  A parametric point process model is developed, with modeling based on the
assumption that sequential observations often share latent phenomena, while
also possessing idiosyncratic effects. An alternating optimization method is
proposed to learn a "registered" point process that accounts for shared
structure, as well as "warping" functions that characterize idiosyncratic
aspects of each observed sequence. Under reasonable constraints, in each
iteration we update the sample-specific warping functions by solving a set of
constrained nonlinear programming problems in parallel, and update the model by
maximum likelihood estimation. The justifiability, complexity and robustness of
the proposed method are investigated in detail, and the influence of sequence
stitching on the learning results is examined empirically. Experiments on both
synthetic and real-world data demonstrate that the method yields explainable
point process models, achieving encouraging results compared to
state-of-the-art methods.
