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.
翻译:Gausian 进程在机器学习、统计和应用数学中无处不在。 它们为接近功能提供了一个灵活的建模框架, 同时对不确定性进行量化。 但是, 只有当模型非常具体时, 这一点才是真实的, 而实际上通常并非如此 。 在本文中, 我们研究Gausian 进程的性质意味着当模型的平滑和和可能性函数被错误描述时, 我们研究高斯进程的性质。 在这个环境中, 一个重要的理论相关性问题是, 高斯 进程近似会如何准确地面对问题的困难、 我们的模型和错误区分的程度。 这个问题的答案特别有用, 因为它可以指导我们对模型和实验设计的选择 。 特别是, 我们描述如何调整实验性设计和选择内核和内核超直径计来减轻模型的错误区分 。