论文标题
融合保证高斯流程的保证意味着具有错误指定的可能性和光滑度
Convergence Guarantees for Gaussian Process Means With Misspecified Likelihoods and Smoothness
论文作者
论文摘要
高斯流程在机器学习，统计和应用数学中无处不在。它们为近似功能提供了灵活的建模框架，同时量化不确定性。但是，只有当模型被良好指定时，这是正确的，在实践中通常不是这种情况。在本文中，我们研究高斯过程的特性，是指模型的平滑度和可能性函数的平稳性。在这种情况下，实用相关性的一个重要的理论问题是，将高斯过程近似值的准确性，我们的模型和错误指定程度的范围的难度。该问题的答案特别有用，因为它可以为我们选择模型和实验设计提供信息。特别是，我们描述了如何将实验设计和内核和内核超参数的选择来调整以减轻模型错误指定。
Gaussian processes are ubiquitous in machine learning, statistics, and applied mathematics. They provide a flexible modelling framework for approximating functions, whilst simultaneously quantifying uncertainty. However, this is only true when the model is well-specified, which is often not the case in practice. In this paper, we study the properties of Gaussian process means when the smoothness of the model and the likelihood function are misspecified. In this setting, an important theoretical question of practial relevance is how accurate the Gaussian process approximations will be given the difficulty of the problem, our model and the extent of the misspecification. The answer to this problem is particularly useful since it can inform our choice of model and experimental design. In particular, we describe how the experimental design and choice of kernel and kernel hyperparameters can be adapted to alleviate model misspecification.
