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GIDS addresses a critical bottleneck in high-dimensional cross-modal analysis by simultaneously reducing both predictor and response dimensions, overcoming the computational and interpretability limits of existing methods that only filter predictors. The framework's ability to efficiently handle massive, noisy datasets—demonstrated here with over 865,000 methylation and 49,000 transcriptomic variables—makes it a practical advancement for scalable machine learning pipelines. By uncovering blockwise interaction structures, this approach offers a theoretically grounded solution for improving accuracy and tractability in complex multimodal modeling tasks.
A Fast Screening Approach for High-dimensional Outcomes and High-dimensional Predictors
arXiv:2606.03018v1 Announce Type: cross Abstract: Modeling interactions among multimodal, high-dimensional data is intrinsically challenging due to ultra-high dimensionality and complex dependence structure with high level noise. Screening methods are effective for reducing dimensionality, but most existing approaches shrink only the predictor space while retaining all outcomes. In cross-modal analyses, different outcomes often select different predictor subsets, so the union remains large and the response dimension is unchanged, limiting the practical benefit of screening. This gives rise to heavy computational burdens and poor interpretability. To address these limitations, we propose a new screening framework, Graph Independence Dual Screening (GIDS), which simultaneously reduces the dimensionality of response variables and predictors. We design computationally efficient algorithms that facilitate downstream selection procedures, improving accuracy and scalability, and establish supporting theoretical results. Extensive simulation studies demonstrate that GIDS outperforms existing methods that screen only predictors. To illustrate its utility, we applied GIDS to the Alzheimer's Disease Neuroimaging Initiative (ADNI) dataset, analyzing interactions between genome-wide 865,353 DNA methylation and 49,386 transcriptomic variables. GIDS reduced the feature space to approximately 9,000 CpGs and 2,000 transcripts, uncovering blockwise interaction structures: clusters of CpG sites and gene transcripts with strong associations. These findings not only improve computational tractability but also yield interpretable biological insights, highlighting coordinated regulatory mechanisms underlying Alzheimer's disease.
Abstract:Modeling interactions among multimodal, high-dimensional data is intrinsically challenging due to ultra-high dimensionality and complex dependence structure with high level noise. Screening methods are effective for reducing dimensionality, but most existing approaches shrink only the predictor space while retaining all outcomes. In cross-modal analyses, different outcomes often select different predictor subsets, so the union remains large and the response dimension is unchanged, limiting the practical benefit of screening. This gives rise to heavy computational burdens and poor interpretability. To address these limitations, we propose a new screening framework, Graph Independence Dual Screening (GIDS), which simultaneously reduces the dimensionality of response variables and predictors. We design computationally efficient algorithms that facilitate downstream selection procedures, improving accuracy and scalability, and establish supporting theoretical results. Extensive simulation studies demonstrate that GIDS outperforms existing methods that screen only predictors. To illustrate its utility, we applied GIDS to the Alzheimer's Disease Neuroimaging Initiative (ADNI) dataset, analyzing interactions between genome-wide 865,353 DNA methylation and 49,386 transcriptomic variables. GIDS reduced the feature space to approximately 9,000 CpGs and 2,000 transcripts, uncovering blockwise interaction structures: clusters of CpG sites and gene transcripts with strong associations. These findings not only improve computational tractability but also yield interpretable biological insights, highlighting coordinated regulatory mechanisms underlying Alzheimer's disease.
Methodology (stat.ME); Machine Learning (cs.LG); Statistics Theory (math.ST); Machine Learning (stat.ML)
arXiv:2606.03018 [stat.ME]
(or arXiv:2606.03018v1 [stat.ME] for this version)
https://doi.org/10.48550/arXiv.2606.03018 Focus to learn more arXiv-issued DOI via DataCite (pending registration)
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