  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.

Machine Learning;Machine Learning