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Abstract:
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Supersaturated screening experiments denote the scenario where there are more experimental factors than experimental runs. In this case, traditional Ordinary Least Squares (OLS) methods of factor selection are not possible, and it is common practice to use penalized methods such as the Lasso to select factors. Traditionally, optimal supersaturated design criteria focus on some heuristic measure of orthogonality of the information matrix. These heuristic measures optimize designs with OLS-like analyses in mind. They do not, however, consider the screening properties of the penalized regression analysis methods usually employed to select factors in a supersaturated setting. This paper proposes a design criteria based on the Lasso probability of support recovery and develops the theoretical implications of this criterion. Additionally, an algorithmic approach to constructing Lasso optimal supersaturated designs is presented, with practical considerations to computational expense.
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