Novel approximation hierarchy for sparse quadratic programs.
problem Sparse Quadratic Programs with Cardinality Constraints.
method Exploits rank-dominating eigenvectors for min-max optimization over binary variables.
result Efficient screening of nonzero elements with scalable optimization algorithms.
We consider a proximal operator given by a quadratic function subject to bound constraints and give an optimization algorithm using the alternating direction method of multipliers (ADMM). The algorithm is particularly efficient to solve a collection of proximal operators that share the same quadratic form, or if the qu…
A novel formulation and training procedure for full Boltzmann machines in terms of a mixed binary quadratic feasibility problem is given. As a proof of concept, the theory is analytically and numerically tested on XOR patterns.
Improves scalability of Bayesian optimization for combinatorial spaces.
problem Optimizing expensive functions over large combinatorial spaces.
method Parametrized Submodular Relaxation (PSR) to solve AFO problems for BOCS.
result Significant improvements in scalability and accuracy for BOCS model.
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.
The support vector machine (SVM) was originally designed for binary classifications. A lot of effort has been put to generalize the binary SVM to multiclass SVM (MSVM) which are more complex problems. Initially, MSVMs were solved by considering their dual formulations which are quadratic programs and can be solved by s…
New method uses binary quadratic forms to classify Seifert surfaces in 4-ball.
problem Classifying non-isotopic Seifert surfaces in 4-ball.
method Composition of binary quadratic forms and number-theoretic approach.
result Established a new connection between Bhargava cube and Gauss composition.
We provide a geometric characterisation of binary sextics with vanishing quadratic invariant.
Paper proposes a QUBO formulation that reduces binary variables in Bayesian network learning.
problem Reducing the number of binary variables in QUBO formulations for Bayesian network learning.
method Proposes a new QUBO formulation that minimizes binary variables.
result Significantly reduces the number of binary variables required for Bayesian network structure learning.
Exact simulation of correlated binary outcomes using PMF constraints and linear programming.
problem Simulating dependent Bernoulli outcomes with specific means and correlations.
method Formulate the problem over the joint Bernoulli PMF, impose constraints, and solve as a linear program. Use convex-hull characterization and truncated-moment completion scheme for feasibility and simulation.
result Exact simulation framework for correlated binary outcomes, providing a convex-hull characterization and truncated-moment completion scheme.
Optimizes train schedules and maintenance using CP and QA.
problem Optimizing train schedules and maintenance considering constraints.
method Used Constraint Programming and Quantum Annealing to model and solve the problem.
result Both CP and QA approaches produce comparable results on real quantum computers.
Abstract perspective on quadratic programming for optimal portfolio allocation.
problem Optimal allocation problems in long portfolio theory.
method Using maximum principles and distinguished boundaries in reproducing kernel Hilbert spaces.
result Support of an optimal distribution lies in a variety intersecting a distinguished boundary.
We consider the problem of solving a large-scale Quadratically Constrained Quadratic Program. Such problems occur naturally in many scientific and web applications. Although there are efficient methods which tackle this problem, they are mostly not scalable. In this paper, we develop a method that transforms the quadra…
Tackling binary program analysis problems has traditionally implied manually defining rules and heuristics, a tedious and time-consuming task for human analysts. In order to improve automation and scalability, we propose an alternative direction based on distributed representations of binary programs with applicability…
Paper presents an ADMM-based approach to efficiently integrate quadratic programming layers into neural networks.
problem Integrating quadratic programs into neural networks for optimization.
method An ADMM-based network layer architecture for solving quadratic programs efficiently.
result The ADMM layer is approximately an order of magnitude faster than existing methods for medium scaled problems.
Eigen-decomposition simplifies quadratic programming with equality constraints.
problem Optimizing solutions under linear equality constraints in quadratic programming.
method Eigenvalue decomposition of the quadratic term matrix to project optimal solutions.
result Established a linear mapping between EQP formulations with and without diagonalized Q. MPWTSVM improves multi-view learning by reducing redundancy and enhancing accuracy.
problem Improving multi-view learning models for better accuracy and efficiency.
method Proposes MPWTSVM, which combines WLTSVM's strengths with multi-view learning principles.
result Demonstrates better accuracy and efficiency compared to existing multi-view classification models.
Novel link classification connects quadratic forms and knot theory.
problem Classifying isotopy classes of links in 3D space.
method Established a correspondence between quadratic forms and isotopy classes of links.
result Class numbers of quadratic number fields measure link distinguishability.
Faster algorithms for structured SVMs reduce computation time.
problem Efficiently solving quadratic programming problems with specific structures.
method Designing nearly-linear time algorithms for quadratic programs with low-rank factorizations and few linear constraints.
result First nearly-linear time algorithms for solving quadratic programs with specific structures.
A new reinforcement learning method improves Max-Cut solutions without needing training data.
problem Max-Cut problem is NP-hard, and existing methods struggle with generalizability and scalability.
method Training-data-free reinforcement learning approach to hyperplane rounding for Max-Cut optimization.
result Our method consistently achieves better Max-Cut solutions across various graph types.
New method for finding function correspondences in binary programs.
problem Finding a correspondence between functions of two binary programs.
method Formulated as a network alignment problem and solved using belief propagation.
result QBinDiff prototype outperforms state-of-the-art diffing tools.
