论文标题
稀疏的高斯过程超参数：优化还是集成？
Sparse Gaussian Process Hyperparameters: Optimize or Integrate?
论文作者
论文摘要
内核函数及其超参数是高斯过程中的中央模型选择选择（Rasmussen和Williams，2006年）。通常，通过最大化边际可能性（一种称为II型最大可能性（ML-II））来选择内核的超参数。但是，ML-II并未解释高参数的不确定性，众所周知，这可能导致严重偏见的估计值和预测不确定性的低估。虽然有几种作品采用了全GP的贝叶斯表征，但相对较少的GPS范式提出了这种方法。在这项工作中，我们提出了一种用于稀疏高斯工艺回归的算法，该算法利用MCMC从蒂蒂亚斯（Titsias）变异诱导点框架（2009）内的高参数后部采样。这项工作与Hensman等人密切相关。 （2015b），但侧架需要采样诱导点，从而显着提高了高斯可能性情况下的采样效率。我们将该方案与文献中的天然基线以及随机变异GPS（SVGP）以及广泛的计算分析进行了比较。
The kernel function and its hyperparameters are the central model selection choice in a Gaussian proces (Rasmussen and Williams, 2006). Typically, the hyperparameters of the kernel are chosen by maximising the marginal likelihood, an approach known as Type-II maximum likelihood (ML-II). However, ML-II does not account for hyperparameter uncertainty, and it is well-known that this can lead to severely biased estimates and an underestimation of predictive uncertainty. While there are several works which employ a fully Bayesian characterisation of GPs, relatively few propose such approaches for the sparse GPs paradigm. In this work we propose an algorithm for sparse Gaussian process regression which leverages MCMC to sample from the hyperparameter posterior within the variational inducing point framework of Titsias (2009). This work is closely related to Hensman et al. (2015b) but side-steps the need to sample the inducing points, thereby significantly improving sampling efficiency in the Gaussian likelihood case. We compare this scheme against natural baselines in literature along with stochastic variational GPs (SVGPs) along with an extensive computational analysis.
