An Optimal Design Framework for Lasso Sign Recovery

Oregon Convention Center 

Screening designs that do not allow estimation of all effects of interest are often compared under one or more heuristic criteria that in some way measure their proximity to an unattainable orthogonal design. Such criteria do not directly measure a design's quality in terms of screening. To address this disconnect, we develop an optimal design framework to maximize the lasso's sign recovery probability. The proposed criteria have varying amounts of prior knowledge about the model's parameters. We show that an orthogonal design is an ideal structure when the signs of the active factors are unknown. When the signs are assumed known, we show that a design whose columns exhibit small, positive correlations are ideal. These conclusions are based on a new approximate design framework. From this justification, we propose a computationally-efficient design search algorithm that filters through optimal designs under different heuristic criteria to select the one that maximizes the sign recovery probability under the lasso.