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

Hierarchical Gaussian Process Modeling and Estimation of State-action Transition Dynamics in Breast Cancer

Breast cancer is the most prevalent type of cancer in the US. Available treatments, including mastectomy, radiation, and chemotherapy, vary in curability, cost, and mortality probability of patients. This research aims at tracking the result of post-treatment for evidence-based decision making in breast cancer. Based on available big data, we implemented conditional probability to estimate multi-age transition probability matrices to predict the progression of disease conditions. The patient state is defined based on patients' age, cancer stage, and treatment history. To tackle the incomplete data in the matrix, we design a novel Hierarchical Gaussian Distribution (HGP) to estimate the missing part of the table. The HGP model leads to the lowest Root Mean Square Error (RMSE), which is 35% lower than the Gaussian Process and 40% lower than Linear Regression. Results of transition probability estimation show that the chance of survival within a year for 40 to 50 years old patient with the distant stage of cancer is 96.5%, which is higher than even younger age groups.

Intrinsic recurrence quantification analysis of nonlinear and nonstationary short-term time series

Recurrence analysis is a powerful tool to appraise the nonlinear dynamics of complex systems and delineate the inherent laminar, divergent, or transient behaviors. Oftentimes, the effectiveness of recurrence quantification hinges upon the accurate reconstruction of the state space from a univariate time series with a uniform sampling rate. Few, if any, existing approaches quantify the recurrence properties from a short-term time series, particularly those sampled at a non-uniform rate, which are fairly ubiquitous in studies of rare or extreme events. This paper presents a novel intrinsic recurrence quantification analysis to portray the recurrence behaviors in complex dynamical systems with only short-term observations. As opposed to the traditional recurrence analysis, the proposed approach represents recurrence dynamics of a short-term time series in an intrinsic state space formed by proper rotations, attained from intrinsic time-scale decomposition (ITD) of the short time series. It is shown that intrinsic recurrence quantification analysis (iRQA), patterns harnessed from the corresponding recurrence plot, captures the underlying nonlinear and nonstationary dynamics of those short time series. In addition, as ITD does not require uniform sampling of the time series, iRQA is also applicable to unevenly spaced temporal data. Our findings are corroborated in two case studies: change detection in the Lorenz time series and early-stage identification of atrial fibrillation using short-term electrocardiogram signals.

Heterogeneous Recurrence Analysis of Disease-Altered Spatiotemporal Patterns in Multi-Channel Cardiac Signals

Heart diseases alter the rhythmic behaviors of cardiac electrical activity. Recent advances in sensing technology bring the ease to acquire space-time electrical activity of the heart such as vectorcardiogram (VCG) signals. Recurrence analysis of successive heartbeats is conducive to detect the disease-altered cardiac activities. However, conventional recurrence analysis is more concerned about homogeneous recurrences, and overlook heterogeneous types of recurrence variations in VCG signals (i.e., in terms of state properties and transition dynamics). This paper presents a new framework of heterogeneous recurrence analysis for the characterization and modeling of disease-altered spatiotemporal patterns in multi-channel cardiac signals. Experimental results show that the proposed approach yields an accuracy of 96.9%, a sensitivity of 95.0%, and a specificity of 98.7% for the identification of myocardial infarctions. The proposed method of heterogeneous recurrence analysis shows strong potential to be further extended for the analysis of other physiological signals such as electroencephalogram (EEG) and electromyography (EMG) signals towards medical decision making.

Multi-fidelity modeling in sequential design for stability identification in dynamic time-delay systems

Time delay arises in a variety of real-world complex systems. A high-fidelity simulation generally renders high accuracy to simulate the dynamic evolution of such complex systems and appraise quantity of interest for process design and response optimization. Identification of limit states exemplifies such applications, which outlines the boundary that separates distinct regions (e.g., stability region) in parameter space. While design of experiments is the common procedure to evaluate decision functions to sketch the boundary, it crucially relies on the quantity and quality of sampling points. This has made it infeasible to explore a large parameter design space with expensive-to-evaluate high-fidelity simulations. Furthermore, the complex contour of stability region in time-delay systems nullifies most existing sequential design paradigms, including adaptive classification approaches. On the other hand, low-fidelity surrogate modeling efficiently emulates a high-fidelity simulation, albeit at the expense of accuracy, not ideal to inspect the system behavior near the critical boundary. In this study, we investigate a multifidelity approach to delineate the stability region in a sequential fashion: sampling points are first evaluated by the low-fidelity surrogate modeling, and only those selected according to the exploration-exploitation trade-off principle are then assessed by a high-fidelity simulation to approximate the stability boundary. The application in a numerical case study of the delayed Mathieu equation as well as a real-world machining process corroborates the proposed approach.