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.
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48 results for “mixed integer quadratic programming”
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.
ExDBN: Learning Dynamic Bayesian Networks using Extended Mixed-Integer Programming Formulationscs.LG
ExDBN learns dynamic Bayesian networks using mixed-integer programming.
problem Learning dynamic causal relationships from time series data.
method Score-based learning algorithm using mixed-integer quadratic programming with branch-and-cut method.
result The proposed method produces more accurate results than state-of-the-art approaches.
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.
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.
We present a global optimization approach for solving the maximum a-posteriori (MAP) clustering problem under the Gaussian mixture model.Our approach can accommodate side constraints and it preserves the combinatorial structure of the MAP clustering problem by formulating it asa mixed-integer nonlinear optimization pro…
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.
This study proposes a graph partitioning method to improve spatial prediction models.
problem Improving interpretability of spatial prediction models in industries.
method Graph partitioning problem to minimize within-segment variances, formulated as mixed-integer quadratic programming.
result Approximation scheme efficiently identifies spatial segments, improving computational efficiency.
Mixed integer programming identifies critical neurons in neural networks.
problem Identifying neurons critical for network performance and generalization.
method Developed a mixed integer program (MIP) to assign importance scores to neurons, guiding pruning decisions.
result The method identifies multiple 'lucky' sub-networks resulting in optimized architectures that generalize across datasets.
A hybrid algorithm combines optimization and enumeration for symbolic regression.
problem Finding any function from a set of operators without prior specification.
method Mixed-integer nonlinear optimization with explicit enumeration and constraints.
result The hybrid algorithm is competitive with state-of-the-art methods.
Optimizes marketing strategies with practical constraints.
problem Adjusting marketing activities with minimum and maximum changes.
method Formulated as a mixed integer nonlinear program (MINLP), reformulated for computational efficiency.
result Significant improvements in solution process for realistic problems.
The paper develops mixed-integer formulations for neural networks using partitioning.
problem Optimizing trained ReLU neural networks with balanced model size and tightness.
method Partitioning node inputs into groups, forming the convex hull via disjunctive programming.
result The proposed formulations outperform existing ones, especially with fewer partitions.
The paper proposes a new portfolio optimization model that includes VaR risk measure.
problem Computational hardness of portfolio optimization models with VaR as a risk measure.
method Formulated as a Mixed-Integer Quadratic Programming (MIQP) problem, the model minimizes variance with constraints on expected return and VaR.
result The proposed Mean-Variance-VaR portfolios outperform traditional Mean-Variance and Mean-VaR portfolios in out-of-sample performance.
New MIP approach for efficient change-point detection.
problem Offline multiple change-point detection in data streams.
method Mixed-integer programming (MIP) for globally optimal PWL fitting.
result Provable tighter relaxations for segment assignment variables.
A new portfolio model considers investor aversion to loss and risk.
problem Constructing a robust portfolio under uncertain asset returns and investor aversion.
method Distributional robust optimization (DRP) with a Wasserstein ball centered on empirical distribution, mixed-integer quadratic programming, and hybrid algorithm.
result Empirical testing shows superior performance in asset allocation compared to common strategies.
Proposes a method to select variables for kernel two-sample tests.
problem Determining whether two samples have the same distribution using informative variables.
method A framework based on kernel maximum mean discrepancy (MMD) for selecting a subset of variables.
result The sample size requirements for the three kernels depend on the number of selected variables, not the data dimension.
The Slope Conjecture relates a quantum knot invariant, (the degree of the colored Jones polynomial of a knot) with a classical one (boundary slopes of incompressible surfaces in the knot complement). The degree of the colored Jones polynomial can be computed by a suitable (almost tight) state sum and the solution of a …
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 …
ExDAG solves DAG learning problems with low structural Hamming distance.
problem Learning DAGs with low structural Hamming distance under identifiability assumptions.
method Mixed-integer quadratic programming (MIQP) with branch-and-bound-and-cut algorithm and lazy constraints.
result ExDAG guarantees global convergence and provides a real-time quality assessment.
Quantum algorithm speeds up MIP solving by a near-quadratic factor.
problem Solving Mixed Integer Programs (MIPs) efficiently.
method Incremental-Quantum-Branch-and-Bound algorithm combining quantum speedup with classical search heuristics.
result Universal near-quadratic speedup over classical Branch-and-Bound algorithms.
New method improves portfolio selection by filtering noisy covariance matrices.
problem Noisy covariance matrices in financial datasets affect portfolio performance evaluation.
method Combinatorial Optimization approach using Mixed Integer Quadratic Programming.
result Our method outperforms existing filtering strategies for real financial datasets.
Paper introduces DP methods for high-dimensional variable selection.
problem Sparse variable selection in high-dimensional learning.
method Pure differentially private estimators using Integer Programming.
result Achieves state-of-the-art empirical support recovery.
