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.

通过集成卡尔曼滤波器（EnKF）近似推断隐藏状态的后验分布，我们提出了一种改进的变分推断方法，有效地训练高斯过程状态空间模型（GPSSM），并在学习和推断性能方面优于现有方法。

集合卡尔曼滤波辅助变分推断在高斯过程态空间模型中的应用

Ensemble Kalman Filtering-Aided Variational Inference for Gaussian  Process State-Space Models

In order for robots to safely navigate in unseen scenarios using
learning-based methods, it is important to accurately detect
out-of-training-distribution (OoD) situations online. Recently, Gaussian
process state-space models (GPSSMs) have proven useful to discriminate
unexpected observations by comparing them against probabilistic predictions.
However, the capability for the model to correctly distinguish between in- and
out-of-training distribution observations hinges on the accuracy of these
predictions, primarily affected by the class of functions the GPSSM kernel can
represent. In this paper, we propose (i) a novel approach to embed existing
domain knowledge in the kernel and (ii) an OoD online runtime monitor, based on
receding-horizon predictions. Domain knowledge is assumed given as a dataset
collected either in simulation or using a nominal model. Numerical results show
that the informed kernel yields better regression quality with smaller
datasets, as compared to standard kernel choices. We demonstrate the
effectiveness of the OoD monitor on a real quadruped navigating an indoor
setting, which reliably classifies previously unseen terrains.

提出了一种利用现有领域知识嵌入核函数的新方法，以及一种基于滚动预测的离线在线监控器，用于使机器人在未知情况下使用基于学习的方法安全导航。数值结果表明，与标准的核函数选择相比，具有领域知识的核函数在小数据集上具有更好的回归质量。通过对一个室内设置中的四足机器人进行测试，演示了 OoD 监控器的有效性，可可靠地对以前未见的地形进行分类。

基于领域信息的高斯过程状态空间模型的区分外分布检测

Out of Distribution Detection via Domain-Informed Gaussian Process State  Space Models

We investigate active learning in Gaussian Process state-space models
(GPSSM). Our problem is to actively steer the system through latent states by
determining its inputs such that the underlying dynamics can be optimally
learned by a GPSSM. In order that the most informative inputs are selected, we
employ mutual information as our active learning criterion. In particular, we
present two approaches for the approximation of mutual information for the
GPSSM given latent states. The proposed approaches are evaluated in several
physical systems where we actively learn the underlying non-linear dynamics
represented by the state-space model.

本文研究了高斯过程状态空间模型的主动学习。通过决定其输入，我们可以通过 GPSSM 最优地学习系统的潜在状态，以便选择最具信息量的输入。我们提出了两种逼近潜在状态下 GPSSM 的互信息的方法，并在多个物理系统中进行了评估。