arXiv subjects

Dimitris Bertsimas

Publications and source records attributed to Dimitris Bertsimas.

At least 37 records · Page 2Linked to original sources

arXiv2025

Detection and Localization of Subdural Hematoma Using Deep Learning on Computed Tomography

Background. Subdural hematoma (SDH) is a common neurosurgical emergency, with increasing incidence in aging populations. Rapid and accurate identification is essential to guide timely intervention, yet existing automated tools focus primarily on detection and provide limited interpretability or spatial localization. There remains a need for transparent, high-performing systems that integrate multimodal clinical and imaging information to support real-time decision-making. Methods. We developed a multimodal deep-learning framework that integrates structured clinical variables, a 3D convolutional neural network trained on CT volumes, and a transformer-enhanced 2D segmentation model for SDH detection and localization. Using 25,315 head CT studies from Hartford HealthCare (2015--2024), of which 3,774 (14.9\%) contained clinician-confirmed SDH, tabular models were trained on demographics, comorbidities, medications, and laboratory results. Imaging models were trained to detect SDH and generate voxel-level probability maps. A greedy ensemble strategy combined complementary predictors. Findings. Clinical variables alone provided modest discriminatory power (AUC 0.75). Convolutional models trained on CT volumes and segmentation-derived maps achieved substantially higher accuracy (AUCs 0.922 and 0.926). The multimodal ensemble integrating all components achieved the best overall performance (AUC 0.9407; 95\% CI, 0.930--0.951) and produced anatomically meaningful localization maps consistent with known SDH patterns. Interpretation. This multimodal, interpretable framework provides rapid and accurate SDH detection and localization, achieving high detection performance and offering transparent, anatomically grounded outputs. Integration into radiology workflows could streamline triage, reduce time to intervention, and improve consistency in SDH management.

cs.CV↗

arXiv2025

Towards Optimal Valve Prescription for Transcatheter Aortic Valve Replacement (TAVR) Surgery: A Machine Learning Approach

Transcatheter Aortic Valve Replacement (TAVR) has emerged as a minimally invasive treatment option for patients with severe aortic stenosis, a life-threatening cardiovascular condition. Multiple transcatheter heart valves (THV) have been approved for use in TAVR, but current guidelines regarding valve type prescription remain an active topic of debate. We propose a data-driven clinical support tool to identify the optimal valve type with the objective of minimizing the risk of permanent pacemaker implantation (PPI), a predominant postoperative complication. We synthesize a novel dataset that combines U.S. and Greek patient populations and integrates three distinct data sources (patient demographics, computed tomography scans, echocardiograms) while harmonizing differences in each country's record system. We introduce a leaf-level analysis to leverage population heterogeneity and avoid benchmarking against uncertain counterfactual risk estimates. The final prescriptive model shows a reduction in PPI rates of 26% and 16% compared with the current standard of care in our internal U.S. population and external Greek validation cohort, respectively. To the best of our knowledge, this work represents the first unified, personalized prescription strategy for THV selection in TAVR.

cs.LG↗

arXiv2025

Sparse Multiple Kernel Learning: Alternating Best Response and Semidefinite Relaxations

We study Sparse Multiple Kernel Learning (SMKL), which is the problem of selecting a sparse convex combination of prespecified kernels for support vector binary classification. Unlike prevailing l1 regularized approaches that approximate a sparsifying penalty, we formulate the problem by imposing an explicit cardinality constraint on the kernel weights and add an l2 penalty for robustness. We solve the resulting non-convex minimax problem via an alternating best response algorithm with two subproblems: the alpha subproblem is a standard kernel SVM dual solved via LIBSVM, while the beta subproblem admits an efficient solution via the Greedy Selector and Simplex Projector algorithm. We reformulate SMKL as a mixed integer semidefinite optimization problem and derive a hierarchy of semidefinite convex relaxations which can be used to certify near-optimality of the solutions returned by our best response algorithm and also to warm start it. On ten UCI benchmarks, our method with random initialization outperforms state-of-the-art MKL approaches in out-of-sample prediction accuracy on average by 3.34 percentage points (relative to the best performing benchmark) while selecting a small number of candidate kernels in comparable runtime. With warm starting, our method outperforms the best performing benchmark's out-of-sample prediction accuracy on average by 4.05 percentage points. Our convex relaxations provide a certificate that in several cases, the solution returned by our best response algorithm is the globally optimal solution.

