Learning Registered Point Processes from Idiosyncratic Observations
This addresses the challenge of modeling sequential data with mixed shared and individual variations, which is incremental as it builds on existing point process methods.
The paper tackled the problem of learning point process models from sequential observations with both shared and idiosyncratic effects, proposing an alternating optimization method to estimate a registered point process and warping functions, and demonstrated encouraging results compared to state-of-the-art methods on synthetic and real-world data.
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.