This paper uses MIO to select features for kernel SVM classification.
problem Feature selection for kernel SVM classification.
method Mixed-integer optimization (MIO) for feature subset selection.
result The MIO approach can often outperform linear-SVM-based methods in prediction performance.
Solves the film scheduling and staggered showtimes problem for movie theaters.
problem Maximize attendance and revenue by scheduling films with staggered showtimes.
method Binary integer linear optimization to find optimal schedules for each cluster of neighboring locations.
result Optimal scheduling cannot be done for all locations at once, but must be done for each cluster.
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 proble…
Paper proposes algorithms for BMF using integer programming.
problem Approximating binary input matrix as product of two smaller binary factors.
method Alternating optimization strategy using integer programming to solve subproblems and combine solutions.
result Proposed algorithms outperform state of the art on medium-scale problems.
We introduce Supersparse Linear Integer Models (SLIM) as a tool to create scoring systems for binary classification. We derive theoretical bounds on the true risk of SLIM scoring systems, and present experimental results to show that SLIM scoring systems are accurate, sparse, and interpretable classification models.
Transformers improve solving mixed-integer programs, especially CLSP.
problem Solving Capacitated Lot Sizing Problem (CLSP) with mixed-integer programming.
method Employing transformer models to predict binary variables in CLSP.
result Transformer model outperforms CPLEX and LSTM in solving CLSP.
MIP-GNN uses graph neural networks to predict variable biases for MIP solvers.
problem Improving combinatorial optimization through data-driven insights.
method Encoding MILP interactions as graphs, training a graph neural network to predict variable biases, and guiding the MIP solver with these predictions.
result Significant improvements in solving binary MILPs compared to default settings of state-of-the-art solvers.
We propose a faster and more accurate method for learning classification trees.
problem Learning optimal binary classification trees is challenging and slow.
method We introduce a stronger MIP formulation and Benders' decomposition method.
result Our method is 50 times faster and improves out-of-sample performance.
New MIP algorithms improve sparse classifier learning times.
problem Sparse classifier learning at large scales.
method Developed exact and approximate MIP algorithms for ℓ0-regularized classification. result Significantly improved statistical performance compared to existing methods.
New conic quadratic formulations improve outlier detection in regression models.
problem Detecting outliers in regression models with corrupted data.
method Deriving stronger second-order conic relaxations without big-M constraints.
result Proposed formulations are significantly faster than existing methods.
New method learns BN structures from data efficiently.
problem Learning sparse DAG structure of BN from continuous data.
method Consistent second-order conic integer programming with early stopping criterion.
result Near-optimal solutions to medium-size problems within reasonable time.
Paper proposes methods to improve SVM classifiers in noisy data scenarios.
problem Improving SVM classifiers when training data contains label noise.
method Mixed Integer Linear and Non Linear models with relabeling and clustering.
result Effective methods improve SVM performance in noisy data scenarios.
A new framework for sparse regression models with slow variations.
problem Parameter estimation for sparse regression models with slow variations.
method Formulated as a mixed-integer optimization problem, then reformulated as a binary convex optimization problem with a novel relaxation technique.
result Efficiently solves the problem to provable optimality using a cutting plane-type algorithm.
The paper develops algorithms for Boolean matrix factorization using IP and heuristics.
problem Approximating binary input matrices as products of smaller binary factors.
method Alternating optimization with integer programming and greedy/local-search heuristics.
result Proposed methods improve scalability and performance compared to existing techniques.
New model guarantees integer optimal solutions for combinatorial problems.
problem Finding optimal solutions for combinatorial problems with costly or noisy evaluations.
method Developed a surrogate model with integer-valued minima for combinatorial optimization.
result Outperforms other optimization algorithms on specific combinatorial problems.
Paper develops machine learning algorithms to learn optimal integer weights for clinical risk scores.
problem Deriving optimal integer weights for clinical risk scores without computational burden.
method Flexible greedy optimization strategy to directly optimize a value function.
result Constructed an integer-weighted comorbidity score for measuring post-discharge mortality risk.
Paper proposes a novel optimization method for disaggregating smart meter data.
problem Energy disaggregation, inferring appliance-specific energy consumption from aggregate meter data.
method Two-stage optimization approach: first phase uses mixed integer programming, second phase binary quadratic optimization with penalty terms and appliance constraints.
result Proposed method successfully reconstructs appliance signatures, overcoming previous optimization-based methods' limitations.
