K θ (X, X) is a kernel matrix such that each entry [K θ ] i,j = k (x i , x j ). σ 2 y I is the variance of Gaussian noise on the measurements y. Note that the first term encourages the model's fit to the training data, while the second penalizes overly complex models. This inherent regularization is attractive for modelling in a low-data setting, such as the initial stages of a sequntial model-based optimization campaign.