A Unified Information Bottleneck Framework for Multimodal Biomedical Machine Learning

Multimodal biomedical machine learning increasingly integrates heterogeneous data sources (including medical imaging, multi-omics profiles, electronic health records, and wearable sensor signals) to support clinical diagnosis, prognosis, and treatment response prediction. Despite strong empirical performance, most existing multimodal systems lack a principled theoretical foundation for understanding why fusion improves prediction, how information is distributed across modalities, and when models can be trusted under incomplete or shifting data. This paper develops a unified information-theoretic framework that formalizes multimodal biomedical learning as an information optimization problem. We formulate multimodal representation learning through the information bottleneck principle, deriving a variational objective that balances predictive sufficiency against informational compression in an architecture-agnostic manner. Building on this foundation, we introduce information-theoretic tools for decomposing modality contributions via conditional mutual information, quantifying redundancy and synergy, and diagnosing fusion collapse. We further show that robustness to missing modalities can be cast as an information consistency problem and extend the framework to longitudinal disease modeling through transfer entropy and sequential information bottleneck objectives. Applications to multimodal foundation models, uncertainty quantification, calibration, and out-of-distribution detection are developed. Empirical case studies across three biomedical datasets (TCGA breast cancer multi-omics, TCGA glioma clinical-plus-molecular data, and OASIS-2 longitudinal Alzheimer's data) show that the framework's key quantities are computable and interpretable on real data: MI decomposition identifies modality dominance and redundancy; the VMIB traces a compression-prediction tradeoff in the information plane; entropy-based selective prediction raises accuracy from 0.787 to 0.939 at 50% coverage; transfer entropy reveals stage-dependent modality influence in disease progression; and pretraining/adaptation diagnostics distinguish efficient from wasteful fine-tuning strategies. Together, these results develop entropy and mutual information as organizing principles for the design, analysis, and evaluation of multimodal biomedical AI systems.