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）为潜在状态的动力学建模提供了一种原理性且灵活的方法，该潜在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及其间强时间依赖性，GPSSMs的推断在计算和统计上都极具挑战性。本文提出了一种新的贝叶斯GPSSMs推断方法，该方法克服了先前方法过度简化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通过随机梯度哈密顿蒙特卡罗实现的自由形式变分推断。此外，通过利用我们提出的变分分布，我们提供了该方法的坍缩扩展，其中诱导变量被解析地边缘化。我们还展示了将所提框架与粒子马尔可夫链蒙特卡罗方法结合的结果。在六个真实数据集上的实验表明，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。