A Dirichlet Mixture Model of Hawkes Processes for Event Sequence Clustering

TL;DR

This paper introduces a novel Dirichlet mixture model for Hawkes processes to effectively cluster event sequences, demonstrating superior performance and robustness through theoretical analysis and experiments on synthetic and real data.

Contribution

It develops a new Dirichlet mixture model for Hawkes processes, along with an EM-type inference algorithm, enabling automatic cluster number determination and improved clustering of event sequences.

Findings

The method automatically learns the number of clusters.

It outperforms competitors in clustering purity and consistency.

The approach is robust to model misspecification.

Abstract

We propose an effective method to solve the event sequence clustering problems based on a novel Dirichlet mixture model of a special but significant type of point processes --- Hawkes process. In this model, each event sequence belonging to a cluster is generated via the same Hawkes process with specific parameters, and different clusters correspond to different Hawkes processes. The prior distribution of the Hawkes processes is controlled via a Dirichlet distribution. We learn the model via a maximum likelihood estimator (MLE) and propose an effective variational Bayesian inference algorithm. We specifically analyze the resulting EM-type algorithm in the context of inner-outer iterations and discuss several inner iteration allocation strategies. The identifiability of our model, the convergence of our learning method, and its sample complexity are analyzed in both theoretical and empirical ways, which demonstrate the superiority of our method to other competitors. The proposed method learns the number of clusters automatically and is robust to model misspecification. Experiments on both synthetic and real-world data show that our method can learn diverse triggering patterns hidden in asynchronous event sequences and achieve encouraging performance on clustering purity and consistency.