Gaussian processes (GPs) are powerful tools for nonlinear classification in which latent GPs are combined with link functions. But GPs do not scale well to large training data. This is compounded for classification where the latent GPs require Markov chain Monte Carlo integration. Consequently, fully Bayesian, sampling-based approaches had been largely abandoned. Instead, maximization-based alternatives, such as Laplace/variational inference (VI) combined with low rank approximations, are preferred. Though feasible for large training data sets, such schemes sacrifice uncertainty quantification and modeling fidelity, two aspects that are important to our work on surrogate modeling of computer simulation experiments. Here we are motivated by a large scale simulation of binary black hole (BBH) formation. We propose an alternative GP classification framework which uses elliptical slice sampling for Bayesian posterior integration and Vecchia approximation for computational thrift. We demonstrate superiority over VI-based alternatives for BBH simulations and other benchmark classification problems. We then extend our setup to warped inputs for "deep" nonstationary classification.

翻译：高斯过程（GPs）是非线性分类的强大工具，其中隐高斯过程与链接函数结合使用。然而，高斯过程难以扩展到大规模训练数据。对于分类问题，隐高斯过程需要进行马尔可夫链蒙特卡洛积分，这进一步加剧了计算负担。因此，完全贝叶斯、基于采样的方法在很大程度上已被弃用。取而代之的是，人们更倾向于采用基于最大化的替代方案，例如拉普拉斯/变分推断（VI）结合低秩近似。尽管这类方案对于大规模训练数据集是可行的，但它们牺牲了不确定性量化和建模保真度，而这两个方面对于我们计算机仿真实验的代理建模工作至关重要。本文的动机源于一个大规模的双黑洞（BBH）形成模拟。我们提出了一种替代的高斯过程分类框架，该框架使用椭圆切片采样进行贝叶斯后验积分，并采用Vecchia近似以实现计算节俭。我们证明了该方法在BBH模拟及其他基准分类问题上优于基于变分推断的替代方案。随后，我们将该框架扩展到使用扭曲输入以实现"深度"非平稳分类。