The original Broad Learning System (BLS) on new added nodes and its existing efficient implementation both assume the ridge parameter lambda -> 0 in the ridge inverse to approximate the generalized inverse, and compute the generalized inverse solution for the output weights. In this paper, we propose two ridge solution…
On-device research index
arXiv research
A locally-built, LLM-digested index of recent arXiv papers in quant finance, geometry/topology, and statistical ML — keyword search served straight from SQLite on this machine.
168,695 papers · 148 categories
Trend · papers per month
48 results for “efficient solutions”
Efficient algorithms find solutions in a rare well-connected cluster at low constraint densities.
problem Finding solutions in the symmetric binary perceptron at low density.
method Formal proof of existence of a subdominant connected cluster and application of an efficient multiscale majority algorithm.
result An efficient algorithm can find solutions in a subdominant connected cluster with high probability.
Randomized matrix compression techniques, such as the Johnson-Lindenstrauss transform, have emerged as an effective and practical way for solving large-scale problems efficiently. With a focus on computational efficiency, however, forsaking solutions quality and accuracy becomes the trade-off. In this paper, we investi…
GFlowNets improve combinatorial optimization by efficiently sampling from solution spaces.
problem NP-hard combinatorial optimization problems with structured constraints.
method Design Markov decision processes and train conditional GFlowNets to sample solutions.
result GFlowNet policies find high-quality solutions efficiently on various CO tasks.
Efficiently finds sparse solutions to max-plus equations for convex regression.
problem Finding sparse solutions to max-plus equations for convex multivariate regression.
method Polynomial-time algorithm for sparse approximate solutions.
result Optimal piecewise-linear fitting with minimum number of regions.
Efficient kernel method learns differential equations with fewer data.
problem Learning differential equations with limited data and computational resources.
method Kernel-based framework for differential equations with theoretical error bounds.
result Significant improvements in accuracy and computational efficiency.
Continuous Parallel Relaxation for Finding Diverse Solutions in Combinatorial Optimization Problemsstat.ML
CPRA efficiently finds diverse solutions in CO problems using UL and parallelization.
problem Finding optimal solutions often requires diverse outcomes in real-world applications.
method CPRA, an UL-based framework, discovers shared representations to generate diverse solutions.
result CPRA outperforms existing UL-based solvers in generating diverse solutions.
Efficiently solves heterogeneous QPs by reducing variables using instance-specific projections.
problem Solving high-dimensional quadratic programming problems efficiently.
method Data-driven framework with a graph neural network generating projections tailored to each QP instance.
result Produces high-quality solutions with reduced computation time, outperforming existing methods.
In the paper, we consider three quadratic optimization problems which are frequently applied in portfolio theory, i.e, the Markowitz mean-variance problem as well as the problems based on the mean-variance utility function and the quadratic utility.Conditions are derived under which the solutions of these three optimiz…
Efficiently solves high-dimensional ODEs with probabilistic methods.
problem Solving high-dimensional ODEs with uncertainty quantification.
method Probabilistic numerical algorithm based on independence assumptions or Kronecker structure.
result Efficient probabilistic solutions for ODEs with millions of dimensions.
Paper proposes an efficient method to optimize neural networks without backpropagation.
problem Computational inefficiency and scalability issues in neural network optimization.
method Derives explicit solutions to optimize neural networks, reducing computational costs.
result Explicit solutions achieve near-optimality and can discover better optima than backpropagation.
We develop an efficient method to calibrate CDS spreads using asymptotic approximations.
problem Calibrating CDS spreads in the SSRD model with correlated processes.
method Asymptotic coefficient expansion to approximate solutions of nonlinear PDEs.
result Our approximation does not require uncorrelated interest rate and default intensity processes.
This paper tackles efficient federated learning for generalized linear bandits.
problem Limited communication efficiency restricts existing federated learning solutions to linear models.
method Proposes a communication-efficient solution framework using online and offline regression.
result Proves sub-linear regret and communication cost for generalized linear bandits.
ACOWA improves distributed sparse classification with extra communication round.
problem Efficiently optimizing sparse classification with limited communication.
method Introducing ACOWA, a new technique with an extra communication round.
result ACOWA achieves better approximation quality and higher accuracy.
