In the context of Gaussian process regression with functional inputs, it is common to treat the input as a vector. The parameter space becomes prohibitively complex as the number of functional points increases, effectively becoming a hindrance for automatic relevance determination in high-dimensional problems. Generalizing a framework for time-varying inputs, we introduce the asymmetric Laplace functional weight (ALF): a flexible, parametric function that drives predictive relevance over the index space. Automatic dynamic relevance determination (ADRD) is achieved with three unknowns per input variable and enforces smoothness over the index space. Additionally, we discuss a screening technique to assess under complete absence of prior and model information whether ADRD is reasonably consistent with the data. Such tool may serve for exploratory analyses and model diagnostics. ADRD is applied to remote sensing data and predictions are generated in response to atmospheric functional inputs. Fully Bayesian estimation is carried out to identify relevant regions of the functional input space. Validation is performed to benchmark against traditional vector-input model specifications. We find that ADRD outperforms models with input dimension reduction via functional principal component analysis. Furthermore, the predictive power is comparable to high-dimensional models, in terms of both mean prediction and uncertainty, with 10 times fewer tuning parameters. Enforcing smoothness on the predictive relevance profile rules out erratic patterns associated with vector-input models.

翻译：在高斯进程回归和功能性投入的背景下,通常将输入视为矢量。参数空间随着功能点数量的增加而变得令人望而却步地复杂。参数空间随着功能点数量的增加而变得令人望而却步地复杂,实际上成为了在高度问题中自动确定相关性的障碍。对时间变化输入框架的概括化,我们引入了不对称拉皮尔功能重量(ALF):一个灵活和参数性功能性功能性功能性功能性功能性功能性功能性功能性功能性功能性功能性功能(ADRD):一个灵活和参数性功能性功能性功能性输入空间的关联性能确定(ADRD),以三种未知的输入变量变量变量来进行自动动态相关性确定(ADRD), 并在完全缺乏先前和模型性能性信息性信息性信息性的情况下,我们讨论一种筛选技术,以便在完全没有事先和模型性能性能性能性能评估ADRDD是否与数据相对一致。ADRDRDD可用于探索和稳定度模型的高度相关性,在10级值性模型上,在稳定性模型上与稳定性模型上比。