论文标题
在单调性约束下的高维加性高斯过程
High-dimensional additive Gaussian processes under monotonicity constraints
论文作者
论文摘要
我们引入了一个添加性高斯流程框架，该框架对单调性约束，可扩展到高维度。我们的贡献是三倍。首先，我们证明我们的框架使能够满足输入空间中各地的约束。我们还表明，可以类似地处理更通用的构成线性不等式约束，例如componentwise凸度。其次，我们提出了用于顺序尺寸降低的添加剂maxmod算法。通过依次最大化平方标准标准，MaxMod可以识别活动的输入尺寸并完善最重要的输入尺寸。可以以线性成本明确计算此标准。最后，我们为我们的完整框架提供开源代码。我们在几个合成示例中证明了该方法的性能和可伸缩性，这些综合示例在单调性约束以及现实世界的洪水应用下具有数百个维度。
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.
