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.
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.
Proposes a new SVM model for binary classification with theoretical and practical advantages.
problem Binary classification in supervised learning.
method Quadratic surface support vector machine with L1 norm regularization.
result The model can detect true sparsity patterns and is efficient for both synthetic and real data.
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…
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.
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.
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.
Explains LDA and QDA for binary and multiple classes.
problem Classification methods in statistical and probabilistic learning.
method Optimization of decision boundaries, estimation of parameters, relation to other methods.
result Equivalence of LDA and Fisher discriminant analysis.
The paper develops efficient estimators for semi-parametric binary models in distributed computing.
problem Estimation and inference challenges in large-scale data under non-smooth objective functions.
method Proposes one-shot and multi-round divide-and-conquer estimators with adaptive kernel smoothing to relax constraints and achieve superlinear optimization error.
result Establishes quadratic convergence up to optimal statistical error rate and handles dataset heterogeneity and high-dimensional sparse parameters.
Optimized reverse quantum annealing speeds up portfolio optimization.
problem Optimizing portfolios using quantum and classical methods.
method Hybrid quantum-classical approach, including reverse quantum annealing.
result Optimized reverse quantum annealing is 100 times faster than forward quantum annealing.
Quantum algorithm improves sparse vector recovery from noisy measurements.
problem Accurately recover sparse vectors from noisy linear measurements.
method Formulated as a QUBO task, solved using quantum technology.
result Quantum approach outperforms classical methods in sparse coding.
A new framework improves solving mixed-integer convex problems with binary indicators.
problem Optimizing mixed-integer convex problems with binary indicators controlling continuous variables.
method Coordinate Optimality Reformulation (CORe) framework, incorporating coordinate-wise optimality information.
result CORe reformulations improve branch-and-bound performance, especially in sparse and structured settings.
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.
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…
Extends quadratic loss for SVM and deep learning to improve pattern correlation.
problem Improving generalization in supervised binary classification and regression tasks.
method Extends quadratic loss, restarts from problem (8) in [3], proposes new algorithms, uses multiple kernel learning.
result Comparable results with standard losses and parameterized quadratic loss.
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 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.
Bayesian optimization selects wavelengths for sugar content estimation in NIR spectroscopy.
problem Improving prediction accuracy and interpretability of spectral data for sugar content estimation.
method Formulated as a binary black-box optimization problem, proposed method uses Bayesian optimization with a sparse quadratic surrogate model and Thompson sampling.
result Improves prediction accuracy of partial least squares regression and yields more consistent wavelength regions.
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.
Improved VQE for large DPO problems in finance.
problem Dynamic Portfolio Optimization (DPO) with many assets.
method Tailored VQE workflow, ISQR routine, VQE Constrained method.
result Achieved financial performance similar to classical methods.
This paper aims at refined error analysis for binary classification using support vector machine (SVM) with Gaussian kernel and convex loss. Our first result shows that for some loss functions such as the truncated quadratic loss and quadratic loss, SVM with Gaussian kernel can reach the almost optimal learning rate, p…
Simulated Bifurcation outperforms quantum machines in community detection.
problem Community detection in complex networks
method Quantum-inspired Simulated Bifurcation algorithm for QUBO formulation
result Simulated Bifurcation achieves highest modularity in community detection
We consider support recovery in the quadratic logistic regression setting - where the target depends on both p linear terms xi and up to p2 quadratic terms xixj. Quadratic terms enable prediction/modeling of higher-order effects between features and the target, but when incorporated naively may involve solvi…
Quantum optimization for portfolios with risk and diversification constraints.
problem Implementing complex constraints in portfolio optimization for financial applications.
method Transformed portfolio optimization into a quadratic binary optimization problem suitable for quantum annealers.
result Demonstrated practical implementation of daily constraints in real data using quantum processors.
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…
New lower bounds improve logistic log-likelihood optimization and inference.
problem Designing computationally tractable lower bounds for logistic log-likelihoods.
method Developed a piece-wise quadratic lower bound that uniformly improves tangent quadratic minorizers.
result Improves the speed of convergence and accuracy of variational Bayes approximations.
The F-measure, which has originally been introduced in information retrieval, is nowadays routinely used as a performance metric for problems such as binary classification, multi-label classification, and structured output prediction. Optimizing this measure is a statistically and computationally challenging problem, s…
Study Alexander polynomials of modular knots, revealing finite and infinite coefficient properties.
problem Investigate Alexander polynomials of modular knots.
method Use Burau representation and geometric SL2(Z)-invariants. result Alexander polynomials of modular knots have both finite and infinite coefficient properties.
