  Learning the causal-interaction network of multivariate Hawkes processes is a
useful task in many applications. Maximum-likelihood estimation is the most
common approach to solve the problem in the presence of long observation
sequences. However, when only short sequences are available, the lack of data
amplifies the risk of overfitting and regularization becomes critical. Due to
the challenges of hyper-parameter tuning, state-of-the-art methods only
parameterize regularizers by a single shared hyper-parameter, hence limiting
the power of representation of the model. To solve both issues, we develop in
this work an efficient algorithm based on variational expectation-maximization.
Our approach is able to optimize over an extended set of hyper-parameters. It
is also able to take into account the uncertainty in the model parameters by
learning a posterior distribution over them. Experimental results on both
synthetic and real datasets show that our approach significantly outperforms
state-of-the-art methods under short observation sequences.
