Paper uses integer programming for non-convex boosting in classification.
problem Improving classification performance using non-convex optimization.
method Non-convex boosting via integer programming.
result Results comparable to or better than state-of-the-art.
This paper tackles minimizing clipped convex functions with heuristics and mixed-integer convex programming.
problem Minimizing a sum of clipped convex functions.
method Heuristics and mixed-integer convex programming.
result Heuristics can find good solutions, and the perspective transformation yields tractable lower bounds.
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.
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.
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.
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.
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.
The paper solves a maximum entropy sampling problem with efficient algorithms and performance guarantees.
problem Selecting the most informative principal submatrix from a covariance matrix.
method Derive a novel convex integer program, develop efficient sampling algorithms with approximation bounds, and analyze local search algorithms.
result Efficient algorithms with near-optimal performance guarantees for solving MESP and A-MESP.
Algorithm finds near-optimal VaR portfolios using MILP, improving risk management.
problem Computing optimal VaR portfolios is hard due to non-convexity and combinatorial nature.
method Formulates VaR portfolio problem as MILP, uses alternate formulations for guarantees.
result Near-optimal VaR portfolios with near-optimality guarantees.
The paper uses clustering and integer programming to optimize stock selection for investment funds.
problem Maximizing profits and minimizing risk in stock markets.
method Data-oriented analysis and clustering techniques with integer programming.
result Reconstructed NASDAQ 100 index fund example demonstrates effectiveness.
Optimizes intervention design for causal discovery using integer programming.
problem Identifying causal structures from observational data due to confounding variables.
method Uses integer programming to design minimal intervention sets for causal structure identifiability.
result Provides exact and modular solutions adaptable to various experimental settings and constraints.
We consider the problem of learning decision rules for prediction with feature budget constraint. In particular, we are interested in pruning an ensemble of decision trees to reduce expected feature cost while maintaining high prediction accuracy for any test example. We propose a novel 0-1 integer program formulation …
Optimizes routing in decentralized exchanges with gas fees.
problem Routing in decentralized exchanges with fixed gas fees.
method General optimization framework with mixed-integer model, incorporating gas fees.
result Explicit Karush-Kuhn-Tucker system linking prices, fees, and activation.
Paper characterizes MDM for consumer choice modeling and prediction.
problem Modeling consumer choice behavior with parsimonious models.
method Establishes necessary and sufficient conditions for MDM consistency.
result Characterization leads to exact set of representable choice probabilities.
We study the problem of instance segmentation in biological images with crowded and compact cells. We formulate this task as an integer program where variables correspond to cells and constraints enforce that cells do not overlap. To solve this integer program, we propose a column generation formulation where the prici…
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.
Regularized empirical risk minimization with constrained labels (in contrast to fixed labels) is a remarkably general abstraction of learning. For common loss and regularization functions, this optimization problem assumes the form of a mixed integer program (MIP) whose objective function is non-convex. In this form, t…
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.
The crosscap number of a knot is an invariant describing the non-orientable surface of smallest genus that the knot bounds. Unlike knot genus (its orientable counterpart), crosscap numbers are difficult to compute and no general algorithm is known. We present three methods for computing crosscap number that offer varyi…
New LNS framework improves integer program solving.
problem Solving large-scale integer linear programs efficiently.
method Large neighborhood search with imitation and reinforcement learning.
result Framework significantly outperforms commercial solvers.
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.
This dissertation uses ILP to learn Bayesian network structures efficiently.
problem Learning the structure of Bayesian networks from data.
method Integer Linear Programming formulation with cluster constraints and cutting planes.
result The approach finds feasible solutions for Bayesian network structures efficiently.
We consider the problem of estimating the discrete clustering structures under the Sub-Gaussian Mixture Model. Our main results establish a hidden integrality property of a semidefinite programming (SDP) relaxation for this problem: while the optimal solution to the SDP is not integer-valued in general, its estimation …
Systemic risk is concerned with the instability of a financial system whose members are interdependent in the sense that the failure of a few institutions may trigger a chain of defaults throughout the system. Recently, several systemic risk measures have been proposed in the literature that are used to determine capit…
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 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.
