We provide a comprehensive overview and tooling for GP modeling with
non-Gaussian likelihoods using state space methods. The state space formulation
allows for solving one-dimensional GP models in $\mathcal{O}(n)$ time and
memory complexity. While existing literature has focused on the connection
between GP regression and state space methods, the computational primitives
allowing for inference using general likelihoods in combination with the
Laplace approximation (LA), variational Bayes (VB), and assumed density
filtering (ADF, a.k.a. single-sweep expectation propagation, EP) schemes has
been largely overlooked. We present means of combining the efficient
$\mathcal{O}(n)$ state space methodology with existing inference methods. We
extend existing methods, and provide unifying code implementing all approaches.

本文提供 GP 建模的全面概述和工具，并使用状态空间方法处理非高斯似然。该方法使得在 o（n）时间和内存复杂度下解决一维 GP 模型成为可能。我们提出将高效的状态空间方法与现有 infernece 方法相结合的手段，包括拉普拉斯近似，变分贝叶斯和 assumed density filtering 等方法。