Block-Additive Gaussian Processes under Monotonicity Constraints

We generalize the additive constrained Gaussian process framework to handle interactions between input variables while enforcing monotonicity constraints everywhere on the input space. The block-additive structure of the model is particularly suitable in the presence of interactions, while maintaining tractable computations. In addition, we develop a sequential algorithm, MaxMod, for model selection (i.e., the choice of the active input variables and of the blocks). We speed up our implementations through efficient matrix computations and thanks to explicit expressions of criteria involved in MaxMod. The performance and scalability of our methodology are showcased with several numerical examples in dimensions up to 120, as well as in a 5D real-world coastal flooding application, where interpretability is enhanced by the selection of the blocks.