  Many real-world applications require robust algorithms to learn point
processes based on a type of incomplete data --- the so-called short
doubly-censored (SDC) event sequences. We study this critical problem of
quantitative asynchronous event sequence analysis under the framework of Hawkes
processes by leveraging the idea of data synthesis. Given SDC event sequences
observed in a variety of time intervals, we propose a sampling-stitching data
synthesis method --- sampling predecessors and successors for each SDC event
sequence from potential candidates and stitching them together to synthesize
long training sequences. The rationality and the feasibility of our method are
discussed in terms of arguments based on likelihood. Experiments on both
synthetic and real-world data demonstrate that the proposed data synthesis
method improves learning results indeed for both time-invariant and
time-varying Hawkes processes.
