With the increasing interest in deploying Artificial Intelligence in medicine, our group previously introduced HAIM (Holistic AI in Medicine), a framework that fuses multimodal data to solve downstream clinical tasks. However, HAIM uses data in a task-agnostic manner and lacks explainability. To address these limitations, we introduce xHAIM (Explainable HAIM), a novel framework leveraging Generative AI to enhance both prediction and explainability through four structured steps: (1) automatically identifying task-relevant patient data across modalities, (2) generating comprehensive patient summaries, (3) using these summaries for improved predictive modeling, and (4) providing clinical explanations by linking predictions to patient-specific medical knowledge. Evaluated on the HAIM-MIMIC-MM dataset, xHAIM improves average AUC from 79.9% to 90.3% across chest pathology and operative tasks. Importantly, xHAIM transforms AI from a black-box predictor into an explainable decision support system, enabling clinicians to interactively trace predictions back to relevant patient data, bridging AI advancements with clinical utility.

Many approaches for addressing global optimization problems typically rely on relaxations of nonlinear constraints over specific mathematical primitives. This is restricting in applications with constraints that are implicit or consist of more general primitives. Trying to address such limitations, Bertsimas and Ozturk (2023) proposed OCTHaGOn as a way of solving very general global optimization problems by approximating the nonlinear constraints using hyperplane-based decision-trees and then using those trees to construct a unified MIO approximation of the original problem. We provide extensions to this approach, by (i) approximating the original problem using other MIO-representable ML models besides decision trees, such as gradient boosted trees, multi layer perceptrons and suport vector machines (ii) proposing adaptive sampling procedures for more accurate ML-based constraint approximations, (iii) utilizing robust optimization to account for the uncertainty of the sample-dependent training of the ML models, (iv) leveraging a family of relaxations to address the infeasibilities of the final MIO approximation. We then test the enhanced framework in 81 global optimization instances. We show improvements in solution feasibility and optimality in the majority of instances. We also compare against BARON, showing improved optimality gaps and solution times in more than 9 instances.