Model selection aims to find the best model in terms of accuracy, interpretability or simplicity, preferably all at once. In this work, we focus on evaluating model performance of Gaussian process models, i.e. finding a metric that provides the best trade-off between all those criteria. While previous work considers metrics like the likelihood, AIC or dynamic nested sampling, they either lack performance or have significant runtime issues, which severely limits applicability. We address these challenges by introducing multiple metrics based on the Laplace approximation, where we overcome a severe inconsistency occuring during naive application of the Laplace approximation. Experiments show that our metrics are comparable in quality to the gold standard dynamic nested sampling without compromising for computational speed. Our model selection criteria allow significantly faster and high quality model selection of Gaussian process models.

翻译：模型选择旨在找到准确性、可解释性或简洁性方面最优的模型，理想情况下能同时满足所有标准。本研究聚焦于评估高斯过程模型的性能，即寻找能够平衡上述所有准则的指标。现有方法采用的似然函数、AIC或动态嵌套采样等指标，要么性能不足，要么存在显著的计算耗时问题，严重限制了实际应用。我们通过引入基于拉普拉斯近似的多个指标来解决这些挑战，并克服了直接应用拉普拉斯近似时出现的严重不一致性。实验表明，我们的指标在不牺牲计算速度的前提下，其质量可与金标准动态嵌套采样相媲美。所提出的模型选择准则能够实现高斯过程模型快速且高质量的模型选择。