[论文解读] Wasserstein Learning of Deep Generative Point Process Models

Shuai Xiao, Mehrdad Farajtabar+4 more|arXiv (Cornell University)|May 23, 2017

Point processes and geometric inequalities参考文献 17被引用 61

一句话总结

本文提出一种用于时间点过程的强度无关生成模型，在 Wasserstein GAN 框架（WGANTPP）下进行训练，显示在模型错误指定和数据混合情况下对似然法方法有更好的拟合表现。

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.

研究动机与目标

• Motivate removing restrictive parametric intensity forms in point processes.
• Develop a likelihood-free training framework via Wasserstein distance for point processes.
• Propose a generator–discriminator architecture based on recurrent networks for sequence generation and evaluation.
• Introduce a practical Lipschitz regularization scheme to stabilize training of WGANTPP.
• Demonstrate robustness and superior performance across synthetic and real-world datasets.

提出的方法

• Define point processes and introduce an intensity-free modeling framework.
• Adopt Wasserstein distance between point process distributions with a tractable sequence distance ||ξ−ρ||⋆.
• Use a neural network-based generator gθ to transform a Poisson-based noise process into event sequences.
• Use a neural network-based discriminator f_w to assign scores to sequences and enforce a 1-Lipschitz constraint.
• Regularize the Wasserstein objective with a Lipschitz-based penalty to avoid explicit gradient clipping (equation 10).
• Train with a recurrent neural network architecture for both generator and discriminator to handle sequential event data.

实验结果

研究问题

• RQ1 Can an intensity-free, likelihood-free GAN framework accurately learn temporal point processes from data without specifying a parametric intensity function?
• RQ2 How does Wasserstein-based training compare to maximum-likelihood estimation across synthetic and real datasets, including mixed-process scenarios?
• RQ3 Does WGANTPP retain performance when the underlying generative process is misspecified or multimodal (data mixtures)?

主要发现

Data	Estimator	MLE-IP	MLE-SE	MLE-SC	MLE-NN	WGAN
MIMIC	Deviation	0.150	0.160	0.339	0.686	0.122
Meme	Deviation	0.839	1.008	0.701	0.920	0.351
MAS	Deviation	1.089	1.693	1.592	2.712	0.849
NYSE	Deviation	0.799	0.426	0.361	0.347	0.303

• WGANTPP yields better empirical intensities than likelihood-based models across synthetic processes when the parametric form is unknown or misspecified.
• WGANTPP provides more faithful QQ-plot behavior and reduces mode dropping in mixtures of processes.
• On real-world datasets (MIMIC, MemeTracker, MAS, NYSE), WGANTPP achieves lower intensity deviation than MLE-based methods.
• The method robustly handles diverse data sources and outperforms MLE-based neural point process models (MLE-NN) in many settings.
• Empirical results demonstrate that intensity-free learning with Wasserstein distance can outperform parametric MLE in scenarios with model misspecification.