Towards Flexibility and Interpretability of Gaussian Process State-Space Model
This work addresses the flexibility and interpretability of GPSSMs for researchers and practitioners in probabilistic modeling and time-series analysis, representing an incremental improvement.
The authors tackled the limited representation power of Gaussian process state-space models (GPSSMs) by proposing TGPSSMs, which use normalizing flows to enrich GP priors, and developed a scalable variational inference algorithm, resulting in superior performance on synthetic and real datasets compared to state-of-the-art methods.
The Gaussian process state-space model (GPSSM) has garnered considerable attention over the past decade. However, the standard GP with a preliminary kernel, such as the squared exponential kernel or Matérn kernel, that is commonly used in GPSSM studies, limits the model's representation power and substantially restricts its applicability to complex scenarios. To address this issue, we propose a new class of probabilistic state-space models called TGPSSMs, which leverage a parametric normalizing flow to enrich the GP priors in the standard GPSSM, enabling greater flexibility and expressivity. Additionally, we present a scalable variational inference algorithm that offers a flexible and optimal structure for the variational distribution of latent states. The proposed algorithm is interpretable and computationally efficient due to the sparse GP representation and the bijective nature of normalizing flow. Moreover, we incorporate a constrained optimization framework into the algorithm to enhance the state-space representation capabilities and optimize the hyperparameters, leading to superior learning and inference performance. Experimental results on synthetic and real datasets corroborate that the proposed TGPSSM outperforms several state-of-the-art methods. The accompanying source code is available at \url{https://github.com/zhidilin/TGPSSM}.