  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.
