用随机微分网络学习连续时间动力学
Learning Continuous-Time Dynamics by Stochastic Differential Networks
摘要：
连续时间随机动力学的学习是偶发时间序列建模中的一个基本问题，其观测值在时间和维度上都是不规则的和稀疏的。对于一个给定的系统，其潜在状态和观测数据是高维的，它通常是不可能得到一个精确的连续时间随机过程来描述系统的行为。为了解决上述问题，我们采用变分贝叶斯方法，并提出了一个灵活的连续时间随机递归神经网络称为变分随机微分网络（VSDN），它嵌入了零星时间序列的复杂动力学神经随机微分方程（ESDN）。VSDNs通过深度神经网络捕获潜在状态和观测之间的随机依赖性。我们还将两个差异证据下限有效地训练模型。通过全面的实验，我们证明了VSDN优于最先进的连续时间深度学习模型，并在零星时间序列的预测和插值任务上取得了显着的性能。
英文摘要：
Learning continuous-time stochastic dynamics is a fundamental and essential problem in modeling sporadic time series, whose observations are irregular and sparse in both time and dimension. For a given system whose latent states and observed data are high-dimensional, it is generally impossible to derive a precise continuous-time stochastic process to describe the system behaviors. To solve the above problem, we apply Variational Bayesian method and propose a flexible continuous-time stochastic recurrent neural network named Variational Stochastic Differential Networks (VSDN), which embeds the complicated dynamics of the sporadic time series by neural Stochastic Differential Equations (SDE). VSDNs capture the stochastic dependency among latent states and observations by deep neural networks. We also incorporate two differential Evidence Lower Bounds to efficiently train the models. Through comprehensive experiments, we show that VSDNs outperform state-of-the-art continuous-time deep learning models and achieve remarkable performance on prediction and interpolation tasks for sporadic time series.
机构、总结、中文摘要均由AI分析而来，可能存在错误，请以论文正文为准。
