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Communication Dans Un Congrès Année : 2022

High-dimensional additive Gaussian processes under monotonicity constraints

Résumé

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.

Dates et versions

hal-03695058 , version 1 (14-06-2022)

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Andrés F. López-Lopera, François Bachoc, O Roustant. High-dimensional additive Gaussian processes under monotonicity constraints. Advances in Neural Information Processing Systems, Nov 2022, New Orleans, United States. ⟨hal-03695058⟩
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