where ŷ (x) and σ(x) are the predicted property of NPM x and its associated uncertainty, respectively, provided by the surrogate model. The parameter β explicitly trades-off exploration and exploitation. If β is large, the UCB tends to select NPMs with the highest uncertainty to explore the feature space. If β is small, the UCB tends to select NPMs with the highest predicted property to exploit our current approximation of the structure-property relationship f (x). To clarify the UCB terminology, the top boundary of the shaded region that bands ŷ (x) in Fig. the UCB for β = 2.