ i , i ∈ { i 1 ,..., i m 0 } ) toobtaintheestimatedmemberships ofthose i ’s, (i.e., ˆ z ( 0 ) i ,..., ˆ z

TL;DR

Abstract

Authors

References52 items

A Mutually Exciting Latent Space Hawkes Process Model for Continuous-time Networks

Group Network Hawkes Process

Anomaly Detection in Large-Scale Networks With Latent Space Models

A Generalization Bound for Online Variational Inference

Solving the Sparsity Problem in Recommendations via Cross-Domain Item Embedding Based on Co-Clustering

TL;DR

Abstract

Authors

References52 items

A Mutually Exciting Latent Space Hawkes Process Model for Continuous-time Networks

Group Network Hawkes Process

Anomaly Detection in Large-Scale Networks With Latent Space Models

A Generalization Bound for Online Variational Inference

Solving the Sparsity Problem in Recommendations via Cross-Domain Item Embedding Based on Co-Clustering

Change Point Estimation in a Dynamic Stochastic Block Model

Modelling sparsity, heterogeneity, reciprocity and community structure in temporal interaction data

A block model for node popularity in networks with community structure

Temporal Exponential Random Graph Models with btergm: Estimation and Bootstrap Confidence Intervals

Hawkes processes and their applications to finance: a review

A Tutorial on Hawkes Processes for Events in Social Media

Community Discovery in Dynamic Networks

Concentration of tempered posteriors and of their variational approximations

Spectral clustering in the dynamic stochastic block model

An Initial Condition

Varying-coefficient models for dynamic networks

Community detection in networks: A user guide

Variational Inference: A Review for Statisticians

A semiparametric extension of the stochastic block model for longitudinal networks

Latent Space Models for Dynamic Networks

Biclustering on expression data: A review

Statistical clustering of temporal networks through a dynamic stochastic block model

Achieving Optimal Misclassification Proportion in Stochastic Block Models

On comparing partitions

Predicting Taxi–Passenger Demand Using Streaming Data

An Introduction to the Theory of Point Processes

Streaming Variational Bayes

Pseudo-likelihood methods for community detection in large sparse networks

Stochastic variational inference

Online Learning and Online Convex Optimization

Consistency of community detection in networks under degree-corrected stochastic block models

Consistency of maximum-likelihood and variational estimators in the Stochastic Block Model

Online Learning for Latent Dirichlet Allocation

Sentiment Knowledge Discovery in Twitter Streaming Data

Bayesian anomaly detection methods for social networks

A scalable collaborative filtering framework based on co-clustering

Estimation and Prediction for Stochastic Blockstructures

On Spectral Clustering: Analysis and an algorithm

Biclustering of Expression Data

Statistical Models for Earthquake Occurrences and Residual Analysis for Point Processes

A cluster process representation of a self-exciting process

Mean Field for the Stochastic Blockmodel: Optimization Landscape and Convergence Issues

Online Learning for Multivariate Hawkes Processes

Snap datasets

Markov chain Monte Carlo in Practice

Theory of point estimation

C5 [ Boundedness ] For simplicity, we assume the functions λ ij ( t | z ), log λ ij ( t | z ) and their derivatives are continuous bounded function of parameter θ for all z and t

We take out ﬁrst m 0 nodes such that d i m 0 ≥

Temporal exponential con-ﬁdence

NetworkgroupHawkesprocessmodel (2020)

Let d i be the number nodes that individual i connects to. We assume that d i (cid:17) d n for all with d n = n r d (0 < r d < 1)

We perform K -means method again onto center vectors ( θ i , i ∈ { i 1 ,..., i m 0 } ) toobtaintheestimatedmemberships ofthose i ’s, (i.e., ˆ z ( 0 ) i ,..., ˆ z

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