Proposes a quantum-inspired algorithm for selecting representative data subsets.
problem Selecting the most representative subset of data from a larger dataset.
method Uses a Quadratic Unconstrained Binary Optimization (QUBO) problem approach.
result Demonstrates the effectiveness of the selector algorithm in finance applications.
Graphical theory of binary Hamiltonian forms and their values.
problem Understanding values of binary Hamiltonian forms.
method Graphical theory, maximal orders, Busemann distances, equivariant cellulation.
result Combinatorial description of binary Hamiltonian form values.
The paper analyzes consistency of graph-based semi-supervised learning methods for binary and multi-class classification.
problem Consistency of semi-supervised learning algorithms on graphs with noisy labels and well-clustered unlabelled data.
method The study examines graph-based probit and one-hot encoding methods for binary and multi-class classification, analyzing the consistency of optimization-based techniques.
result The analysis reveals insights into the rational function choice for optimization, improving the consistency of semi-supervised learning algorithms.
A new method for few-shot learning using Laplacian regularization.
problem Few-shot learning with limited labeled data.
method Transductive Laplacian-regularized inference for feature embeddings.
result Our method outperforms state-of-the-art methods across various benchmarks.
Quantum machine learns to clean up blurry images.
problem Cleaning up blurry images using quantum computing.
method Uses Boltzmann machines, QUBO, and quantum annealing to balance image quality and noise.
result Quantum method produces cleaner images than noisy originals on average.
Paper proposes a robust deep graph-based classifier for noisy labels.
problem Difficulty in feature learning with noisy training labels.
method Convolutional neural networks with graph Laplacian regularization (GLR).
result Proposed method outperforms state-of-the-art classifiers on noisy datasets.
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.
Unified approach tackles logical constraints in mixed-integer optimization.
problem Logical constraints in mixed-integer optimization problems.
method Express logical constraints non-linearly, reformulate as convex binary optimization, solve using outer-approximation.
result Solves problems faster and at larger scale than existing methods.
Quantum computing aids in predicting financial crashes.
problem Predicting financial crashes when markets are disrupted.
method Mapped financial network to quantum Hamiltonian, solved using quantum annealing.
result Quantum computing can efficiently assess financial equilibrium and predict crashes.
We provide a general theoretical analysis of expected out-of-sample utility, also referred to as decision-theoretic classification, for non-decomposable binary classification metrics such as F-measure and Jaccard coefficient. Our key result is that the expected out-of-sample utility for many performance metrics is prov…
We study the problem of determining the optimal low dimensional projection for maximising the separability of a binary partition of an unlabelled dataset, as measured by spectral graph theory. This is achieved by finding projections which minimise the second eigenvalue of the graph Laplacian of the projected data, whic…
A scalable gradient-based framework for sparse portfolio selection.
problem Sparse minimum-variance portfolio selection with cardinality constraint.
method Gradient-based optimization with Boolean relaxation and tunable parameter.
result Matches commercial solvers in most instances, differing by a few assets with negligible error in portfolio variance.
In this paper are given explicit calculations of Laplace operator spectrum for smooth real/complex-valued functions on all connected compact simple rank three Lie groups with biinvariant Riemannian metric and established a connection of obtained formulas with the number theory and integer ternary and binary quadratic f…
Quantum computers can optimize foreign exchange reserves management.
problem Optimizing foreign exchange reserves management using quantum computing.
method Demonstrated through quantum Monte Carlo risk measurement and quantum algorithms for portfolio optimization.
result Quantum computers can theoretically optimize FX reserves management in the future.
Research classifies quadratic forms over various fields.
problem Classifying conjugacy classes in PSL(2, K).
method Synthetic approach, focusing on Lie groups and their actions.
result Provides a complete description of PSL(2, Z)-classes of integral binary quadratic forms.
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…
We introduce a new discriminant analysis method (Empirical Discriminant Analysis or EDA) for binary classification in machine learning. Given a dataset of feature vectors, this method defines an empirical feature map transforming the training and test data into new data with components having Gaussian empirical distrib…
Classifies quotients of SnimesSn by Z/pimesZ/p actions.
problem Classifying quotients of SnimesSn by Z/pimesZ/p actions. method Classification via first p-localized k-invariant, with restrictions on possibilities. result Complete classification of free Z/pimesZ/p actions on S3imesS3 for p>3. Study counts simple knots with specific Alexander polynomials, suggesting asymptotic formula.
problem Counting simple knots with specific Alexander polynomials.
method Classification of simple knots, algebraic and arithmetic formulations, Cohen-Lenstra heuristics, sieve methods.
result Asymptotic formula for the count of simple knots, with prime contributions bounded.