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.

翻译：非线性状态-空间模型是描述复杂时间序列中动态结构的有力工具。在一次处理一个样本数据的流流环境中,同时对状态和非线性动态的推论在实践中提出了重大挑战。我们开发了一个新的在线学习框架,利用变式推论和接连的蒙特卡洛,从而可以灵活和准确地进行贝叶西亚联合过滤。我们的方法提供了过滤后继器的近似值,可以任意接近一系列广泛的动态模型和观测模型的真实过滤分布。具体地说,拟议框架可以有效地利用稀有高斯进程将后继器与动态相近,并允许对潜在动态进行可解释的模型。每个样本的持续时间复杂性使得我们的方法适合在线学习情景,适合实时应用。