stat.ML↗

arXiv2025

Overfitting in Adaptive Robust Optimization

Adaptive robust optimization (ARO) extends static robust optimization by allowing decisions to depend on the realized uncertainty - weakly dominating static solutions within the modeled uncertainty set. However, ARO makes previous constraints that were independent of uncertainty now dependent, making it vulnerable to additional infeasibilities when realizations fall outside the uncertainty set. This phenomenon of adaptive policies being brittle is analogous to overfitting in machine learning. To mitigate against this, we propose assigning constraint-specific uncertainty set sizes, with harder constraints given stronger probabilistic guarantees. Interpreted through the overfitting lens, this acts as regularization: tighter guarantees shrink adaptive coefficients to ensure stability, while looser ones preserve useful flexibility. This view motivates a principled approach to designing uncertainty sets that balances robustness and adaptivity.

math.OC↗

arXiv2025

Adaptive Forests For Classification

Random Forests (RF) and Extreme Gradient Boosting (XGBoost) are two of the most widely used and highly performing classification and regression models. They aggregate equally weighted CART trees, generated randomly in RF or sequentially in XGBoost. In this paper, we propose Adaptive Forests (AF), a novel approach that adaptively selects the weights of the underlying CART models. AF combines (a) the Optimal Predictive-Policy Trees (OP2T) framework to prescribe tailored, input-dependent unequal weights to trees and (b) Mixed Integer Optimization (MIO) to refine weight candidates dynamically, enhancing overall performance. We demonstrate that AF consistently outperforms RF, XGBoost, and other weighted RF in binary and multi-class classification problems over 20+ real-world datasets.

cs.LG↗

arXiv2025

Improving Survival Models in Healthcare by Balancing Imbalanced Cohorts: A Novel Approach

We explore whether survival model performance in underrepresented high- and low-risk subgroups - regions of the prognostic spectrum where clinical decisions are most consequential - can be improved through targeted restructuring of the training dataset. Rather than modifying model architecture, we propose a novel risk-stratified sampling method that addresses imbalances in prognostic subgroup density to support more reliable learning in underrepresented tail strata. We introduce a novel methodology that partitions patients by baseline prognostic risk and applies matching within each stratum to equalize representation across the risk distribution. We implement this framework on a cohort of 1,799 patients with resected colorectal liver metastases (CRLM), including 1,197 who received adjuvant chemotherapy and 602 who did not. All models used in this study are Cox proportional hazards models trained on the same set of selected variables. Model performance is assessed via Harrell's C index, time-dependent AUC, and Integrated Calibration Index (ICI), with internal validation using Efron's bias-corrected bootstrapping. External validation is conducted on two independent CRLM datasets. Cox models trained on risk-balanced cohorts showed consistent improvements in internal validation compared to models trained on the full dataset while noticeably enhancing stratified C-index values in underrepresented high- and low-risk strata of the external cohorts. Our findings suggest that survival model performance in observational oncology cohorts can be meaningfully improved through targeted rebalancing of the training data across prognostic risk strata. This approach offers a practical and model-agnostic complement to existing methods, especially in applications where predictive reliability across the full risk continuum is critical to downstream clinical decisions.

stat.ME↗

arXiv2025

TabText: Language-Based Representations of Tabular Health Data for Predictive Modelling

