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.
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.
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
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.
Our paper explains deep neural collapse in multiple layers.
problem Understanding deep neural collapse in multi-layered neural networks.
method Generalized unconstrained features model for deep networks.
result Deep unconstrained features model exhibits deep neural collapse.
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.
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.
Quantum computing improves feature selection in machine learning.
problem Optimizing feature selection in machine learning problems.
method Formulated feature selection as a QUBO problem and compared quantum and classical methods.
result Quantum computing can outperform classical methods in feature selection, depending on data set.
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.
Yau's Affine Normal Descent optimizes smooth unconstrained problems with geometrically adapted directions.
problem Optimizing smooth unconstrained problems with geometrically adapted directions.
method Yau's Affine Normal Descent (YAND) uses the equi-affine normal of level-set hypersurfaces as search directions.
result YAND converges globally under standard smoothness assumptions and locally quadratically near nondegenerate minimizers.
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.
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.
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.
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. Quantum computing speeds up linear regression training.
problem Reducing training time for machine learning models.
method Formulated regression problem as QUBO, used D-Wave 2000Q for adiabatic optimization.
result Quantum approach achieves up to 2.8x speedup on larger datasets.
A key problem in financial mathematics is the forecasting of financial crashes: if we perturb asset prices, will financial institutions fail on a massive scale? This was recently shown to be a computationally intractable (NP-hard) problem. Financial crashes are inherently difficult to predict, even for a regulator whic…
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.
Integrates prediction models into portfolio optimization for better asset allocation.
problem Traditional portfolio optimization ignores prediction models, leading to suboptimal decisions.
method Developed a framework that combines regression prediction with mean-variance optimization, providing analytical solutions and neural-network-based optimization for inequality constraints.
result Demonstrated through simulations that integrating prediction models improves portfolio performance.
We provide a geometric characterisation of binary sextics with vanishing quadratic invariant.
Quantum machine learning: Adiabatic quantum SVM outperforms classical methods.
problem Training support vector machines efficiently on large datasets.
method Adiabatic quantum computing for SVM training.
result Quantum approach outperforms classical methods in accuracy and scalability.
Paper proves fair classification can be done via simple thresholding.
problem Achieving fair binary classification subject to group fairness constraints.
method Proves Bayes optimal fair learning rule is a group-wise thresholding rule over the Bayes regressor with randomization.
result Proposes an efficient unconstrained optimization algorithm for post-processing fair classification.
AdaRound improves post-training quantization of neural networks.
problem Improving the accuracy of quantized weights in neural networks.
method Adaptive rounding mechanism that adapts to data and task loss.
result AdaRound outperforms rounding-to-nearest and achieves state-of-the-art performance.
Investigates portfolio optimization with and without gearing constraints.
problem Improving portfolio weights for better alignment with expected returns.
method Extends the alpha-weight angle bound to include gearing constraints and uses theoretical arguments and simulations.
result Equally weighted portfolios are not preferable to mean-variance portfolios even with poor forecast ability and a badly conditioned covariance matrix.
Study uses RL to optimize investment with financial constraints, showing exploration benefits.
problem Optimal investment with financial constraints in continuous time.
method Reinforcement learning framework, focusing on Gaussian and truncated Gaussian distributions.
result Exploration leads to more dispersed wealth distribution with heavier tails, especially with smaller exploration parameters.
Hybrid classical-quantum framework optimizes portfolio rebalancing with reduced transaction costs.
problem Optimizing portfolio rebalancing with reduced transaction costs and lookahead bias.
method Combining Ledoit-Wolf shrinkage covariance estimation, hierarchical correlation clustering, entropy-regularised Genetic Algorithm, minimum-variance and equal-weight benchmarks, QUBO formulation, and QAOA for solving the combinatorial optimisation problem.
result GA + QAOA strategy outperforms classical methods with reduced rebalances and transaction costs.
Quantum algorithm finds extrema in discrete optimisation problems.
problem Finding extrema in discrete optimisation functions.
method Quantum unstructured search algorithm (QSERA) to map and find extrema.
result Quadratic speed-up over classical algorithms for discrete optimisation.
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.
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.
This paper uses quantum computing to solve sparse linear regression problems efficiently.
problem Sparse linear regression to identify important features from a large set of variables.
method Formulates the ℓ0 optimization problem as a QUBO problem and solves it using the D-Wave adiabatic quantum computer. result The QUBO solution matches the optimal solution for a wide range of sparsity penalty values across datasets.
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.
Quantum Annealing Enhanced Reinforcement Learning for Accurate RUL Prediction
problem RUL estimation in predictive maintenance
method QAQL framework combining quantum annealing and Q-learning
result Outperforms classical and quantum baselines
We propose ℓ1 norm regularized quadratic surface support vector machine models for binary classification in supervised learning. We establish their desired theoretical properties, including the existence and uniqueness of the optimal solution, reduction to the standard SVMs over (almost) linearly separable data s…
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…
Four decades after their invention, quasi-Newton methods are still state of the art in unconstrained numerical optimization. Although not usually interpreted thus, these are learning algorithms that fit a local quadratic approximation to the objective function. We show that many, including the most popular, quasi-Newto…
In this paper, we introduce a novel and robust approach to Quantized Matrix Completion (QMC). First, we propose a rank minimization problem with constraints induced by quantization bounds. Next, we form an unconstrained optimization problem by regularizing the rank function with Huber loss. Huber loss is leveraged to c…
Quantum computing speeds up neural network training and retraining.
problem Inefficient classical training and retraining of neural networks.
method Adiabatic quantum computing to optimize Kolmogorov-Arnold Networks using Bezier curves.
result Quantum optimization achieves 100x faster retraining compared to classical methods.
Quantum annealing solves matrix factorization for large datasets.
problem Finding low-rank approximations of large real-valued matrices.
method Transformed real optimization into QUBO problems, solved on D-Wave quantum annealer.
result Quantum approach outperforms classical methods and finds better results.
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 approach reduces unconstrained linear bandits to simpler optimization problems.
problem Unconstrained linear bandits problem.
method Perturbation-based approach combined with comparator-adaptive OLO algorithms.
result First high-probability guarantees for both static and dynamic regret in unconstrained linear bandits.
Proposes ConstraintMatch for semi-supervised clustering with unconstrained data.
problem Leveraging unconstrained data alongside constraints for clustering models.
method Semi-supervised context with pseudo-constraining and pseudo-labeling mechanisms.
result Demonstrates effectiveness of ConstraintMatch over baselines.
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.
This tutorial explains Linear Discriminant Analysis (LDA) and Quadratic Discriminant Analysis (QDA) as two fundamental classification methods in statistical and probabilistic learning. We start with the optimization of decision boundary on which the posteriors are equal. Then, LDA and QDA are derived for binary and mul…
A new penalty-free method optimizes portfolios without quantum annealing penalties.
problem Optimizing portfolios with quantum annealing penalties.
method Removing the penalty term and using a classical feasibility projector.
result Significant reduction in chain-break fractions and post-processed regret.
Develops parameter-free online mirror descent for optimal dynamic regret.
problem Optimal online linear optimization in unbounded domains.
method Modified online mirror descent framework for parameter-free algorithms.
result First unconstrained online linear optimization achieving optimal dynamic regret.
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.
This paper uses QUBO to train machine learning models on quantum computers.
problem Efficiently training machine learning models on quantum computers.
method Formulated three machine learning models (linear regression, SVM, k-means) as QUBO problems.
result Formulations are more efficient or equivalent in time and space complexity to classical methods.