Gaussian process state-space models (GPSSMs) provide a principled and flexible approach to modeling the dynamics of a latent state, which is observed at discrete-time points via a likelihood model. However, inference in GPSSMs is computationally and statistically challenging due to the large number of latent variables in the model and the strong temporal dependencies between them. In this paper, we propose a new method for inference in Bayesian GPSSMs, which overcomes the drawbacks of previous approaches, namely over-simplified assumptions, and high computational requirements. Our method is based on free-form variational inference via stochastic gradient Hamiltonian Monte Carlo within the inducing-variable formalism. Furthermore, by exploiting our proposed variational distribution, we provide a collapsed extension of our method where the inducing variables are marginalized analytically. We also showcase results when combining our framework with particle MCMC methods. We show that, on six real-world datasets, our approach can learn transition dynamics and latent states more accurately than competing methods.

翻译：高斯过程状态空间模型（GPSSMs）提供了一种原则性且灵活的方法来建模潜在状态的动力学，该状态通过似然模型在离散时间点被观测。然而，由于模型中存在大量潜在变量以及它们之间强的时间依赖性，GPSSMs的推断在计算和统计上具有挑战性。本文提出了一种用于贝叶斯GPSSM推断的新方法，该方法克服了先前方法（即过度简化的假设和高计算需求）的缺陷。我们的方法基于诱导变量框架下的随机梯度哈密顿蒙特卡洛自由形式变分推断。此外，通过利用我们提出的变分分布，我们提供了方法的坍缩扩展，其中诱导变量被解析地边缘化。我们还展示了将我们的框架与粒子MCMC方法结合的结果。在六个真实世界数据集上，我们证明了我们的方法能够比竞争方法更准确地学习转移动力学和潜在状态。