Fast Fully Bayesian Gaussian Processes

高斯过程是一种强大的非参数贝叶斯模型，可用于各种机器学习任务，包括回归、分类、生成性建模和仿真。简单地实现高斯过程回归模型会产生立方时间和二次存储成本，并且不利于并行计算体系结构。现代计算体系结构，如图形处理单元(GPU)，已经很好地配备来执行浮点算术中的矩阵乘积，这见证了完全依赖于简单矩阵运算的深度学习方法的适用性的显著增长。这篇论文旨在批判性地分析高斯过程实现中的类似进展，这些实现只将矩阵向量乘积作为其主要计算开销。最近在使用迭代方法来计算高斯过程推理中的相关量方面的复兴导致了大量的技术来驯服高斯过程以通过GPU运行的框架来实现，然而对于使用哪种方法以及何时使用没有统一的观点。本文提供了帮助解决这一问题的建议。

Gaussian Processes are powerful non-parametric Bayesian models, and can be used in a variety of machine learning tasks including regression, classification, generative modelling and emulation. Naive implementations of Gaussian Process regression models incur cubic time and quadratic memory costs and are not conducive to parallel compute architecture. Modern compute architecture, such as Graphics Processing Units (GPUs), are well equipped to perform matrix products in floating point arithmetic which has seen a significant growth in the applicability of deep learning methods which rely entirely on simple matrix operations. This thesis aims to critically analyse similar advances in Gaussian Process implementations that only perform matrix-vector products as their main computational overhead. Recent resurgence in the use of iterative methods to compute the relevant quantities in Gaussian Process inference has led to a wide array of techniques that tame Gaussian Processes for implementation through GPU-run frameworks, however there is no unifying view on which method to use and when. This thesis provides recommendations to help combat such a problem.