We formulate approximate Bayesian inference in non-conjugate temporal and
spatio-temporal Gaussian process models as a simple parameter update rule
applied during Kalman smoothing. This viewpoint encompasses most inference
schemes, including expectation propagation (EP), the classical (Extended,
Unscented, etc.) Kalman smoothers, and variational inference. We provide a
unifying perspective on these algorithms, showing how replacing the power EP
moment matching step with linearisation recovers the classical smoothers. EP
provides some benefits over the traditional methods via introduction of the
so-called cavity distribution, and we combine these benefits with the
computational efficiency of linearisation, providing extensive empirical
analysis demonstrating the efficacy of various algorithms under this unifying
framework. We provide a fast implementation of all methods in JAX.

本研究提出了一种在 Kalman 平滑过程中应用的简单参数更新规则，将非共轭时空高斯过程模型中的近似贝叶斯推理公式化，包括大部分推理方案，如 EP、经典 Kalman 平滑器和变分推理，并提供了这些算法的统一视角。

状态空间期望传播：时态高斯过程的高效推断方案

State Space Expectation Propagation: Efficient Inference Schemes for  Temporal Gaussian Processes

State-space smoothing has found many applications in science and engineering.
Under linear and Gaussian assumptions, smoothed estimates can be obtained using
efficient recursions, for example Rauch-Tung-Striebel and Mayne-Fraser
algorithms. Such schemes are equivalent to linear algebraic techniques that
minimize a convex quadratic objective function with structure induced by the
dynamic model.
These classical formulations fall short in many important circumstances. For
instance, smoothers obtained using quadratic penalties can fail when outliers
are present in the data, and cannot track impulsive inputs and abrupt state
changes. Motivated by these shortcomings, generalized Kalman smoothing
formulations have been proposed in the last few years, replacing quadratic
models with more suitable, often nonsmooth, convex functions. In contrast to
classical models, these general estimators require use of iterated algorithms,
and these have received increased attention from control, signal processing,
machine learning, and optimization communities.
In this survey we show that the optimization viewpoint provides the control
and signal processing community great freedom in the development of novel
modeling and inference frameworks for dynamical systems. We discuss general
statistical models for dynamic systems, making full use of nonsmooth convex
penalties and constraints, and providing links to important models in signal
processing and machine learning. We also survey optimization techniques for
these formulations, paying close attention to dynamic problem structure.
Modeling concepts and algorithms are illustrated with numerical examples.

通过最优化视角，我们讨论了动态系统的常规统计模型，并充分利用了非光滑凸惩罚和约束，提供了与信号处理和机器学习中重要模型的联系。我们调查了这些问题的优化技术，特别关注动态问题结构，并用数值例子说明了建模概念和算法。