Interpretable generative and discriminative learning for multimodal and incomplete clinical data

• OSIRIS unifies generative and discriminative formulation in a compact multimodal framework. • Generative part enables semisupervised learning, imputation, and cross-modal links discovery. • Discriminative part enables supervised tasks and biomarker extraction. • Its linear formulation yields interpretable and meaningful results. • OSIRIS clearly outperforms state-of-the-art baselines in classification performance and missing value imputation. Real-world clinical problems are often characterized by multimodal data, usually associated with incomplete views and limited sample sizes in their cohorts, posing significant limitations for machine learning algorithms. In this work, we propose a Bayesian approach designed to efficiently handle these challenges while providing interpretable solutions. Our approach integrates (1) a generative formulation to capture cross-view relationships with a semi-supervised strategy, and (2) a discriminative task-oriented formulation to identify relevant information for specific downstream objectives. This dual generative-discriminative formulation offers both general understanding and task-specific insights; thus, it provides an automatic imputation of the missing views while enabling robust inference across different data sources. The potential of this approach becomes evident when applied to the multimodal clinical data, where our algorithm is able to capture and disentangle the complex interactions among biological, psychological, and sociodemographic modalities. Across nine multimodal datasets, OSIRIS improves the average AUC from about 0.87 for existing methods to 0.92 and increases balanced accuracy from 0.66 to 0.83, achieving state-of-the-art performance on all benchmarks. Notably, OSIRIS remains robust under missing-data conditions, consistently outperforming existing imputation-based approaches. These results show that explicitly disentangling generative and discriminative latent factors yields reliable multimodal learning in low-data regimes.