Linear State-Space Model with Time-Varying Dynamics
This addresses the need for more accurate modeling of physical processes with smoothly varying parameters, such as weather systems, though it is incremental in improving existing state-space methods.
The paper tackles the problem of modeling time-varying dynamics in linear state-space models by introducing a continuous linear combination of matrices, outperforming previous switching models on stochastic advection-diffusion and real-world weather processes.
This paper introduces a linear state-space model with time-varying dynamics. The time dependency is obtained by forming the state dynamics matrix as a time-varying linear combination of a set of matrices. The time dependency of the weights in the linear combination is modelled by another linear Gaussian dynamical model allowing the model to learn how the dynamics of the process changes. Previous approaches have used switching models which have a small set of possible state dynamics matrices and the model selects one of those matrices at each time, thus jumping between them. Our model forms the dynamics as a linear combination and the changes can be smooth and more continuous. The model is motivated by physical processes which are described by linear partial differential equations whose parameters vary in time. An example of such a process could be a temperature field whose evolution is driven by a varying wind direction. The posterior inference is performed using variational Bayesian approximation. The experiments on stochastic advection-diffusion processes and real-world weather processes show that the model with time-varying dynamics can outperform previously introduced approaches.