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。

具有非高斯似然函数的状态空间高斯过程

State Space Gaussian Processes with Non-Gaussian Likelihood

We introduce stochastic variational inference for Gaussian process models.
This enables the application of Gaussian process (GP) models to data sets
containing millions of data points. We show how GPs can be vari- ationally
decomposed to depend on a set of globally relevant inducing variables which
factorize the model in the necessary manner to perform variational inference.
Our ap- proach is readily extended to models with non-Gaussian likelihoods and
latent variable models based around Gaussian processes. We demonstrate the
approach on a simple toy problem and two real world data sets.

介绍了一种基于随机变分推断方法的高斯过程模型，该方法使高斯过程模型能够应用于包含数百万数据点的数据集，并在需要执行变分推断的情况下，演示了如何将高斯过程分解为依赖于一组全局相关的引出变量的方法，并将其扩展到基于高斯过程的潜变量模型和具有非高斯似然度的模型。作者在简单玩具问题和两个真实数据集上展示了这种方法。