Decomposing Temporal High-Order Interactions via Latent ODEs
Decomposing Temporal High-Order Interactions via Latent ODEs
复制标题
DOI：
--
复制
发表时间：
2022
期刊：
影响因子：
--
通讯作者：
Shibo Li;Robert M. Kirby;Shandian Zhe
中科院分区：
文献类型：
--
作者：
Shibo Li;Robert M. Kirby;Shandian Zhe
多个对象之间的高阶交互在实际应用程序中很常见。虽然张量分解是高阶交互分析和预测的常用框架，但大多数方法不能很好地利用数据中有价值的时间戳信息。现有的方法要么放弃时间戳，要么将它们转换为离散的步骤，要么使用过于简单的分解模型。因此，这些方法可能无法捕获复杂的、细粒度的时间动态，也无法对长期交互结果做出准确的预测。为了克服这些限制，我们提出了一种新的基于常微分方程的时间高阶相互作用分解模型（蒂斯ode）。我们用一个潜在的ODE来模拟时变的相互作用结果。为了捕获复杂的时间动态，我们使用神经网络（NN）来学习ODE状态的时间导数。我们使用交互对象的表示来建模ODE的初始值，并构成神经网络输入的一部分来计算状态。通过这种方式，可以估计参与对象的时间关系并将其编码到它们的表示中。为了便于处理和扩展推理，我们使用前向灵敏度分析来有效地计算ODE状态梯度，并在此基础上使用积分变换开发了随机小批量学习算法。我们在模拟和四个实际应用中展示了我们的方法的优势。
High-order interactions between multiple objects are common in real-world applications. Although tensor decomposition is a popular framework for high-order interaction analysis and prediction, most methods cannot well exploit the valuable timestamp information in data. The existent meth-ods either discard the timestamps or convert them into discrete steps or use over-simplistic decomposition models. As a result, these methods might not be capable enough of capturing complex, fine-grained temporal dynamics or making accurate predictions for long-term interaction results. To overcome these limitations, we propose a novel Temporal High-order Interaction decompoSition model based on Ordinary Differential Equations (THIS-ODE). We model the time-varying interaction result with a latent ODE. To capture the complex temporal dynamics, we use a neural network (NN) to learn the time derivative of the ODE state. We use the representation of the interaction objects to model the initial value of the ODE and to constitute a part of the NN input to compute the state. In this way, the temporal relationships of the participant objects can be estimated and encoded into their representations. For tractable and scalable inference, we use forward sensitivity analysis to efficiently compute the gradient of ODE state, based on which we use integral transform to develop a stochastic mini-batch learning algorithm. We demonstrate the advantage of our approach in simulation and four real-world applications.