Learning a Sparse Polynomial Approximation to the Transition Function of General State-Space Models

State-space models are a statistical framework for modelling temporal phenomena via a hidden state. In this framework, the hidden state is not observed, and instead a series of related observations are obtained. A state-space model is defined by the state dynamics, which is encoded as a distribution. The parameters of this distribution are often unknown, and must be estimated in order to perform inference. In real-world systems, it is common that not all dimensions of the hidden state directly interact, which implies a sparse system. Most parameter estimation methods for state-space models cannot recover sparsity. In this work, we propose PolyGrad, a fully automatic method for obtaining sparse estimates of the state interactions of a non-linear state-space model via a polynomial approximation. This novel versatile methodology allows to infer both the structure and values of a generic parameterisation of a state-space model. The proposed method is computationally efficient and can represent a large class of complex systems.