Emulation and Model Mixing with Random Path Bayesian Additive Regression Trees

Music City Center 

The Bayesian Additive Regression Tree model (BART) has received much attention in recent years as an alternative to Gaussian Process (GP) emulators, particularly in the large sample size and high input dimension settings where GPs struggle with the curse of dimensionality. However, a longstanding limitation has been the discontinuous response surface of the BART model since many emulation problems involve computer simulators which feature smooth, differentiable responses. A smooth version of BART, SBART, was previously introduced, however the approach required joint updates of terminal nodes, and calibration of the prior, particularly balancing the tradeoff between tree-implied localization versus global continuity, could be a challenge. In our work, we introduce a new approach to creating smooth BART response surfaces by using randomized paths (RP). Our proposed RP-BART model retains the conditionally independent updates of terminal node parameters while introducing a cohesive modeling structure that integrates both the localization of the tree and the continuity-inducing randomized splits in a complimentary manner. Borrowing from the GP literature, a lightly data-informed prior calibration of our model is facilitated by deriving the RP-BART semivariogram, which provides for a natural extension of the original BART prior calibration technique. We demonstrate RP-BART on a climate model application where smooth latent RP-BART weight functions are learned to combine an ensemble of climate models for predicting global mean surface temperature.

Digital Engineering