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.

翻译：我们引入了一个加加加高斯进程框架, 计算单一度限制, 并且可以伸缩到高维。 我们的贡献是三重的。 首先, 我们显示我们的框架能够满足输入空间中任何地方的限制。 我们还显示, 更一般的成份线性不平等限制可以相似地处理, 比如成份调和。 其次, 我们提出相继降低维度的添加式 MaxMod 算法。 通过按顺序最大化平方- 北度标准, MaxMod 确定积极的输入维度, 并完善最重要的维度。 这个标准可以用直线成本来明确计算。 最后, 我们为我们的整个框架提供了开放源代码。 我们用数个合成例子展示了该方法的性能和可缩缩放性, 在单一度制约下有数百个维度的合成例子中, 以及在现实世界的洪水应用中 。