Sensing, Modeling and Optimization of Cardiac Systems by Hui Yang & Bing Yao

Author:Hui Yang & Bing Yao
Language: eng
Format: epub
ISBN: 9783031359521
Publisher: Springer Nature Switzerland

Second, we will model using a level-II GP model as , where represents the covariance between patients (e.g., and ). This proposed hierarchical design handles nonstationarity in the underlying stochastic process through GP modeling of mean functions. In real-world environment, the joint distribution of tensor data will change over time. Traditional models with stationary assumptions (e.g., principal component analysis and regression models) are limited in their ability to readily address time-varying structures. The proposed level-II GP model leverages covariance structure among patients to model the nonstationary mean function . If two patients share closer values in clinical variables, they tend to have a stronger correlation. Therefore, the covariance function is defined as: .

Third, the level-III GP is constructed to model the mean function of as , where the covariance function is to capture the similarity between clinical variables (e.g., and ), and it is akin to the definition of . Here, is the average of tensor data across the time and patient dimensions, for a specific clinical variable. Here, is the time duration for patient . As opposed to 1-dimensional correlation in traditional models, the NGP model formulation captures 3-dimensional correlation structure (i.e., time, patients, and clinical variables) specific to order-3 tensor data. As a result, the NGP model offers a higher level of capability and flexibility to impute missing values in high-dimensional tensor data.

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