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Found 66 papers, 24 papers with code
Towards Stable Machine Learning Model Retraining via Slowly Varying Sequences
In this study, we develop a mixed integer optimization algorithm that holistically considers the problem of retraining machine learning models across different data batch updates.
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.
Universal Neurons in GPT2 Language Models
In other words, are neural mechanisms universal across different models?
Robust Regression over Averaged Uncertainty
We propose a new formulation of robust regression by integrating all realizations of the uncertainty set and taking an averaged approach to obtain the optimal solution for the ordinary least-squared regression problem.
Global Optimization: A Machine Learning Approach
Many approaches for addressing Global Optimization problems typically rely on relaxations of nonlinear constraints over specific mathematical primitives.
The R.O.A.D. to precision medicine
We applied our framework to observational data of patients with gastrointestinal stromal tumors (GIST) and validated the OPTs in an external cohort using the sensitivity and specificity metrics.
Optimal Control of Multiclass Fluid Queueing Networks: A Machine Learning Approach
We use numerical solutions of MFQNET control problems as a training set and apply OCT-H to learn explicit control policies.
A Machine Learning Approach to Two-Stage Adaptive Robust Optimization
We propose an approach based on machine learning to solve two-stage linear adaptive robust optimization (ARO) problems with binary here-and-now variables and polyhedral uncertainty sets.
Compressed Sensing: A Discrete Optimization Approach
We derive a second order cone relaxation of this problem and show that under mild conditions on the regularization parameter, the resulting relaxation is equivalent to the well studied basis pursuit denoising problem.
Improving Stability in Decision Tree Models
Owing to their inherently interpretable structure, decision trees are commonly used in applications where interpretability is essential.
Patient Outcome Predictions Improve Operations at a Large Hospital Network
Problem definition: Access to accurate predictions of patients' outcomes can enhance medical staff's decision-making, which ultimately benefits all stakeholders in the hospitals.
Optimal Low-Rank Matrix Completion: Semidefinite Relaxations and Eigenvector Disjunctions
Low-rank matrix completion consists of computing a matrix of minimal complexity that recovers a given set of observations as accurately as possible.
Finding Neurons in a Haystack: Case Studies with Sparse Probing
Despite rapid adoption and deployment of large language models (LLMs), the internal computations of these models remain opaque and poorly understood.
Ensemble Modeling for Time Series Forecasting: an Adaptive Robust Optimization Approach
Accurate time series forecasting is critical for a wide range of problems with temporal data.
Reducing Air Pollution through Machine Learning
The predictive component of our framework employs various machine learning models, such as gradient-boosted tree-based models and ensemble methods, for time series forecasting.
Multistage Stochastic Optimization via Kernels
We prove that the proposed approach is asymptotically optimal for multistage stochastic optimization with side information.
Global Flood Prediction: a Multimodal Machine Learning Approach
This work presents a novel multimodal machine learning approach for multi-year global flood risk prediction, combining geographical information and historical natural disaster dataset.
Distributionally Robust Causal Inference with Observational Data
We consider the estimation of average treatment effects in observational studies and propose a new framework of robust causal inference with unobserved confounders.
TabText: A Flexible and Contextual Approach to Tabular Data Representation
We show that 1) applying our TabText framework enables the generation of high-performing and simple machine learning baseline models with minimal data pre-processing, and 2) augmenting pre-processed tabular data with TabText representations improves the average and worst-case AUC performance of standard machine learning models by as much as 6%.
Learning Sparse Nonlinear Dynamics via Mixed-Integer Optimization
Discovering governing equations of complex dynamical systems directly from data is a central problem in scientific machine learning.
Integrated multimodal artificial intelligence framework for healthcare applications
The generalizable properties and flexibility of our Holistic AI in Medicine (HAIM) framework could offer a promising pathway for future multimodal predictive systems in clinical and operational healthcare settings.
Robust Upper Bounds for Adversarial Training
We introduce a new approach to adversarial training by minimizing an upper bound of the adversarial loss that is based on a holistic expansion of the network instead of separate bounds for each layer.
Mixed-Integer Optimization with Constraint Learning
The case studies illustrate the framework's ability to generate high-quality prescriptions as well as the value added by the trust region, the use of ensembles to control model robustness, the consideration of multiple machine learning methods, and the inclusion of multiple learned constraints.
