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High-dimensional Additive Gaussian Processes under Monotonicity Constraints
Andrés López-Lopera · Francois Bachoc · Olivier Roustant

Wed Nov 30 02:00 PM -- 04:00 PM (PST) @ Hall J #503

We introduce an additive Gaussian process (GP) 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.

Author Information

Andrés López-Lopera (Univ. Polytechnique Hauts-de-France (UPHF))
Francois Bachoc (Institut de Mathématiques de Toulouse)
Olivier Roustant (Institut National des Sciences Appliquées de Toulouse)

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