Convolutional neural network (CNN)-based feature learning has become state of the art, since given sufficient training data, CNN can significantly outperform traditional methods for various classification tasks. However, feature learning becomes more difficult if some training labels are noisy. With traditional regular…
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 generalize Conway's approach to integral binary quadratic forms on Q to study integral binary hermitian forms on quadratic imaginary extensions of Q. In Conway's case, an indefinite form that doesn't represent 0 determines a line ("river") in the spine T associated with SL(2,Z) in the hyperbolic plane. In our genera…
New method solves constrained stochastic optimization problems efficiently.
problem Online statistical inference of constrained stochastic nonlinear optimization problems.
method Stochastic Sequential Quadratic Programming (StoSQP) with iterative sketching solver.
result The rescaled primal-dual sequence converges to a mean-zero Gaussian distribution.
Method solves complex optimization problems with high probability bounds.
problem Nonlinear equality constrained stochastic optimization problems.
method Step-search sequential quadratic programming method.
result High-probability bound on iteration complexity for first-order stationarity.
Simplifies multi-label classification with stochastic sketch strategy.
problem Complex training processes in multi-label classification.
method Simple stochastic sketch strategy for multi-label classification.
result Competitive performance without complex training processes.
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.
This paper addresses a novel data science problem, prescriptive price optimization, which derives the optimal price strategy to maximize future profit/revenue on the basis of massive predictive formulas produced by machine learning. The prescriptive price optimization first builds sales forecast formulas of multiple pr…
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.
New method improves submodular maximization for machine learning applications.
problem Inexact monotonicity in submodular functions limits traditional algorithms' performance.
method Introduces monotonicity ratio as a continuous version of monotonicity, leading to improved approximation guarantees.
result Improved approximation ratios for movie recommendation, quadratic programming, and image summarization.
New BDEs reveal singular surfaces from line congruences.
problem Understanding binary differential equations associated with line congruences.
method Applied pointwise to quadratic differential forms, studying quotients of quadratic forms and associated polar lines.
result Introduced a new singular surface in Euclidean 3-space.
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.
Novel method solves group synchronization with robust corruption tolerance.
problem Group synchronization with high corruption tolerance.
method Quadratic programming formulation exploiting cycle consistency.
result Global minimum recovers corruption levels under mild conditions.
Tensor decomposition has been extensively used as a tool for exploratory analysis. Motivated by neuroscience applications, we study tensor decomposition with Boolean factors. The resulting optimization problem is challenging due to the non-convex objective and the combinatorial constraints. We propose Binary Matching P…
New method solves nonseparable stochastic control problems.
problem Nonseparable and non-monotonic stochastic control problems.
method Scenario-decomposition solution framework using progressive hedging algorithm.
result Extends reach of stochastic optimal control.
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…
In this paper we present an incremental variant of the Twin Support Vector Machine (TWSVM) called Fuzzy Bounded Twin Support Vector Machine (FBTWSVM) to deal with large datasets and learning from data streams. We combine the TWSVM with a fuzzy membership function, so that each input has a different contribution to each…
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 …
New method solves optimization problems with stochastic objectives and constraints.
problem Optimization problems with stochastic objectives and deterministic constraints.
method Trust-region interior-point stochastic sequential quadratic programming (TR-IP-SSQP) method.
result Global almost-sure convergence to first-order stationary points under standard assumptions.
We propose a randomized second-order method for optimization known as the Newton Sketch: it is based on performing an approximate Newton step using a randomly projected or sub-sampled Hessian. For self-concordant functions, we prove that the algorithm has super-linear convergence with exponentially high probability, wi…
Proposes a novel classification criterion for high-dimensional data with few samples.
problem Challenges in classifying high-dimensional data with limited samples.
method Tolerance similarity criterion and No-separated Data Maximum Dispersion classifier (NPDMD).
result NPDMD outperforms state-of-the-art methods in various real-world applications.
We study constrained clustering, where constraints guide the clustering process. In existing works, two categories of constraints have been widely explored, namely pairwise and cardinality constraints. Pairwise constraints enforce the cluster labels of two instances to be the same (must-link constraints) or different (…
New algorithm speeds up path computation for optimal models.
problem Finding the exact path of optimal models from a finite set.
method Dynamic programming approach for linear time computation.
result Dynamic programming achieves linear time for breakpoints computation.
In this paper we propose a tractable quadratic programming formulation for calculating the equilibrium term structure of electricity prices. We rely on a theoretical model described in [21], but extend it so that it reflects actually traded electricity contracts, transaction costs and liquidity considerations. Our nume…
New method finds 198,846 toric-colorable seeds of Picard number 5.
problem Enumerating toric-colorable seeds of Picard number 5.
method Binary matroid approach and dynamic programming algorithm.
result 198,846 mod 2 toric-colorable seeds of dimension four and Picard number five.
Multimodal deep learning improves flaw detection in software programs.
problem Current flaw detection relies on single software representations.
method Adapted multimodal deep learning models for flaw detection.
result Multimodal models outperform traditional deep learning models.
Markov's theorem classifies the worst irrational numbers with respect to rational approximation and the indefinite binary quadratic forms whose values for integer arguments stay farthest away from zero. The main purpose of this paper is to present a new proof of Markov's theorem using hyperbolic geometry. The main ingr…