Closed-form Inference and Prediction in Gaussian Process State-Space Models
This work addresses the challenge of modeling non-linear dynamics with noise in time-series data, offering a more efficient and deterministic alternative to previous sampling-based methods, though it is incremental as it builds on existing GPSSM frameworks.
The paper tackles the problem of performing efficient inference and prediction in Gaussian Process State-Space Models (GPSSMs) for system identification and time-series modeling, achieving linear time complexity and eliminating the need for Monte Carlo sampling through a deterministic variational inference scheme.
We examine an analytic variational inference scheme for the Gaussian Process State Space Model (GPSSM) - a probabilistic model for system identification and time-series modelling. Our approach performs variational inference over both the system states and the transition function. We exploit Markov structure in the true posterior, as well as an inducing point approximation to achieve linear time complexity in the length of the time series. Contrary to previous approaches, no Monte Carlo sampling is required: inference is cast as a deterministic optimisation problem. In a number of experiments, we demonstrate the ability to model non-linear dynamics in the presence of both process and observation noise as well as to impute missing information (e.g. velocities from raw positions through time), to de-noise, and to estimate the underlying dimensionality of the system. Finally, we also introduce a closed-form method for multi-step prediction, and a novel criterion for assessing the quality of our approximate posterior.