AdapDISCOM: An Adaptive Sparse Regression Method for High-Dimensional Multimodal Data With Block-Wise Missingness and Measurement Errors

TL;DR

AdapDISCOM is a new adaptive sparse regression method designed to handle high-dimensional multimodal data with block-wise missingness and measurement errors, improving prediction and feature selection in biomedical applications.

Contribution

It introduces modality-specific weighting schemes and robust variants, with theoretical guarantees and superior performance over existing methods in challenging data scenarios.

Findings

Outperforms existing methods like DISCOM, SCOM, and CoCoLasso in simulations.

Provides reliable biomarker selection and prediction in ADNI data.

Demonstrates robustness under heavy-tailed distributions and data contamination.

Abstract

Multimodal high-dimensional data are increasingly prevalent in biomedical research, yet they are often compromised by block-wise missingness and measurement errors, posing significant challenges for statistical inference and prediction. We propose AdapDISCOM, a novel adaptive direct sparse regression method that simultaneously addresses these two pervasive issues. Building on the DISCOM framework, AdapDISCOM introduces modality-specific weighting schemes to account for heterogeneity in data structures and error magnitudes across modalities. We establish the theoretical properties of AdapDISCOM, including model selection consistency and convergence rates under sub-Gaussian and heavy-tailed settings, and develop robust and computationally efficient variants (AdapDISCOM-Huber and Fast-AdapDISCOM). Extensive simulations demonstrate that AdapDISCOM consistently outperforms existing methods such as DISCOM, SCOM, and CoCoLasso, particularly under heterogeneous contamination and heavy-tailed distributions. Finally, we apply AdapDISCOM to Alzheimers Disease Neuroimaging Initiative (ADNI) data, demonstrating improved prediction of cognitive scores and reliable selection of established biomarkers, even with substantial missingness and measurement errors. AdapDISCOM provides a flexible, robust, and scalable framework for high-dimensional multimodal data analysis under realistic data imperfections.