Gaussian process state-space models (GPSSMs) provide a principled and flexible approach to model latent state dynamics observed through emission models. However, existing variational methods for learning GPSSMs face a substantial challenge in optimizing a large number of parameters, particularly with the introduction of amortized inference networks. To address this challenge, we leverage the ensemble Kalman filter (EnKF), a well-established model-based filtering technique, to approximate the posterior distribution of latent states within the variational inference framework. This approach eliminates the need for inference networks, significantly reducing the number of variational parameters. Moreover, we demonstrate that with the aid of EnKF, the straightforward evaluation of approximated evidence lower bound (ELBO) in the variational inference can be easily obtained through the summation of multiple terms with closed-form solutions. By leveraging automatic differentiation tools, we thus can maximize the ELBO and train the GPSSM efficiently. We also extend the proposed method to an online setting and provide comprehensive algorithm analyses and insights. Extensive testing on diverse real and simulated datasets demonstrates that our variational inference algorithms, integrated with EnKF, outperform existing methods in terms of learning and inference performance.

翻译：高斯过程状态空间模型（GPSSM）提供了一种原理性且灵活的方法来建模通过发射模型观测到的潜在状态动力学。然而，现有用于学习GPSSM的变分方法在优化大量参数时面临重大挑战，尤其是在引入摊销推理网络的情况下。为应对这一挑战，我们利用集成卡尔曼滤波（EnKF）——一种成熟的基于模型的滤波技术——在变分推断框架内近似潜在状态的后验分布。该方法消除了对推理网络的需求，从而显著减少了变分参数的数量。此外，我们证明借助EnKF，变分推断中近似证据下界（ELBO）的直接评估可通过多个闭合解项的和轻松获得。通过利用自动微分工具，我们可以最大化ELBO并高效训练GPSSM。我们还将所提出方法扩展到在线设置，并提供全面的算法分析与见解。在多样化真实与模拟数据集上的大量实验表明，我们集成EnKF的变分推断算法在学习和推理性能上均优于现有方法。