Sequential Supersaturated Screening Experiments
Abstract
Supersaturated screening experiments study many candidate factors with few runs. The experimenter must first identify the active factors, then optimize the response. One-shot regularized regression tends to select many factors, and the second-order response surface model in the selected factors is then large and needs many further runs to fit. We propose Sequential Supersaturated Screening (S3), a two-stage framework for supersaturated designs. S3 builds each screening round by coordinate exchange under a new positive-cone design criterion that uses no practitioner-chosen Welch calibration constant. It then removes low-importance factors one round at a time, using a graduated quantile rule. The criterion scores a design by how far its column correlations sit above the Welch lower bound, and it adapts to the current number of runs and candidate factors. We give a round-by-round bound on the probability that a noise factor is ever fixed, under conditions on noise survival and commitment at each round, together with an explicit upper bound on the total number of Stage 1 runs. Across simulated screening problems and the Borehole benchmark, S3 achieves lower Type I error and higher F1 scores than one-shot cross-validated Lasso (LassoCV). It also improves optimization quality in most settings and runs faster.
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BibTeX
@misc{han2026sequential,
title = {{Sequential Supersaturated Screening Experiments}},
author = {Songqiao Han and Kalliopi Mylona and Steven Gilmour and Matteo Borrotti},
howpublished = {arXiv},
year = {2026},
month = sep,
doi = {10.48550/arxiv.2609.37756},
eprint = {2609.37756},
archivePrefix = {arXiv},
url = {https://arxiv.org/abs/2609.37756},
}
RIS
TY - UNPB
TI - Sequential Supersaturated Screening Experiments
AU - Songqiao Han
AU - Kalliopi Mylona
AU - Steven Gilmour
AU - Matteo Borrotti
PY - 2026
DA - 2026/09/29
PB - arXiv
DO - 10.48550/arxiv.2609.37756
UR - https://arxiv.org/abs/2609.37756
AB - Supersaturated screening experiments study many candidate factors with few runs. The experimenter must first identify the active factors, then optimize the response. One-shot regularized regression tends to select many factors, and the second-order response surface model in the selected factors is then large and needs many further runs to fit. We propose Sequential Supersaturated Screening (S^3), a two-stage framework for supersaturated designs. S^3 builds each screening round by coordinate exchange under a new positive-cone design criterion that uses no practitioner-chosen Welch calibration constant. It then removes low-importance factors one round at a time, using a graduated quantile rule. The criterion scores a design by how far its column correlations sit above the Welch lower bound, and it adapts to the current number of runs and candidate factors. We give a round-by-round bound on the probability that a noise factor is ever fixed, under conditions on noise survival and commitment at each round, together with an explicit upper bound on the total number of Stage 1 runs. Across simulated screening problems and the Borehole benchmark, S^3 achieves lower Type I error and higher F_1 scores than one-shot cross-validated Lasso (LassoCV). It also improves optimization quality in most settings and runs faster.
ER -