Learning Registered Point Processes from Idiosyncratic Observations

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

PoPPy: A Point Process Toolbox Based on PyTorch

PoPPy is a Point Process toolbox based on PyTorch, which achieves flexible designing and efficient learning of point process models. It can be used for interpretable sequential data modeling and analysis, e.g., Granger causality analysis of multi-variate point processes, point process-based simulation and prediction of event sequences. In practice, the key points of point process-based sequential data modeling include: 1) How to design intensity functions to describe the mechanism behind observed data? 2) How to learn the proposed intensity functions from observed data? The goal of PoPPy is providing a user-friendly solution to the key points above and achieving large-scale point process-based sequential data analysis, simulation and prediction