Landmark-embedded Gaussian process with applications for functional data modeling
Landmark-embedded Gaussian process with applications for functional data modeling
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DOI：
10.1080/24725854.2021.1974129
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发表时间：
2021-10
影响因子：
2.6
通讯作者：
Jaesung Lee;Chao Wang;Xiaoyu Sui;Shiyu Zhou;Junhong Chen
中科院分区：
文献类型：
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作者：
Jaesung Lee;Chao Wang;Xiaoyu Sui;Shiyu Zhou;Junhong Chen
摘要在实际应用中，我们经常需要从函数观测数据中推断出目标变量的值。这项任务的一个挑战是函数数据和目标变量之间的关系非常复杂：目标变量不仅影响函数数据的形状，还影响函数数据的位置。此外，由于环境中的不确定性，这种关系是概率的，即对于给定的固定目标变量值，我们仍然可以看到函数数据的形状和位置的变化。为了解决这一挑战，我们提出了一个具有里程碑意义的嵌入的高斯过程模型，该模型描述了函数数据和目标变量之间的关系。该模型的一个独特特点是将地标信息嵌入到高斯过程模型中，从而以统一的方式同时考虑功能数据的形状和位置信息。模型参数估计和目标变量推理采用Gibbs-Metropolis-Hasting算法。通过大量的数值研究和纳米传感器标定的实例研究，对该框架的性能进行了评估。
Abstract 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.