Tabular medical records remain the most readily available data format for applying machine learning in healthcare. However, traditional data preprocessing ignores valuable contextual information in tables and requires substantial manual cleaning and harmonisation, creating a bottleneck for model development. We introduce TabText, a preprocessing and feature extraction method that leverages contextual information and streamlines the curation of tabular medical data. This method converts tables into contextual language and applies pretrained large language models (LLMs) to generate task-independent numerical representations. These fixed embeddings are then used as input for various predictive tasks. TabText was evaluated on nine inpatient flow prediction tasks (e.g., ICU admission, discharge, mortality) using electronic medical records across six hospitals from a US health system, and on nine publicly available datasets from the UCI Machine Learning Repository, covering tasks such as cancer diagnosis, recurrence, and survival. TabText models trained on unprocessed data from a single hospital (572,964 patient-days, Jan 2018-Dec 2020) achieved accurate performance (AUC 0.75-0.94) when tested prospectively on 265,917 patient-days from Jan 2021-Apr 2022, and generalised well to five additional hospitals not used for training. When augmenting preprocessed tabular records with these contextual embeddings, out-of-sample AUC improved by up to 4 additive percentage points in challenging tasks such as ICU transfer and breast cancer recurrence, while providing little to no benefit for already high-performing tasks. Findings were consistent across both private and public datasets.

cs.LG↗

arXiv2025

Should We Relax Stability in Matching Markets?

Centralized assignment markets have historically relied on Deferred-Acceptance (DA) algorithms, which do not incorporate multiple objectives into the assignment. In this work, we propose an optimization-based many-to-one assignment algorithm that explores the trade-offs between minimizing the number of blocking pairs in the match and other important objectives. In order to scale to high-dimensional problems, we develop an algorithm using inverse optimization to obtain the optimal cost vector that implicitly optimizes for stability. This is empirically tested on two application areas for which the DA algorithm is widely used: school assignment and medical residency match. Computational tests on a simulated Boston Public Schools (BPS) match show that this method effectively reduces transportation cost and increases number of students receiving an offer in the first round of match at the expense of a small percentage of blocking pairs. Similar improvement in the number of couples matched to the same location is observed in a synthetic residency match.

math.OC↗

arXiv2025

Global Nonconvex Optimization with Integer Variables

Nonconvex optimization refers to the process of solving problems whose objective or constraints are nonconvex. Historically, this type of problems have been very difficult to solve to global optimality, with traditional solvers often relying on approximate solutions. Bertsimas et al. introduce a novel approach for solving continuous nonconvex optimization problems to provable optimality, called the Relaxation Perspectification Technique - Branch and Bound (RPT-BB). In this paper, we extend the RPT-BB approach to the binary, mixed-binary, integer, and mixed-integer variable domains. We outline a novel branch-and-bound algorithm that makes use of the Relaxation Perspectification Technique (RPT), as well as binary, integer, and eigenvector cuts. We demonstrate the performance of this approach on four representative nonconvex problems, as well as one real-world nonconvex optimization problem, and we benchmark its performance on BARON and SCIP, two state-of-the-art optimization solvers for nonconvex mixed-integer problems. Our results show that our method stands well against BARON, and often outperforms BARON, in terms of computational time and optimal objective value. Moreover, our results show that, while SCIP continues to lead as the state-of-the-art solver, the proposed algorithm demonstrates strong performance on challenging instances, successfully solving problems to global optimality that SCIP and BARON are unable to solve within the time limit.

