We consider a nonlinear state-space model with the state transition and
observation functions expressed as basis function expansions. The coefficients
in the basis function expansions are learned from data. Using a connection to
Gaussian processes we also develop priors on the coefficients, for tuning the
model flexibility and to prevent overfitting to data, akin to a Gaussian
process state-space model. The priors can alternatively be seen as a
regularization, and helps the model in generalizing the data without
sacrificing the richness offered by the basis function expansion. To learn the
coefficients and other unknown parameters efficiently, we tailor an algorithm
using state-of-the-art sequential Monte Carlo methods, which comes with
theoretical guarantees on the learning. Our approach indicates promising
results when evaluated on a classical benchmark as well as real data.

本文介绍了一种基于基函数扩展表达的非线性状态空间模型，通过连接高斯过程发展先验条件对系数进行学习，进而使用最先进的序贯蒙特卡罗方法进行系数学习，结果表明该方法在经典基准数据集和真实数据上取得了良好的结果。