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We introduce an additive Gaussian process framework accounting formonotonicity constraints and scalable to high dimensions. Our contributions arethreefold. First, we show that our framework enables to satisfy the constraintseverywhere in the input space. We also show that more general componentwiselinear inequality constraints can be handled similarly, such as componentwiseconvexity. Second, we propose the additive MaxMod algorithm for sequentialdimension reduction. By sequentially maximizing a squared-norm criterion,MaxMod identifies the active input dimensions and refines the most importantones. This criterion can be computed explicitly at a linear cost. Finally, weprovide open-source codes for our full framework. We demonstrate theperformance and scalability of the methodology in several synthetic exampleswith hundreds of dimensions under monotonicity constraints as well as on areal-world flood application.

High-dimensional additive Gaussian processes under monotonicity constraints