Towards Flexibility and Interpretability of Gaussian Process State-Space Model
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Gaussian process state-space model (GPSSM) has attracted much attention over the past decade. However, the model representation power of GPSSM is far from satisfactory. Most GPSSM works rely on the standard Gaussian process (GP) with a preliminary kernel, such as squared exponential (SE) kernel and Matérn kernel, which limit the model representation power and its application in complex scenarios. To address this issue, this paper proposes a novel class of probabilistic state-space model named TGPSSM that enriches the GP priors in the standard GPSSM through parametric normalizing flow, making the state-space model more flexible and expressive. In addition, by inheriting the advantages of sparse representation of GP models, we propose a scalable and interpretable variational learning algorithm to learn the TGPSSM and infer the latent dynamics simultaneously. By integrating a constrained optimization framework and explicitly constructing a non-Gaussian state variational distribution, the proposed learning algorithm enables the TGPSSM to significantly improve the capabilities of state space representation and model inference. Experimental results based on various synthetic and real datasets corroborate that the proposed TGPSSM yields superior learning and inference performance compared to several state-of-the-art methods. The accompanying source code is available at https://github.com/zhidilin/TGPSSM.
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