What question did this study set out to answer?

To develop computationally efficient and theoretically guaranteed screening procedures for identifying critical pairwise interaction effects in ultrahigh-dimensional settings.

February 18, 2014Journal of the American Statistical Association

Interaction Screening for Ultrahigh-Dimensional Data

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To develop computationally efficient and theoretically guaranteed screening procedures for identifying critical pairwise interaction effects in ultrahigh-dimensional settings.
Proposed the forward-selection based framework iFOR, comprising two algorithms (iFORT and iFORM), which greedily identifies interactions while preserving hierarchical model structure.
Utilized ordinary least squares (OLS)-style computations that avoid storing or manipulating the full n × (p² + 3p)/2 augmented design matrix.
Evaluated finite-sample performance through numerical simulations and mathematically derived asymptotic sure screening properties.
Achieved linear computational complexity in terms of predictor count p for sparse models, enabling analysis when predictor dimensions vastly exceed sample size (p ≫ n).
Proved theoretically that the iFOR algorithms retain the sure screening property in ultrahigh-dimensional regimes despite heavy-tailed interaction distributions.
Demonstrated robust finite-sample selection accuracy across numerical experiments without requiring complex numerical optimization solvers.

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Implication

Methodological analysis reveals efficient interaction selection in ultrahigh-dimensional data using forward selection, indicating sure screening properties with minimal computational cost.

Cite This Study

Hao et al. (2014) studied this question.

synapsesocial.com/papers/69d6a4e9f174babf6cab3089 https://doi.org/10.1080/01621459.2014.881741

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Implication

Methodological analysis reveals efficient interaction selection in ultrahigh-dimensional data using forward selection, indicating sure screening properties with minimal computational cost.

Interaction Screening for Ultrahigh-Dimensional Data

Key Points

Discussion

Implication

Cite This Study

Interaction Screening for Ultrahigh-Dimensional Data

Key Points

Discussion

Implication

Cite This Study

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