块加性高斯过程在单调性约束下的研究
Block-Additive Gaussian Processes under Monotonicity Constraints
AI总结：
本文提出块加性高斯过程，在输入空间全局施加单调性约束，处理变量交互，开发MaxMod序贯算法用于模型选择，并通过高效计算在高达120维及5D沿海洪水应用中验证性能与可解释性。
摘要：
我们将加性约束高斯过程框架推广到处理输入变量之间的交互作用，同时在输入空间的所有位置强制执行单调性约束。模型的块加性结构特别适合存在交互作用的情况，同时保持计算的可处理性。此外，我们开发了一种用于模型选择（即选择活跃输入变量和块）的序贯算法MaxMod。我们通过高效的矩阵计算以及MaxMod中涉及准则的显式表达式来加速实现。我们的方法的性能和可扩展性通过多个数值示例（维度高达120）以及一个5D真实世界沿海洪水应用得以展示，其中通过选择块增强了可解释性。
英文摘要：
We generalize the additive constrained Gaussian process framework to handle interactions between input variables while enforcing monotonicity constraints everywhere on the input space. The block-additive structure of the model is particularly suitable in the presence of interactions, while maintaining tractable computations. In addition, we develop a sequential algorithm, MaxMod, for model selection (i.e., the choice of the active input variables and of the blocks). We speed up our implementations through efficient matrix computations and thanks to explicit expressions of criteria involved in MaxMod. The performance and scalability of our methodology are showcased with several numerical examples in dimensions up to 120, as well as in a 5D real-world coastal flooding application, where interpretability is enhanced by the selection of the blocks.
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