Holistic Deep Learning
This paper presents a novel holistic deep learning framework that simultaneously addresses the challenges of vulnerability to input perturbations, overparametrization, and performance instability from different train-validation splits.
Sparse Plus Low Rank Matrix Decomposition: A Discrete Optimization Approach
We study the Sparse Plus Low-Rank decomposition problem (SLR), which is the problem of decomposing a corrupted data matrix into a sparse matrix of perturbations plus a low-rank matrix containing the ground truth.
The Price of Diversity
Systemic bias with respect to gender, race and ethnicity, often unconscious, is prevalent in datasets involving choices among individuals.
Algorithmic Insurance
Specifically, we present an optimization formulation to estimate the risk exposure of a binary classification model given a pre-defined range of premiums.
A new perspective on low-rank optimization
We invoke the matrix perspective function - the matrix analog of the perspective function - and characterize explicitly the convex hull of epigraphs of simple matrix convex functions under low-rank constraints.
Simple Imputation Rules for Prediction with Missing Data: Contrasting Theoretical Guarantees with Empirical Performance
Missing data is a common issue in real-world datasets.
Stochastic Cutting Planes for Data-Driven Optimization
We introduce a stochastic version of the cutting-plane method for a large class of data-driven Mixed-Integer Nonlinear Optimization (MINLO) problems.
Slowly Varying Regression under Sparsity
The algorithm is highly scalable, allowing us to train models with thousands of parameters.
Where to locate COVID-19 mass vaccination facilities?
As compared to benchmarks based on demographic and epidemiological information, the proposed optimization approach increases the effectiveness of the vaccination campaign by an estimated $20\%$, saving an extra $4000$ extra lives in the United States over a three-month period.
Optimal Survival Trees
Tree-based models are increasingly popular due to their ability to identify complex relationships that are beyond the scope of parametric models.
Hurricane Forecasting: A Novel Multimodal Machine Learning Framework
In summary, our work demonstrates that utilizing machine learning techniques to combine different data sources can lead to new opportunities in tropical cyclone forecasting.
Mixed-Projection Conic Optimization: A New Paradigm for Modeling Rank Constraints
We propose a framework for modeling and solving low-rank optimization problems to certifiable optimality.
Frequency Estimation in Data Streams: Learning the Optimal Hashing Scheme
We present a novel approach for the problem of frequency estimation in data streams that is based on optimization and machine learning.
From predictions to prescriptions: A data-driven response to COVID-19
Specifically, we propose a comprehensive data-driven approach to understand the clinical characteristics of COVID-19, predict its mortality, forecast its evolution, and ultimately alleviate its impact.
The Backbone Method for Ultra-High Dimensional Sparse Machine Learning
We present the backbone method, a generic framework that enables sparse and interpretable supervised machine learning methods to scale to ultra-high dimensional problems.
Solving Large-Scale Sparse PCA to Certifiable (Near) Optimality
Sparse principal component analysis (PCA) is a popular dimensionality reduction technique for obtaining principal components which are linear combinations of a small subset of the original features.
Fast Exact Matrix Completion: A Unified Optimization Framework for Matrix Completion
We formulate the problem of matrix completion with and without side information as a non-convex optimization problem.
Personalized Treatment for Coronary Artery Disease Patients: A Machine Learning Approach
We are able to estimate with average R squared = 0. 801 the time from diagnosis to a potential adverse event (TAE) and gain accurate approximations of the counterfactual treatment effects.
On Polyhedral and Second-Order Cone Decompositions of Semidefinite Optimization Problems
We study a cutting-plane method for semidefinite optimization problems (SDOs), and supply a proof of the method's convergence, under a boundedness assumption.
Dynamic optimization with side information
Through a novel measure concentration result for a class of machine learning methods, we prove that the proposed approach is asymptotically optimal for multi-period stochastic programming with side information.
The Price of Interpretability
When quantitative models are used to support decision-making on complex and important topics, understanding a model's ``reasoning'' can increase trust in its predictions, expose hidden biases, or reduce vulnerability to adversarial attacks.
Optimal Explanations of Linear Models
We propose a general optimization framework to create explanations for linear models.
Online Mixed-Integer Optimization in Milliseconds
Compared to state-of-the-art MIO routines, the online running time of our method is very predictable and can be lower than a single matrix factorization time.
