High-dimensional additive Gaussian processes under monotonicity constraints
This work addresses scalability and constraint satisfaction for Gaussian processes in high-dimensional settings, which is important for applications like flood modeling, though it appears incremental as it builds on existing additive GP methods.
The authors tackled the problem of scaling additive Gaussian processes with monotonicity constraints to high dimensions by introducing a framework that guarantees constraint satisfaction everywhere and developing the MaxMod algorithm for dimension reduction. They demonstrated performance on synthetic examples with hundreds of dimensions and a real-world flood application.
We introduce an additive Gaussian process framework accounting for monotonicity constraints and scalable to high dimensions. Our contributions are threefold. First, we show that our framework enables to satisfy the constraints everywhere in the input space. We also show that more general componentwise linear inequality constraints can be handled similarly, such as componentwise convexity. Second, we propose the additive MaxMod algorithm for sequential dimension reduction. By sequentially maximizing a squared-norm criterion, MaxMod identifies the active input dimensions and refines the most important ones. This criterion can be computed explicitly at a linear cost. Finally, we provide open-source codes for our full framework. We demonstrate the performance and scalability of the methodology in several synthetic examples with hundreds of dimensions under monotonicity constraints as well as on a real-world flood application.