Paper designs optimal ECOCs using IP for robust multiclass classification.
problem Designing robust ECOCs for multiclass classification.
method Integer Programming formulation to minimize codebooks with desirable error-correcting properties, leveraging graph-theoretic structure and edge clique covers.
result IP-generated codebooks achieve high nominal and robust adversarial accuracy.
New method learns binary decision trees efficiently.
problem Learning binary decision trees for data partitioning.
method Argmin differentiation for discrete and continuous parameters.
result Produces competitive binary trees with fast training.
The paper analyzes financial networks with default charges and defines a model using fixpoint problems.
problem Modeling systemic risk in interbank networks with crossholdings and default charges.
method Mixed integer-linear programming and Gaussian elimination algorithm for computing clearing pairs.
result Developed methods to compute maximal and minimal clearing pairs.
We propose a novel high-dimensional linear regression estimator: the Discrete Dantzig Selector, which minimizes the number of nonzero regression coefficients subject to a budget on the maximal absolute correlation between the features and residuals. Motivated by the significant advances in integer optimization over the…
Differentiable cutting-plane layers solve parametric mixed-integer linear optimization problems.
problem Solving parametric mixed-integer linear optimization problems with changing data.
method Introducing cutting-plane layers (CPLs) for differentiable cutting-plane generation.
result The algorithm computes solutions with low integrality gaps and generalizes to unseen instances.
Optimal binning method for numeric targets using mathematical programming.
problem Optimizing the discretization of numeric variables for classification.
method Mathematical programming formulation for binary, continuous, and multi-class targets with constraints.
result Convex mixed-integer programming formulations for all target types.
Unified framework designs LK structures using integer twists on non-manifold meshes.
problem Binary twisting limits topological possibilities and structural behaviors.
method Generalizes twist formulation to arbitrary integer labels for non-manifold meshes.
result Integer twists enable full connectivity and dynamic folding/articulation.
Proposes a novel SVM model for binary classification with different misclassification costs.
problem Real-world classification problems with varying misclassification costs.
method Incorporates performance constraints in SVM formulation to seek a hyperplane with maximal margin and misclassification rates below given thresholds.
result The proposed model gives users control over misclassification rates in one class at the expense of the other.
A novel method relaxes binary constraints to non-negative spheres for multi-matching and clustering.
problem Optimization problems over binary matrices with injectivity constraints.
method Non-negative spherical relaxation followed by conditional power iteration.
result Automatic adjustment of the continuous parameter related to universe size.
Study counterfactuals in combinatorial choice using a representative agent model.
problem Analyzing decision-making from aggregated binary polytope data.
method Nonparametric approach based on a representative agent model, solving polynomial and mixed-integer convex programs.
result Developed a method for counterfactual prediction that works even under model misspecification.
AF improves classification models by adaptively weighting trees.
problem Improving classification model performance.
method AF combines OP2T for input-dependent weights and MIO for dynamic refinement.
result AF consistently outperforms RF, XGBoost, and other weighted RF.
MVRSM optimizes expensive functions with mixed variables, outperforming state-of-the-art methods.
problem Minimizing expensive functions with mixed continuous and integer variables.
method Mixed-Variable ReLU-based Surrogate Modelling (MVRSM) using rectified linear units.
result MVRSM outperforms state-of-the-art methods on synthetic and real-life benchmarks.
We present a binary code for spinors and Clifford multiplication using non-negative integers and their binary expressions, which can be easily implemented in computer programs for explicit calculations. As applications, we present explicit descriptions of the triality automorphism of Spin(8), explicit representations…
The European market clearing problem is characterized by a set of heterogeneous orders and rules that force the implementation of heuristic and iterative solving methods. In particular, curtailable block orders and the uniform purchase price (UPP) pose serious difficulties. A block is an order that spans over multiple …
Sharp bounds on binary model inference performance.
problem High-dimensional inference in binary models.
method Convex empirical risk minimization, sharp asymptotics, optimal performance bounds.
result Sharp predictions and optimal performance bounds for binary models.
