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

The rapid advancement of multi-omics integration facilitates deep insights into complex diseases. However, incomplete modalities, heterogeneity, and high dimensionality hinder robust analysis. To address these limitations, we propose entropy-guided sample-specific feature selection for robust incomplete multi-omics learning (ESSFS-IMO), a novel framework for accurate disease prediction and interpretable biomarker discovery under missing-data conditions. It combines instance-wise feature selection, entropy-adaptive optimization, and variational representation learning. Specifically, a Gumbel-Softmax-based selector performs per-sample differentiable feature selection, guided by an entropy-based annealing strategy that dynamically adjusts selection sharpness. Selected features are integrated via an information-bottlenecked variational backbone with variance-weighted fusion, enabling robust classification despite missing modalities. Experiments on inflammatory bowel disease datasets demonstrate that ESSFS-IMO outperforms state-of-the-art baselines in accuracy, F1-score, and area under the receiver operating characteristic curve. The model maintains high performance across missing patterns and yields biologically coherent biomarkers, effectively linking microbial, transcriptional, and metabolic profiles to immune regulation. In conclusion, ESSFS-IMO provides a robust, interpretable solution for incomplete multi-omics learning. By integrating entropy-guided selection and variational information bottlenecks, it achieves superior predictive power and resilience while identifying meaningful signatures associated with intestinal inflammation, holding promise for broader biomedical applications.