Nested Gaussian process modeling and imputation of high-dimensional incomplete data under uncertainty

Modern healthcare systems are increasingly investing in advanced sensing and information technology, leading to data-rich environments in hospitals. For example, when patients are admitted into an intensive care unit (ICU), it is a common practice to monitor a number of clinical variables, such as blood pressure, heart rate, gas exchange, pulse oximetry and metabolic panel. However, heterogeneous sensing and measurement methods often lead to data uncertainty and incompleteness. Missing values exist pervasively for ICU clinical variables pertinent to a patient’s health condition. This adversely affects time-critical decision making in patient care. Hence, there is an urgent need to develop advanced analytical methods that address the challenges of ICU data uncertainty, provide a robust estimate of health conditions and derive in-depth knowledge for decision making from heterogeneous healthcare recordings. This article presents a novel nested Gaussian process (NGP) model that is tailored to represent multi-dimensional covariance structure of time, variable and patient for high-dimensional data imputation. We evaluate and validate the proposed NGP method on both simulation and real tensor-form ICU data with high-level missing information. Experimental results show that the proposed methodology effectively handles the data uncertainty in ICU settings, which helps further improve the biomarker extraction, patient monitoring and decision making. The proposed NGP model can also be generally applicable to a variety of engineering and medical domains that entail high-dimension data imputation and analytics.