Deep neural networks (DNN) are powerful models for many pattern recognition tasks, yet their high computational complexity and memory requirement limit them to applications on high-performance computing platforms. In this paper, we propose a new method to evaluate DNNs trained with 32bit floating point (float32) accura…
New algorithm for nonnegative tensor completion with linear convergence rate.
problem Tensor completion without known optimal sample complexity rate.
method Integer optimization using a specific 0-1 polytope gauge norm.
result Achieves information-theoretic rate with linear convergence.
A new portfolio optimization model minimizes maximum drawdown, offering faster and more robust solutions.
problem Optimizing portfolios during financial distress, especially during crises.
method Linearization of Markowitz model based on maximum drawdown, with a Mixed-Integer Linear Programming variation.
result 200 times faster solving time with a more profitable and robust solution.
New method trains Boltzmann machines without supervision.
problem Training unsupervised learning models.
method Mixed binary quadratic feasibility problem formulation.
result Theory validated on XOR patterns.
Paper proves EM algorithm convergence for mixtures of discrete and continuous parameters.
problem Nontrivial convergence analysis for EM algorithms with mixed-integer parameters.
method Introduces conditions for EM convergence in mixed-integer optimization.
result Proves convergence of EM-based sparse Bayesian learning algorithm.
Improves clustering fairness by learning fair clusters adaptively.
problem Fairness in deep clustering, especially for protected status variables.
method Formulates group-level fairness as ILP, integrates into discriminative deep clustering, refines learning algorithm.
result Consistently outperforms fair clustering algorithms on real-world datasets.
This paper introduces a new specialized algorithm for equilibrium Monte Carlo sampling of binary-valued systems, which allows for large moves in the state space. This is achieved by constructing self-avoiding walks (SAWs) in the state space. As a consequence, many bits are flipped in a single MCMC step. We name the alg…
Optimizes binary regression models with gradient ascent-descent methods.
problem Regression problems with binary weights in quantized learning and digital communication.
method Maximin optimization using gradient ascent-descent methods.
result The approach is optimal in linear regression with low noise and robust regression with few outliers.
New method optimizes mixed integer optimization for hierarchical modeling of clustered and longitudinal data.
problem Optimizing subset selection in hierarchical models with clustered and longitudinal data.
method Distribution-free mixed-integer optimization approach for cluster-aware regression.
result The method efficiently solves problems within minutes and outperforms traditional models in generating sparse solutions with high predictive power.
This paper concerns a method of selecting a subset of features for a sequential logit model. Tanaka and Nakagawa (2014) proposed a mixed integer quadratic optimization formulation for solving the problem based on a quadratic approximation of the logistic loss function. However, since there is a significant gap between …
Study links K-stability of certain surfaces to binary forms, proving stability and non-stability conditions.
problem Investigating K-stability of specific del Pezzo surfaces.
method Relating K-stability to GIT stability of binary forms, proving stability and non-stability conditions.
result K-polystability and non-K-stability of quasi-smooth hypersurfaces.
New algorithm optimizes AUC in binary classification and changepoint detection.
problem Difficult to optimize AUC in binary classification and changepoint detection.
method Proposes efficient path-following algorithms for choosing optimal learning rate.
result Proposed line search algorithm computes complete AUM/AUC representation.
Optimizes financial auditor schedules to reduce time and costs.
problem Efficiently scheduling financial auditors with multiple constraints.
method Used Integer Linear Programming and compared two exact formulations.
result Multi-commodity network flow formulation is 24 times faster.
The paper analyzes how behavioral investors make portfolio decisions using Markowitz Stochastic Dominance criteria.
problem Understanding how behavioral investors make portfolio decisions.
method Developed stochastic optimization problems and MILP models to capture subjective decision weights and probability weighting functions.
result The developed models can be used to formulate computationally tractable portfolio analysis problems.
Scoring systems are linear classification models that only require users to add, subtract and multiply a few small numbers in order to make a prediction. These models are in widespread use by the medical community, but are difficult to learn from data because they need to be accurate and sparse, have coprime integer co…
We consider a high dimensional binary classification problem and construct a classification procedure by minimizing the empirical misclassification risk with a penalty on the number of selected features. We derive non-asymptotic probability bounds on the estimated sparsity as well as on the excess misclassification ris…