math.OC↗

arXiv2025

A novel exact approach to polynomial optimization

Polynomial optimization problems represent a wide class of optimization problems, with a large number of real-world applications. Current approaches for polynomial optimization, such as the sum of squares (SOS) method, rely on large-scale semidefinite programs, and therefore the scale of problems to which they can be applied is limited and an optimality guarantee is not always provided. Moreover, the problem can have other convex nonlinear parts, that cannot be handled by these approaches. In this paper, we propose an alternative approach for polynomial optimization. We obtain a convex relaxation of the original polynomial optimization problem, by deriving a sum of linear times convex (SLC) functions decomposition for the polynomial. We prove that such SLC decompositions always exist for arbitrary degree polynomials. Moreover, we derive the SLC decomposition that results in the tightest lower bound, thus improving significantly the quality of the obtained bounds in each node of the spatial Branch and Bound method. In the numerical experiments, we show that our approach outperforms state-of-the-art methods for polynomial optimization, such as BARON and SOS. We show that with our method, we can solve polynomial optimization problems to optimality with 40 variables and degree 3, as well as 20 variables and degree 4, in less than an hour.

math.OC↗

arXiv2025

Holistic Artificial Intelligence in Medicine; improved performance and explainability

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.

cs.AI↗

arXiv2025

From Data to Uncertainty Sets: a Machine Learning Approach

Existing approaches of prescriptive analytics -- where inputs of an optimization model can be predicted by leveraging covariates in a machine learning model -- often attempt to optimize the mean value of an uncertain objective. However, when applied to uncertain constraints, these methods rarely work because satisfying a crucial constraint in expectation may result in a high probability of violation. To remedy this, we leverage robust optimization to protect a constraint against the uncertainty of a machine learning model's output. To do so, we design an uncertainty set based on the model's loss function. Intuitively, this approach attempts to minimize the uncertainty around a prediction. Extending guarantees from the robust optimization literature, we derive strong guarantees on the probability of violation. On synthetic computational experiments, our method requires uncertainty sets with radii up to one order of magnitude smaller than those of other approaches.

cs.LG↗

arXiv2025

Adaptive Optimization for Prediction with Missing Data

When training predictive models on data with missing entries, the most widely used and versatile approach is a pipeline technique where we first impute missing entries and then compute predictions. In this paper, we view prediction with missing data as a two-stage adaptive optimization problem and propose a new class of models, adaptive linear regression models, where the regression coefficients adapt to the set of observed features. We show that some adaptive linear regression models are equivalent to learning an imputation rule and a downstream linear regression model simultaneously instead of sequentially. We leverage this joint-impute-then-regress interpretation to generalize our framework to non-linear models. In settings where data is strongly not missing at random, our methods achieve a 2-10% improvement in out-of-sample accuracy.

cs.LG↗

arXiv2025

Towards Stable Machine Learning Model Retraining via Slowly Varying Sequences

We consider the problem of retraining machine learning (ML) models when new batches of data become available. Existing approaches greedily optimize for predictive power independently at each batch, without considering the stability of the model's structure or analytical insights across retraining iterations. We propose a model-agnostic framework for finding sequences of models that are stable across retraining iterations. We develop a mixed-integer optimization formulation that is guaranteed to recover Pareto optimal models (in terms of the predictive power-stability trade-off) with good generalization properties, as well as an efficient polynomial-time algorithm that performs well in practice. We focus on retaining consistent analytical insights-which is important to model interpretability, ease of implementation, and fostering trust with users-by using custom-defined distance metrics that can be directly incorporated into the optimization problem. We evaluate our framework across models (regression, decision trees, boosted trees, and neural networks) and application domains (healthcare, vision, and language), including deployment in a production pipeline at a major US hospital. We find that, on average, a 2% reduction in predictive power leads to a 30% improvement in stability.

cs.LG↗

arXiv2025

Multimodal Prescriptive Deep Learning

We introduce a multimodal deep learning framework, Prescriptive Neural Networks (PNNs), that combines ideas from optimization and machine learning, and is, to the best of our knowledge, the first prescriptive method to handle multimodal data. The PNN is a feedforward neural network trained on embeddings to output an outcome-optimizing prescription. In two real-world multimodal datasets, we demonstrate that PNNs prescribe treatments that are able to significantly improve estimated outcomes in transcatheter aortic valve replacement (TAVR) procedures by reducing estimated postoperative complication rates by 32% and in liver trauma injuries by reducing estimated mortality rates by over 40%. In four real-world, unimodal tabular datasets, we demonstrate that PNNs outperform or perform comparably to other well-known, state-of-the-art prescriptive models; importantly, on tabular datasets, we also recover interpretability through knowledge distillation, fitting interpretable Optimal Classification Tree models onto the PNN prescriptions as classification targets, which is critical for many real-world applications. Finally, we demonstrate that our multimodal PNN models achieve stability across randomized data splits comparable to other prescriptive methods and produce realistic prescriptions across the different datasets.

