State Space representation of non-stationary Gaussian Processes

The state space (SS) representation of Gaussian processes (GP) has recently gained a lot of interest. The main reason is that it allows to compute GPs based inferences in O(n), where $n$ is the number of observations. This implementation makes GPs suitable for Big Data. For this reason, it is important to provide a SS representation of the most important kernels used in machine learning. The aim of this paper is to show how to exploit the transient behaviour of SS models to map non-stationary kernels to SS models.