Optimal and Robust Designs for Active Learning and Regression Analysis

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My research program aims to develop both theory and methods of constructing optimal and robust designs of statistical experiments for regression, and of training data selection for active learning. My program consists of the following research problems that I intend to investigate for the next five years. (i) Robust designs for generalized linear mixed models (GLMM). Building on my previous research in this direction, I will continue to work on robust designs for GLMMs with imprecision. Frequently encountered GLMM departures will be considered. I intend to develop a design process that is robust against these departures. I plan to derive sequential designs for a general class of GLMM based on exponential dispersion distributions. Improvement and new methods are expected to better balance the computation complexity and design efficiencies. (ii) Optimal and robust designs for composite quantile regression (CQR). CQR enhances the robustness with least trade-off in efficiency. I intend to construct optimal and robust designs for CQR with two phases: First, I will consider equally weighted CQR and derive robust designs that minimize a specified loss function with respect to the degree of belief on the assumed CQR model. I will then introduce weighted CQR and aim to identify the optimal weights that minimize the estimation bias and further construct optimal designs in order to maximize estimation efficiency. (iii) Optimal and robust designs for accelerated life testing (ALT), incorporating step-stress loading schemes. Building on my research results obtained for optimal/robust constant-stress and simple step-stress ALT designs, I will continue to construct optimal and robust designs for ALT further with step-stress loading. Robustness of the designs will be emphasized to protect possible model departures, including imprecision in life-stress relationship and uncertainty in lifetime distribution. I will extend the previous study to the scenarios that involve heteroscedasticity, multiple factors, multiple step-stress loading, and/or semi-parametric ALT models. (iv) Optimal and robust active learning for linear regression and classification. I will construct optimal and robust designs of training data selection in active learning for both linear regression and classification problems. Optimal active learning is often based on an assumed linear regression model with imprecision, so robustification will be necessary. I also intend to develop optimal and robust active learning process for classification in order to identify a learned discriminant function which can classify the remaining input data points as accurately as possible. As such discriminant functions depend on the parameters in the assumed input distributions, we will use two-stage or sequential designs. Further, I will continue developing and applying the methods of optimal and robust design for various practical applications when optimal planning or finest data selection is needed.