Landmark-embedded Gaussian process with applications for functional data modeling
提出一种嵌入地标的 Gaussian 过程模型，同时考虑函数型数据的形状和位置信息，用于推断目标变量，并通过纳米传感器校准案例验证效果。
In practice, we often need to infer the value of a target variable from functional observation data. A challenge in this task is that the relationship between the functional data and the target variable is very complex: the target variable not only influences the shape but also the location of the functional data. In addition, due to the uncertainties in the environment, the relationship is probabilistic, that is, for a given fixed target variable value, we still see variations in the shape and location of the functional data. To address this challenge, we present a landmark-embedded Gaussian process model that describes the relationship between the functional data and the target variable. A unique feature of the model is that landmark information is embedded in the Gaussian process model so that both the shape and location information of the functional data are considered simultaneously in a unified manner. Gibbs–Metropolis–Hasting algorithm is used for model parameters estimation and target variable inference. The performance of the proposed framework is evaluated by extensive numerical studies and a case study of nano-sensor calibration.