  Hawkes processes are a special class of temporal point processes which
exhibit a natural notion of causality, as occurrence of events in the past may
increase the probability of events in the future. Discovery of the underlying
influence network among the dimensions of multi-dimensional temporal processes
is of high importance in disciplines where a high-frequency data is to model,
e.g. in financial data or in seismological data. This paper approaches the
problem of learning Granger-causal network in multi-dimensional Hawkes
processes. We formulate this problem as a model selection task in which we
follow the minimum description length (MDL) principle. Moreover, we propose a
general algorithm for MDL-based inference using a Monte-Carlo method and we use
it for our causal discovery problem. We compare our algorithm with the
state-of-the-art baseline methods on synthetic and real-world financial data.
The synthetic experiments demonstrate superiority of our method incausal graph
discovery compared to the baseline methods with respect to the size of the
data. The results of experiments with the G-7 bonds price data are consistent
with the experts knowledge.
