Sequential Estimation of Gaussian Process-based Deep State-Space Models
This work addresses sequential estimation for researchers in machine learning and signal processing, but it appears incremental as it builds on existing particle filtering and Gaussian process techniques.
The paper tackles the problem of sequential estimation in state-space and deep state-space models by proposing a method based on particle filtering with Gaussian processes, using random features to integrate out parameters and avoid particles for them. The result shows that the method can track latent processes up to a scale and rotation in experiments.
We consider the problem of sequential estimation of the unknowns of state-space and deep state-space models that include estimation of functions and latent processes of the models. The proposed approach relies on Gaussian and deep Gaussian processes that are implemented via random feature-based Gaussian processes. In these models, we have two sets of unknowns, highly nonlinear unknowns (the values of the latent processes) and conditionally linear unknowns (the constant parameters of the random feature-based Gaussian processes). We present a method based on particle filtering where the parameters of the random feature-based Gaussian processes are integrated out in obtaining the predictive density of the states and do not need particles. We also propose an ensemble version of the method, with each member of the ensemble having its own set of features. With several experiments, we show that the method can track the latent processes up to a scale and rotation.