Wasserstein Learning of Deep Generative Point Process Models

TL;DR

This paper introduces a novel intensity-free point process model trained with Wasserstein distance, overcoming limitations of traditional intensity-based methods and demonstrating superior performance on synthetic and real data.

Contribution

It proposes a new intensity-free approach for point process modeling using Wasserstein distance, enhancing expressiveness and robustness over maximum likelihood methods.

Findings

Outperforms traditional intensity-based models on synthetic data

Effective on real-world asynchronous sequential data

Demonstrates improved modeling of multi-modal sequence distributions

Abstract

Point processes are becoming very popular in modeling asynchronous sequential data due to their sound mathematical foundation and strength in modeling a variety of real-world phenomena. Currently, they are often characterized via intensity function which limits model's expressiveness due to unrealistic assumptions on its parametric form used in practice. Furthermore, they are learned via maximum likelihood approach which is prone to failure in multi-modal distributions of sequences. In this paper, we propose an intensity-free approach for point processes modeling that transforms nuisance processes to a target one. Furthermore, we train the model using a likelihood-free leveraging Wasserstein distance between point processes. Experiments on various synthetic and real-world data substantiate the superiority of the proposed point process model over conventional ones.