A unified approach to mixed-integer optimization problems with logical constraints
We propose a unified framework to address a family of classical mixed-integer optimization problems with logically constrained decision variables, including network design, facility location, unit commitment, sparse portfolio selection, binary quadratic optimization, sparse principal analysis and sparse learning problems.
Certifiably Optimal Sparse Inverse Covariance Estimation
We consider the maximum likelihood estimation of sparse inverse covariance matrices.
From Predictions to Prescriptions in Multistage Optimization Problems
In this paper, we introduce a framework for solving finite-horizon multistage optimization problems under uncertainty in the presence of auxiliary data.
Sparse Regression: Scalable algorithms and empirical performance
A cogent feature selection method is expected to exhibit a two-fold convergence, namely the accuracy and false detection rate should converge to $1$ and $0$ respectively, as the sample size increases.
Methodology
Scalable Holistic Linear Regression
We propose a new scalable algorithm for holistic linear regression building on Bertsimas & King (2016).
The Voice of Optimization
We introduce the idea that using optimal classification trees (OCTs) and optimal classification trees with-hyperplanes (OCT-Hs), interpretable machine learning algorithms developed by Bertsimas and Dunn [2017, 2018], we are able to obtain insight on the strategy behind the optimal solution in continuous and mixed-integer convex optimization problem as a function of key parameters that affect the problem.
Optimization and Control
Interpretable Matrix Completion: A Discrete Optimization Approach
We consider the problem of matrix completion on an $n \times m$ matrix.
Interpretable Clustering via Optimal Trees
State-of-the-art clustering algorithms use heuristics to partition the feature space and provide little insight into the rationale for cluster membership, limiting their interpretability.
Imputation of Clinical Covariates in Time Series
Missing data is a common problem in real-world settings and particularly relevant in healthcare applications where researchers use Electronic Health Records (EHR) and results of observational studies to apply analytics methods.
A Scalable Algorithm For Sparse Portfolio Selection
In numerical experiments, we establish that the outer-approximation procedure gives rise to dramatic speedups for sparse portfolio selection problems.
Optimization and Control
Optimization over Continuous and Multi-dimensional Decisions with Observational Data
We consider the optimization of an uncertain objective over continuous and multi-dimensional decision spaces in problems in which we are only provided with observational data.
Bootstrap Robust Prescriptive Analytics
The associated robust prescriptive methods furthermore reduce to convenient tractable convex optimization problems in the context of local learning methods such as nearest neighbors and Nadaraya-Watson learning.
Sparse Classification and Phase Transitions: A Discrete Optimization Perspective
In this paper, we formulate the sparse classification problem of $n$ samples with $p$ features as a binary convex optimization problem and propose a cutting-plane algorithm to solve it exactly.
Optimization and Control
Sparse High-Dimensional Regression: Exact Scalable Algorithms and Phase Transitions
We present a novel binary convex reformulation of the sparse regression problem that constitutes a new duality perspective.
Sparse Hierarchical Regression with Polynomials
The ability of our method to identify all $k$ relevant inputs and all $\ell$ monomial terms is shown empirically to experience a phase transition.
The Trimmed Lasso: Sparsity and Robustness
Nonconvex penalty methods for sparse modeling in linear regression have been a topic of fervent interest in recent years.
Best Subset Selection via a Modern Optimization Lens
In the last twenty-five years (1990-2014), algorithmic advances in integer optimization combined with hardware improvements have resulted in an astonishing 200 billion factor speedup in solving Mixed Integer Optimization (MIO) problems.
Characterization of the equivalence of robustification and regularization in linear and matrix regression
The notion of developing statistical methods in machine learning which are robust to adversarial perturbations in the underlying data has been the subject of increasing interest in recent years.
A Comparison of Monte Carlo Tree Search and Mathematical Optimization for Large Scale Dynamic Resource Allocation
In this paper, we adapt both MCTS and MO to a problem inspired by tactical wildfire and management and undertake an extensive computational study comparing the two methods on large scale instances in terms of both the state and the action spaces.
From Predictive to Prescriptive Analytics
To demonstrate the power of our approach in a real-world setting we study an inventory management problem faced by the distribution arm of an international media conglomerate, which ships an average of 1bil units per year.
