Learning Granger Causality for Hawkes Processes

Abstract

Learning Granger causality for general point processes is a very challenging task. In this paper, we propose an effective method, learning Granger causality, for a special but significant type of point processes --- Hawkes process. We reveal the relationship between Hawkes process's impact function and its Granger causality graph. Specifically, our model represents impact functions using a series of basis functions and recovers the Granger causality graph via group sparsity of the impact functions' coefficients. We propose an effective learning algorithm combining a maximum likelihood estimator (MLE) with a sparse-group-lasso (SGL) regularizer. Additionally, the flexibility of our model allows to incorporate the clustering structure event types into learning framework. We analyze our learning algorithm and propose an adaptive procedure to select basis functions. Experiments on both synthetic and real-world data show that our method can learn the Granger causality graph and the triggering patterns of the Hawkes processes simultaneously.

International Conference on Machine Learning, 2016

References in corpus (3)

• Scalable Nonparametric Bayesian Inference on Point Processes with Gaussian Processes
• Nonparametric Markovian Learning of Triggering Kernels for Mutually Exciting and Mutually Inhibiting Multivariate Hawkes Processes
• Graphical Modeling for Multivariate Hawkes Processes with Nonparametric Link Functions

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