Spatio-temporal point processes with deep non-stationary kernels
Spatio-temporal point processes with deep non-stationary kernels
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DOI：
10.48550/arxiv.2211.11179
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发表时间：
2022-11
期刊：
影响因子：
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通讯作者：
Zheng Dong;Xiuyuan Cheng;Yao Xie
中科院分区：
文献类型：
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作者：
Zheng Dong;Xiuyuan Cheng;Yao Xie
点过程数据在社交网络、医疗保健和金融等现代应用中变得无处不在。尽管流行的递归神经网络(RNN)模型对点过程数据具有强大的表达能力，但由于其递归结构，它们可能无法成功地捕获数据中复杂的非平稳依赖关系。另一种流行的点过程数据深度模型是基于神经网络表示影响核(而不是强度函数)。我们采用后一种方法，发展了一种新的深度非平稳影响核，它可以模拟非平稳的时空点过程。其主要思想是用一种新颖而通用的低阶分解来逼近影响核，使其能够通过深度神经网络进行有效的表示，并具有更高的计算效率和更好的性能。我们还采用了一种新的方法来保持条件强度的非负性约束，引入了对数障碍惩罚。在模拟数据和真实数据上，我们证明了我们所提出的方法具有良好的性能和计算效率。
Point process data are becoming ubiquitous in modern applications, such as social networks, health care, and finance. Despite the powerful expressiveness of the popular recurrent neural network (RNN) models for point process data, they may not successfully capture sophisticated non-stationary dependencies in the data due to their recurrent structures. Another popular type of deep model for point process data is based on representing the influence kernel (rather than the intensity function) by neural networks. We take the latter approach and develop a new deep non-stationary influence kernel that can model non-stationary spatio-temporal point processes. The main idea is to approximate the influence kernel with a novel and general low-rank decomposition, enabling efficient representation through deep neural networks and computational efficiency and better performance. We also take a new approach to maintain the non-negativity constraint of the conditional intensity by introducing a log-barrier penalty. We demonstrate our proposed method's good performance and computational efficiency compared with the state-of-the-art on simulated and real data.