In multi-modal biomedical research, integrating high-dimensional genomic data with clinical baselines is essential for precision medicine. However, standard deep neural network approaches often entangle these modalities, obscuring the specific predictive impact of genetic features and leading to possibly suboptimal predictive performance. Motivated by the landmark METABRIC cohort primary breast tumors study, we propose the Stein-Encoder, a white-box supervised framework designed to isolate the genetic signal driving clinical outcomes conditional on nuisance covariates. By leveraging Stein's method and residualization techniques, our approach constructs an interpretable single index that summarizes relevant biological heterogeneity while flexibly incorporating clinical factors and can be used to improve downstream prediction. We establish theoretical guarantees for identification, consistency and efficiency improvement. Applied to the METABRIC cohort, the Stein-Encoder outperforms unsupervised benchmarks in predictive accuracy. Crucially, it achieves structural disentanglement by revealing response-specific biological mechanisms: we find that tumor size is driven primarily by mitotic networks, whereas prognostic indices rely on a distinct proliferation-versus-immune axis. This work contributes a unified, computationally efficient framework that bridges statistical rigor with the representational power of neural networks, enabling interpretable, task-specific and efficient compression of multi-modal health data for a wide range of precision medicine applications, beyond biomarker discovery.

Recently, multimodal electroencephalogram (EEG) learning has shown great promise in disease detection. At the same time, ensuring privacy in clinical studies has become increasingly crucial due to legal and ethical concerns. One widely adopted scheme for privacy protection is differential privacy (DP) because of its clear interpretation and ease of implementation. Although numerous methods have been proposed under DP, it has not been extensively studied for multimodal EEG data due to the complexities of models and signal data considered there. In this paper, we propose a novel Differentially Private Multimodal Laplacian Dropout (DP-MLD) scheme for multimodal EEG learning. Our approach proposes a novel multimodal representative learning model that processes EEG data by language models as text and other modal data by vision transformers as images, incorporating well-designed cross-attention mechanisms to effectively extract and integrate cross-modal features. To achieve DP, we design a novel adaptive feature-level Laplacian dropout scheme, where randomness allocation and performance are dynamically optimized within given privacy budgets. In the experiment on an open-source multimodal dataset of Freezing of Gait (FoG) in Parkinson's Disease (PD), our proposed method demonstrates an approximate 4\% improvement in classification accuracy, and achieves state-of-the-art performance in multimodal EEG learning under DP.