cs.LG↗

arXiv2024

Robust and Adaptive Optimization under a Large Language Model Lens

In this paper, we explore the application of ChatGPT in the domain of Robust and Adaptive Robust Optimization. We demonstrate that with appropriate prompting, ChatGPT can be used to auto-formulate and solve simple Robust and Adaptive Optimization Problems. We first develop specialized informational prompts tailored to the domains of Adaptive and Robust Optimization. Then, we show that using these prompts, ChatGPT is able to (i) formulate an optimization problem, (ii) adapt the problem so that it accounts for user-specified uncertainty, (iii) derive the computationally tractable robust counterpart of the problem and (iv) produce executable code that solves the problem. For simple Optimization Problems, we show that ChatGPT is able to perform these steps with little to no errors. We also highlight some instances of erroneous execution of the steps. Overall, we show that using in-context learning, ChatGPT has the potential to adapt to higlhy specialized and niche domains, in which it would otherwise demonstrate very poor out-of-the-box performance.

math.OC↗

arXiv2024

The R.O.A.D. to clinical trial emulation

Observational studies provide the only evidence on the effectiveness of interventions when randomized controlled trials (RCTs) are impractical due to cost, ethical concerns, or time constraints. While many methodologies aim to draw causal inferences from observational data, there is a growing trend to model observational study designs after RCTs, a strategy known as "target trial emulation." Despite its potential, causal inference through target trial emulation cannot fully address the confounding bias in real-world data due to the lack of randomization. In this work, we present a novel framework for target trial emulation that aims to overcome several key limitations, including confounding bias. The framework proceeds as follows: First, we apply the eligibility criteria of a specific trial to an observational cohort. We then "correct" this cohort by extracting a subset that matches both the distribution of covariates and the baseline prognosis of the control group in the target RCT. Next, we address unmeasured confounding by adjusting the prognosis estimates of the treated group to align with those observed in the trial. Following trial emulation, we go a step further by leveraging the emulated cohort to train optimal decision trees, to identify subgroups of patients with heterogeneity in treatment effects (HTE). The absence of confounding is verified using two external models, and the validity of the treatment recommendations is independently confirmed by the team responsible for the original trial we emulate. To our knowledge, this is the first framework to successfully address both observed and unobserved confounding, a challenge that has historically limited the use of randomized trial emulation and causal inference. Additionally, our framework holds promise in advancing precision medicine by identifying patient subgroups that benefit most from specific treatments.

stat.AP↗

arXiv2024

The Benefit of Uncertainty Coupling in Robust and Adaptive Robust Optimization

Despite the modeling power for problems under uncertainty, robust optimization (RO) and adaptive robust optimization (ARO) can exhibit too conservative solutions in terms of objective value degradation compared to the nominal case. One of the main reasons behind this conservatism is that, in many practical applications, uncertain constraints are directly designed as constraint-wise without taking into account couplings over multiple constraints. In this paper, we define a coupled uncertainty set as the intersection between a constraint-wise uncertainty set and a coupling set. We study the benefit of coupling in alleviating conservatism in RO and ARO. We provide theoretical tight and computable upper and lower bounds on the objective value improvement of RO and ARO problems under coupled uncertainty over constraint-wise uncertainty. In addition, we relate the power of adaptability over static solutions with the coupling of uncertainty set. Computational results demonstrate the benefit of coupling in applications.

math.OC↗