  The superposition of temporal point processes has been studied for many
years, although the usefulness of such models for practical applications has
not be fully developed. We investigate superposed Hawkes process as an
important class of such models, with properties studied in the framework of
least squares estimation. The superposition of Hawkes processes is demonstrated
to be beneficial for tightening the upper bound of excess risk under certain
conditions, and we show the feasibility of the benefit in typical situations.
The usefulness of superposed Hawkes processes is verified on synthetic data,
and its potential to solve the cold-start problem of recommendation systems is
demonstrated on real-world data.
