Lasso-optimal supersaturated design and analysis for factor screening in simulation experiments

Complex systems such as large-scale computer simulation models typically involve a large number of factors. When investigating such a system, screening experiments are often used to sift through these factors to identify a subgroup of factors that most significantly influence the interested response. Our work focuses on analysis-method-directed optimal supersaturated designs for high-dimensional screening experiments. A typical screening procedure consists of two steps: the experiment step and the analysis step. With a large number of factors, both of these two steps can be extremely challenging in practice. Currently there exists a disparity between the experimental designs and the analysis methods used for screening experiments. We use supersaturated designs and Lasso for the two steps of screening experiments, respectively. Furthermore, we propose to optimize supersaturated designs toward the best performance of the Lasso. Specifically, we studied the variable selection performances of the lasso under finite samples and establish the exact relationship between the performances and the design matrix; we proposed optimality criteria for constructing supersaturated designs that guarantee optimal variable selection performance, we studied the theoretical properties of the proposed criteria, and further developed efficient algorithms to construct optimal supersaturated designs; and developed a software package capable of constructing optimal supersaturated designs and analyzing data generated from supersaturated experiments, and applied the package and other methods developed to study mission critical computer simulation models. We expect the research to advance the experimental design frontier and have significant impact on analysis of large systems