IEEE Trans Pattern Anal Mach Intell. 2023 Jan;45(1):1150-1161. doi: 10.1109/TPAMI.2022.3153225. Epub 2022 Dec 5.
Nonlinear state-space models are powerful tools to describe dynamical structures in complex time series. In a streaming setting where data are processed one sample at a time, simultaneous inference of the state and its nonlinear dynamics has posed significant challenges in practice. We develop a novel online learning framework, leveraging variational inference and sequential Monte Carlo, which enables flexible and accurate Bayesian joint filtering. Our method provides an approximation of the filtering posterior which can be made arbitrarily close to the true filtering distribution for a wide class of dynamics models and observation models. Specifically, the proposed framework can efficiently approximate a posterior over the dynamics using sparse Gaussian processes, allowing for an interpretable model of the latent dynamics. Constant time complexity per sample makes our approach amenable to online learning scenarios and suitable for real-time applications.
非线性状态空间模型是描述复杂时间序列动态结构的有力工具。在流处理环境中，数据是逐个样本进行处理的，因此同时推断状态及其非线性动态在实践中带来了重大挑战。我们开发了一种新颖的在线学习框架，利用变分推断和序贯蒙特卡罗方法，实现了灵活且准确的贝叶斯联合滤波。我们的方法提供了一种对滤波后验的逼近，可以使它与广泛的动态模型和观测模型的真实滤波分布任意接近。具体来说，所提出的框架可以使用稀疏高斯过程有效地逼近动态的后验分布，从而可以对潜在动态进行可解释的建模。我们的方法每个样本的时间复杂度保持不变，因此适用于在线学习场景，并适合实时应用。
