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

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.