Entropy-Guided Sample-Specific Feature Selection for Robust Incomplete Multi-Omics Learning in Gut Microbiome Disease Prediction and Biomarker Discovery

Abstract The rapid advances in multi-omics data integration technologies have opened unprecedented avenues for dissecting the mechanisms and accelerating the clinical translation of complex diseases. Nevertheless, the frequent absence of certain modalities, coupled with the inherent heterogeneity and high dimensionality of the data, severely restrict the effectiveness of integrative analysis. To address these challenges, we introduce Entropy-guided Sample-Specific Feature Selection for Incomplete Multi-Omics Learning (ESSFS-IMO), a novel framework that couples instance-wise feature selection with entropy-adaptive optimization and variational representation learning. Concretely, ESSFS-IMO leverages a Gumbel– SoftMax selector parameterized by a neural network to achieve per-sample feature selection, while an entropy-based annealing strategy adaptively controls selector sharpness. The selected features are integrated through an information-bottlenecked variational backbone with variance-weighted fusion, enabling robust classification under arbitrary missing patterns. Extensive experiments on inflammatory bowel disease (IBD) multi-omics datasets demonstrate that ESSFS-IMO consistently outperforms state-of-the-art baselines in terms of accuracy, F1 and AUC. Competing Interest Statement The authors have declared no competing interest. Funding Statement Research on this work is partially supported by grants from the National Natural Science Foundation of China (No. 62566041). Author Declarations I confirm all relevant ethical guidelines have been followed, and any necessary IRB and/or ethics committee approvals have been obtained. Yes The details of the IRB/oversight body that provided approval or exemption for the research described are given below: I confirm that all necessary patient/participant consent has been obtained and the appropriate institutional forms have been archived, and that any patient/participant/sample identifiers included were not known to anyone (e.g., hospital staff, patients or participants themselves) outside the research group so cannot be used to identify individuals. Yes I understand that all clinical trials and any other prospective interventional studies must be registered with an ICMJE-approved registry, such as ClinicalTrials.gov. I confirm that any such study reported in the manuscript has been registered and the trial registration ID is provided (note: if posting a prospective study registered retrospectively, please provide a statement in the trial ID field explaining why the study was not registered in advance). Yes I have followed all appropriate research reporting guidelines, such as any relevant EQUATOR Network research reporting checklist(s) and other pertinent material, if applicable. Yes Data Availability All data produced are available online at https://www.ibdmdb.org