A projected nonlinear state-space model for forecasting time series signals
提出一种快速算法，通过投影线上的核函数捕捉非线性动态，从含噪时间序列中学习并预测未来轨迹，同时保持计算效率，适用于需要不确定性估计的预测任务。
Learning and forecasting stochastic time series is essential in various scientific fields. However, despite the proposals of nonlinear filters and deep-learning methods, it remains challenging to capture nonlinear dynamics from a few noisy samples and predict future trajectories with uncertainty estimates while maintaining computational efficiency. Here, we propose a fast algorithm to learn and forecast nonlinear dynamics from noisy time series data. A key feature of the proposed model is kernel functions applied to projected lines, enabling the fast and efficient capture of nonlinearities in the latent dynamics. Through empirical case studies and benchmarking, the model demonstrates its effectiveness at learning and forecasting complex nonlinear dynamics, offering a valuable tool for researchers and practitioners in time series analysis.