State-space models (SSMs) are a highly expressive model class for learning
patterns in time series data and for system identification. Deterministic
versions of SSMs (e.g. LSTMs) proved extremely successful in modeling complex
time series data. Fully probabilistic SSMs, however, are often found hard to
train, even for smaller problems. To overcome this limitation, we propose a
novel model formulation and a scalable training algorithm based on doubly
stochastic variational inference and Gaussian processes. In contrast to
existing work, the proposed variational approximation allows one to fully
capture the latent state temporal correlations. These correlations are the key
to robust training. The effectiveness of the proposed PR-SSM is evaluated on a
set of real-world benchmark datasets in comparison to state-of-the-art
probabilistic model learning methods. Scalability and robustness are
demonstrated on a high dimensional problem.

本篇论文提出了一种基于双重随机变分推断和高斯过程的可扩展训练算法，用于可靠地训练完全概率状态空间模型中的潜在状态时间相关性， 并在真实世界基准数据集集上评估了所提出的 PR-SSM 的效果与最先进的概率模型学习方法进行了比较

概率循环状态空间模型

Probabilistic Recurrent State-Space Models

Gaussian processes (GPs) are a good choice for function approximation as they
are flexible, robust to over-fitting, and provide well-calibrated predictive
uncertainty. Deep Gaussian processes (DGPs) are multi-layer generalisations of
GPs, but inference in these models has proved challenging. Existing approaches
to inference in DGP models assume approximate posteriors that force
independence between the layers, and do not work well in practice. We present a
doubly stochastic variational inference algorithm, which does not force
independence between layers. With our method of inference we demonstrate that a
DGP model can be used effectively on data ranging in size from hundreds to a
billion points. We provide strong empirical evidence that our inference scheme
for DGPs works well in practice in both classification and regression.

本文介绍了一种基于双随机变分推断的方法，用于深度高斯过程模型（Deep Gaussian processes）的推断。该方法能够有效地处理数百个到十亿个数据点的分类和回归任务，验证了其推断模型的实用性。