Many theories of deep learning have shown that a deep network can require dramatically fewer resources to represent a given function compared to a shallow network. But a question remains: can these efficient representations be learned using current deep learning techniques? In this work, we test whether standard deep l…
This paper concerns the continuous time mean-variance portfolio selection problem with a special nonlinear wealth equation. This nonlinear wealth equation has a nonsmooth coefficient and the dual method developed in [6] does not work. We invoke the HJB equation of this problem and give an explicit viscosity solution of…
Method orders Pareto solutions using transformed objective scores.
problem Lack of orderability in multi-objective optimization solutions.
method Probability integral transform to map objectives to scores.
result Pareto efficient solutions can be ordered in score space.
Efficient neural network optimization reduces costs and improves model performance.
problem High computational costs in optimizing neural networks, especially at scale.
method Introduces self-attentive feed-forward neural units (SAFFU) for efficient optimization.
result Explicit solutions outperform models optimized by backpropagation alone, and further training with backpropagation leads to better optima from smaller data sets.
Meta-learning neural networks to solve diverse PDEs efficiently.
problem Efficiently solving new PDE problems with minimal training.
method Neural network meta-learning of PDE problem representations.
result Meta-learned neural networks predict PDE solutions with high accuracy.
The adjoint sensitivity method scalably computes gradients of solutions to ordinary differential equations. We generalize this method to stochastic differential equations, allowing time-efficient and constant-memory computation of gradients with high-order adaptive solvers. Specifically, we derive a stochastic differen…
Efficient algorithm solves best subset selection problem.
problem Sparse learning problems, especially best subset selection.
method Primal-dual method based on dual forms of -regularized problems.
result Improves solutions of best subset selection with reduced redundant computation.
We use convex relaxation techniques to provide a sequence of solutions to the matrix completion problem. Using the nuclear norm as a regularizer, we provide simple and very efficient algorithms for minimizing the reconstruction error subject to a bound on the nuclear norm. Our algorithm iteratively replaces the missing…
We propose an algorithm to calculate the exact solution for utility optimization problems on finite state spaces under a class of non-differentiable preferences. We prove that optimal strategies must lie on a discrete grid in the plane, and this allows us to reduce the dimension of the problem and define a very efficie…
We propose a fast method with statistical guarantees for learning an exponential family density model where the natural parameter is in a reproducing kernel Hilbert space, and may be infinite-dimensional. The model is learned by fitting the derivative of the log density, the score, thus avoiding the need to compute a n…
Efficiently updates beliefs with virtual observations.
problem Incremental belief updates in Bayesian models.
method Constructs weighted virtual observations to match posterior.
result Reconstructed posterior matches original posterior closely.
Study introduces a variational approach for efficient KL divergence estimation in Dirichlet mixture models.
problem Efficient estimation of KL divergence in Dirichlet mixture models.
method Variational approach for a closed-form solution.
result Superior efficiency and accuracy compared to Monte Carlo methods.
This work uses a SI-DNN to predict AC-OPF solutions efficiently.
problem Efficiently predicting AC-OPF solutions in real-time power systems.
method Sensitivity-Informed Deep Neural Network (SI-DNN) for AC-OPF.
result SI-DNN can predict AC-OPF solutions with better generalization and constraint satisfaction.
New neural network approach solves Poisson equations efficiently.
problem Approximating solutions to Poisson equations with Dirichlet boundary conditions.
method Using shallow ReLU-networks to solve Laplace operator equations.
result Neural networks can approximate solutions to the Laplace operator with Dirichlet boundary conditions efficiently.
New algorithm reduces communication in distributed eigenspace estimation.
problem Efficiently estimating eigenspaces in distributed settings without excessive communication.
method Communication-efficient distributed algorithm using Procrustean alignment.
result Achieves similar error rate to centralized estimator for PCA.
The paper deals with the problem of finding sparse solutions to systems of polynomial equations possibly perturbed by noise. In particular, we show how these solutions can be recovered from group-sparse solutions of a derived system of linear equations. Then, two approaches are considered to find these group-sparse sol…
Efficient clustering for large datasets using a sampling-based approach.
problem Clustering high-dimensional data with a large number of clusters efficiently.
method A simple and efficient clustering method that evaluates distances of data points with a subset of cluster centers.
result Optimal solutions of the approximation are the same as in the exact solution, but more efficient at extracting clusters.
Develops weak PINNs for efficient manifold solutions of hyperbolic equations.
problem Challenges in approximating weak solutions of nonlinear hyperbolic equations on manifolds.
method Introduces a novel weak PINN (wPINN) formulation on manifolds leveraging well-posedness theory.
result Demonstrates efficient approximation of entropy solutions on manifolds with a complexity independent of ambient space dimension.