Fisher score is one of the most widely used supervised feature selection methods. However, it selects each feature independently according to their scores under the Fisher criterion, which leads to a suboptimal subset of features. In this paper, we present a generalized Fisher score to jointly select features. It aims …
Optimizes risk assessment tools using mixed-integer programming.
problem Challenges in healthcare risk assessment due to label scarcity and asymmetric misclassification costs.
method Jointly optimizes scoring weights and category thresholds via mixed-integer programming (MIP).
result Prevents label-scarce category collapse and achieves more accurate risk categorization.
This paper proposes new search algorithms for counterfactual explanations based upon mixed integer programming. We are concerned with complex data in which variables may take any value from a contiguous range or an additional set of discrete states. We propose a novel set of constraints that we refer to as a "mixed pol…
ReLU networks trained with MILPs match deep learning accuracy.
problem Training deep neural networks efficiently.
method Iterative training with Mixed Integer Linear Programs (MILPs).
result ReLU networks can be trained with MILPs achieving similar accuracy to deep learning 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 MIP algorithms improve sparse classifier learning times.
problem Sparse classifier learning at large scales.
method Developed exact and approximate MIP algorithms for -regularized classification.
result Significantly improved statistical performance compared to existing methods.
VNA solves large portfolio optimization problems efficiently.
problem Large-scale portfolio optimization under real-world constraints.
method Mapped to Ising-like Hamiltonian and solved with VNA.
result Identifies near-optimal solutions for over 2,000 assets.
Learning directed acyclic graphs (DAGs) from data is a challenging task both in theory and in practice, because the number of possible DAGs scales superexponentially with the number of nodes. In this paper, we study the problem of learning an optimal DAG from continuous observational data. We cast this problem in the f…
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.
New MIP methods improve training of integer-valued neural networks.
problem Training integer-valued neural networks with limited data and resources.
method Formulated new MIP models to optimize training efficiency and handle more data.
result Significantly outperforms previous state-of-the-art methods in accuracy, training time, and data usage.
PNNs improve personalized healthcare policies using mixed integer programming.
problem Learning treatment policies for patients with limited data.
method Prescriptive networks (PNNs) trained with mixed integer programming.
result PNNs outperform existing methods in reducing peak blood pressure.
We consider the problem of estimating the phases of K mixed complex signals from a multichannel observation, when the mixing matrix and signal magnitudes are known. This problem can be cast as a non-convex quadratically constrained quadratic program which is known to be NP-hard in general. We propose three approaches t…
This work analyzes machine learning for Lagrangian Relaxation in MILP.
problem Improving efficiency in solving large-scale MILP problems.
method Data-driven Algorithm Design approach to learn Lagrangian multipliers.
result Stochastic Gradient Ascent achieves the minimax optimal rate for learning multipliers.
Proposes a method to learn both constraints and objective functions from data.
problem Data-driven inverse optimization for mixed-integer linear programs (MILPs).
method Two-stage approach: first learns constraints, then estimates objective-function weights conditioned on learned constraints.
result Proposes and validates a method for learning both objective functions and constraints from data.
Several portfolio selection models take into account practical limitations on the number of assets to include and on their weights in the portfolio. We present here a study of the Limited Asset Markowitz (LAM), of the Limited Asset Mean Absolute Deviation (LAMAD) and of the Limited Asset Conditional Value-at-Risk (LACV…
Portfolio Analysis Based on Markowitz Stochastic Dominance Criteria: A Behavioral Perspectiveq-fin.PM
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.
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.
Method constructs confidence regions for linear models with arbitrary predictors.
problem Constructing confidence regions for linear models with non-linear predictors.
method Mixed Integer Linear Programming for constraints.
result Empty confidence regions for hypothesis testing.
Best-of- improves LLM performance by efficiently allocating inference-time computation.
problem Achieving optimal performance in test-time LLM ensembling with infinite budget.
method Adaptive generation scheme and weighted ensembles of LLMs, formulated as mixed-integer linear program.
result Optimal ensemble weighting improves performance over individual models.
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.
Pattern Decomposition with Complex Combinatorial Constraints: Application to Materials Discoverycs.AI
Identifying important components or factors in large amounts of noisy data is a key problem in machine learning and data mining. Motivated by a pattern decomposition problem in materials discovery, aimed at discovering new materials for renewable energy, e.g. for fuel and solar cells, we introduce CombiFD, a framework …
We improve optimization for data with varying variance.
problem Optimizing data with varying variance.
method Generalized learning and optimization frameworks for data-driven optimization.
result Asymptotic and finite sample guarantees for stochastic programs.
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.
Algorithm removes units and layers of neural networks without losing accuracy.
problem Deploying large neural networks under limited resources.
method Mixed-Integer Linear Programming (MILP) and L1 regularization.
result Lossless compression of neural networks is achieved.
Certified calibration methods protect model confidence from adversarial attacks.
problem Adversarial attacks degrade model calibration, reducing confidence in predictions.
method Developed certified calibration methods to provide worst-case bounds on calibration under adversarial perturbations.
result Certified calibration methods produce analytic and approximate bounds for the Brier score and expected calibration error.
The Discrete Dantzig Selector: Estimating Sparse Linear Models via Mixed Integer Linear Optimizationstat.ME
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…