The Use of Gaussian Processes as Particles for Sequential Monte Carlo Estimation of Time-Varying Functions

We propose modeling of time-varying functions by Gaussian processes based on random features and relying on the sequential Monte Carlo methodology, also known as particle filtering. The models make use of time-varying random features and parameter variables to adapt to changes of the modeled functions with time. The Gaussian processes are treated as latent states and are estimated by using particle filtering, which altogether allows for learning functions at each time instant. The proposed models have the ability to search for optimal functions in the dynamic space over time. The experimental results show that the approach has better performance than existing state-of-the-art methods based on ensemble of Gaussian processes both in accuracy and stability.