Study finds cheapest possible payoff under ambiguity, linking to maxmin expected utility.
problem Finding cost-efficient payoffs in uncertain market conditions.
method Developed a new concept of robust cost-efficient payoff and linked it to maxmin expected utility.
result Solutions to maxmin robust expected utility are robust cost-efficient.
Machine learning for many-body physics: efficient solution of dynamical mean-field theorycond-mat.str-el
Machine learning methods for solving the equations of dynamical mean-field theory are developed. The method is demonstrated on the three dimensional Hubbard model. The key technical issues are defining a mapping of an input function to an output function, and distinguishing metallic from insulating solutions. Both meta…
Proposes Pareto efficient fairness for supervised learning models.
problem Ensuring fairness in machine learning models without sacrificing accuracy.
method Formulates a bilevel optimization problem to find Pareto efficient classifiers.
result Guaranteed solution on Pareto frontier for convex and non-convex objectives.
Develops efficient methods for approximating densities of financial models with jumps.
problem Approximating densities of affine jump diffusions with state-independent jump intensities.
method Recursive approach for deriving closed-form solutions to moments, constructing density approximations via moment matching.
result Superior computational efficiency and precision in option pricing and simulation compared to existing techniques.
We propose a stochastic approximation method for approximating the efficient frontier of chance-constrained nonlinear programs. Our approach is based on a bi-objective viewpoint of chance-constrained programs that seeks solutions on the efficient frontier of optimal objective value versus risk of constraint violation. …
Machine learning identifies boundaries of real solutions in polynomial systems.
problem Locating boundaries in parameter space for real solutions of polynomial systems.
method Supervised machine learning approach using nearest neighbor and deep learning approximations.
result Efficiently approximates the real discriminant locus for multidimensional parameter spaces.
Maximum Likelihood Estimators (MLE) has many good properties. For example, the asymptotic variance of MLE solution attains equality of the asymptotic Cram{é}r-Rao lower bound (efficiency bound), which is the minimum possible variance for an unbiased estimator. However, obtaining such MLE solution requires calculating t…
This paper is concerned with an optimal reinsurance and investment problem for an insurance firm under the criterion of mean-variance. The driving Brownian motion and the rate in return of the risky asset price dynamic equation cannot be directly observed. And the short-selling of stocks is prohibited. The problem is f…
Meta-learning base distributions for efficient PDE solutions.
problem Efficiently solving parametric parabolic PDEs across different scenarios.
method Meta-learning base distributions to compute PDE solutions.
result Improves generalization to new parameter regimes.
Proposes DGCN with trajectory sampling for data-efficient policy search in MBRL.
problem Improving data efficiency in model-based reinforcement learning.
method Combines trajectory sampling and DGCN for uncertainty propagation in probabilistic world models.
result Improves sample-efficiency over other uncertainty propagation methods and probabilistic models.
Paper uses SDP for community detection with side information.
problem Community detection in graphs with additional non-graph data.
method Formulates SDP relaxation for maximum likelihood node labeling with side information.
result SDP achieves same exact recovery threshold as maximum likelihood with side information.
The MAP-Elites algorithm produces a set of high-performing solutions that vary according to features defined by the user. This technique has the potential to be a powerful tool for design space exploration, but is limited by the need for numerous evaluations. The Surrogate-Assisted Illumination algorithm (SAIL), introd…
Efficiently tunes hyperparameters with dynamic accuracy method.
problem Optimizing machine learning hyperparameters with inexact evaluations.
method Dynamic accuracy derivative-free optimization for hyperparameter tuning.
result Demonstrates robust and efficient hyperparameter tuning compared to fixed accuracy methods.
New approach for uniform estimates in complex equations.
problem Uniform estimates for solutions to complex Monge-Ampere equations.
method Efficient new approach to uniform estimates.
result Efficient method for uniform estimates in geometric PDEs.
Quantum annealers aim at solving non-convex optimization problems by exploiting cooperative tunneling effects to escape local minima. The underlying idea consists in designing a classical energy function whose ground states are the sought optimal solutions of the original optimization problem and add a controllable qua…
Developed efficient distributed logistic regression for large datasets.
problem Communication inefficiency and sparsity issues in distributed training of large-scale models.
method Iterative local optimization of a surrogate likelihood to improve initial solutions, handling sparsity and diverging updates.
result Learned a communication-efficient distributed logistic regression model for millions of features.