Georgios Margaritis

Dimitris Bertsimas, Georgios Margaritis

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 black-box, implicit or consist of more general primitives. Trying to address such limitations, Bertsimas and Ozturk (2023) proposed OCTHaGOn as a way of solving black-box global optimization problems by approximating the nonlinear constraints using hyperplane-based Decision-Trees and then using those trees to construct a unified mixed integer optimization (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 machine learning-based constraint approximations, (iii) utilizing robust optimization to account for the uncertainty of the sample-dependent training of the ML models, and (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 or solution times in 11 instances.

Periklis Petridis, Georgios Margaritis, Vasiliki Stoumpou et al.

With the increasing interest in deploying Artificial Intelligence in medicine, we 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.

Georgios Margaritis, Periklis Petridis, Dimitris J. Bertsimas

Recent advancements in machine learning (ML), natural language processing (NLP), and foundational models have shown promise for real-life applications in critical, albeit compute-constrainted fields like healthcare. In such areas, combining foundational models with supervised ML offers potential for automating tasks like diagnosis and treatment planning, but the limited availability of onsite computational resources pose significant challenges before applying these technologies effectively: Current approaches either yield subpar results when using pretrained models without task-specific adaptation, or require substantial computational resources for fine-tuning, which is often a barrier to entry in such environments. This renders them inaccessible in applications where performance and quality standards are high, but computational resources are scarce. To bridge the gap between best-in-class performance and accessibility, we propose a novel method for adapting foundational, multimodal embeddings to downstream tasks, without the need of expensive fine-tuning processes. Our method leverages frozen embeddings from Large Language Models (LLMs) and Vision Models, and uses contrastive learning to train a small, task-specific nonlinear projection that can be used in the downstream task, without having to fine-tune the original foundational models. We show that this efficient procedure leads to significant performance improvements across various downstream tasks, and perhaps more importantly with minimal computational overhead, offering a practical solution for the use of advanced, foundational ML models in resource-constrained settings.