We establish a close connection between stable commutator length in free groups and the geometry of sails (roughly, the boundary of the convex hull of the set of integer lattice points) in integral polyhedral cones. This connection allows us to show that the scl norm is piecewise rational linear in free products of Abe…
Estimating a constrained relation is a fundamental problem in machine learning. Special cases are classification (the problem of estimating a map from a set of to-be-classified elements to a set of labels), clustering (the problem of estimating an equivalence relation on a set) and ranking (the problem of estimating a …
MEC-IP uses IP to efficiently find MECs in BNs from observational data.
problem Discovering Markov Equivalent Classes (MECs) in Bayesian Networks (BNs) efficiently.
method Clique-focusing strategy and EMSG for MEC discovery via Integer Programming.
result Significant reduction in computational time and improved accuracy.
Paper tackles BNSL with IP, improving quality of solutions.
problem Bayesian Network Structure Learning (BNSL) with IP formulations.
method Inexact column generation using difference-of-submodular optimization.
result Improved solutions quality compared to state-of-the-art approaches.
We define a pseudo-inverse for line graphs using linear integer programming.
problem Not all graphs have a corresponding root graph, making the line graph operation non-invertible.
method Propose a linear integer program to edit the smallest number of edges in the line graph to recover a root graph.
result The pseudo-inverse operation is well-behaved and works in practice as shown by empirical experiments.
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.
Adaptive IP approach optimizes intervention design for causal graph recovery.
problem Designing efficient interventions to recover causal relationships from data.
method Iterative integer programming approach for optimizing information gain.
result Adaptive IP approach achieves full causal graph recovery with fewer interventions.
Optimizes portfolios to minimize tax liability, even with monthly trading restrictions.
problem Minimizing tax liability in portfolio construction while adhering to trading restrictions.
method Uses convex optimization to handle the non-convex tax-aware portfolio construction problem, customizing the approach to avoid wash sales.
result The method produces near-optimal trade lists with significantly reduced computational effort compared to globally optimal solutions.
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.
Low-rank approximations of data matrices are an important dimensionality reduction tool in machine learning and regression analysis. We consider the case of categorical variables, where it can be formulated as the problem of finding low-rank approximations to Boolean matrices. In this paper we give what is to the best …
New approach to convex hulls for low-rank problems.
problem Characterizing convex hulls for low-rank sets.
method Matrix perspective function and orthogonal projection matrices.
result Strong relaxations for various low-rank problems.
We study the problem of learning with label proportions in which the training data is provided in groups and only the proportion of each class in each group is known. We propose a new method called proportion-SVM, or ∝SVM, which explicitly models the latent unknown instance labels together with the known group …
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 …
Extends DCP framework to Hadamard manifolds for geodesically convex functions.
problem Verifying convexity in nonlinear programs on Hadamard manifolds.
method Introduces Disciplined Geodesically Convex Programming (DGCP) framework, defining compositions and transformations for geodesically convex functions.
result Allows verification of geodesic convexity for a broader range of functions, including statistical estimators and matrix-valued optimization.
This paper shows how to hedge financial risks with integer investments.
problem Evaluating the minimal super-hedging price with integer-valued strategies for arbitrary payoffs.
method Formulated a dynamic programming principle to evaluate the minimal super-hedging price with integer-valued strategies for continuous piecewise affine terminal claims.
result It is possible to evaluate the minimal super-hedging price with integer-valued strategies for discrete-time, arbitrary Ω.
New method closes certification gap for adversarially trained models.
problem Certifying robustness of adversarially trained neural networks.
method Nonconvex low-rank SDP relaxation with polynomial-time optimization.
result Strong certifications comparable to SDP methods, but with fewer variables.
Differentiable layers for convex optimization problems.
problem Rigidity of existing differentiable optimization layers.
method Disciplined parametrized programming and affine-solver-affine form.
result Efficient analytical differentiation through convex programs.
New algorithm completes nonnegative tensors with fewer samples and faster convergence.
problem Tensor completion tension between sample complexity and computational complexity.
method Integer programming and Blended Conditional Gradients algorithm.
result Achieves information-theoretic sample complexity rate with practical convergence.
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.
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.
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.
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.