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arXiv · 2609.24945

Structured Screen-and-Select for Ultra-High-Dimensional Variable Selection

Nilotpal Sanyal·Padmore N. Prempeh
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Abstract

Ultra-high-dimensional data, with p far exceeding n, are common in genomics and biomedical research. Marginal screening can miss active predictors with weak marginal signals, especially under strong predictor correlation. We develop Structured Screen-and-Select Variable Selection (S3VS), an iterative framework that combines outcome-based screening with correlation-based local predictor sets. At each iteration, S3VS identifies leading variables, forms local sets through predictor associations, applies a model-specific selector, aggregates selected and nonselected variables, and updates the candidate set and, when appropriate, the outcome representation. The framework allows flexible leading-variable, local-set, and aggregation rules, with implementations for linear, generalized linear, accelerated failure-time, and Cox models. For a specified one-step linear configuration, we establish sure screening under conditions on proxy coverage, correlation separation, within-set retention, and active-preserving aggregation. Simulations compare full and first-iteration S3VS with one-pass SIS procedures in linear, logistic, and Cox settings. S3VS can improve variable recovery or prediction when correlated predictors provide useful proxy information, although gains depend on predictor structure and selector choice. In ovarian-cancer data, full S3VS with clinical variables showed the strongest internal discrimination and early prediction, whereas SIS--Cox--LASSO with clinical variables showed the strongest external discrimination. Neither molecular approach consistently reduced prediction error, and no gene was selected in all five outer folds. S3VS provides a flexible framework for exploiting predictor dependence before model-specific selection. The method is implemented in the CRAN R package S3VS.

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BibTeXRIS

Nilotpal Sanyal, Padmore N. Prempeh. 2026-09-21. Structured Screen-and-Select for Ultra-High-Dimensional Variable Selection. https://arxiv.org/abs/2609.24945

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