Optimizes basis for density-based atomic representations to enhance compactness and accuracy.
problem Improving the efficiency and accuracy of machine learning models for atomic properties.
method An unsupervised approach to determine the optimal basis set for atom density representations using splines.
result Optimal basis sets that encode structural information more compactly and accurately.
We study the problem of dynamically trading a futures contract and its underlying asset under a stochastic basis model. The basis evolution is modeled by a stopped scaled Brownian bridge to account for non-convergence of the basis at maturity. The optimal trading strategies are determined from a utility maximization pr…
Optimizes basis functions for learning dynamical systems from data.
problem Learning suitable basis functions for dynamical systems from data.
method Gradient-based optimization framework for learning basis functions.
result Efficacy demonstrated on various benchmark problems.
Sharp results link DLN gradient flow to basis pursuit optimization and GHA phase transitions.
problem Understanding implicit regularization in Diagonal Linear Networks.
method Sharp convergence bounds and characterization of ℓ1 minimizers. result Gradient flow of DLNs with tiny initialization approximates minimizers of basis pursuit optimization problem.
BASIS improves LLM reasoning by sharing batchwise rollout info, reducing MSE by 69%.
problem Improving large language model reasoning with limited rollouts and batch information.
method BASIS samples only one rollout per prompt but uses batch information to improve value function estimation.
result BASIS reduces MSE in value function estimation by 69% compared to REINFORCE++.
BP fails to find sparsest solution for structured matrices.
problem Finding sparsest solution to linear equations with structured matrices.
method Introduced class of structured matrices for BP failure.
result Determines columns corresponding to unrecoverable non-zero entries.
Ordinal Regression (OR) aims to model the ordering information between different data categories, which is a crucial topic in multi-label learning. An important class of approaches to OR models the problem as a linear combination of basis functions that map features to a high dimensional non-linear space. However, most…
Gradient-based training and pruning for radial basis function networks in materials physics.
problem Interpretable and robust machine learning for materials physics problems.
method Gradient-based training and pruning of radial basis function networks with closed-form optimization criteria.
result Pruned models provide compact and interpretable versions of larger models, offering insights into atom-level migration processes.
Proposes a new method to learn entire solution paths without discretization.
problem Optimizing a family of problems indexed by hyperparameters.
method Parameterizes the solution path with basis functions and solves a single stochastic optimization problem.
result Uniform error of learned path converges linearly to a constant related to basis expressiveness.
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…
A new kernel improves statistical surrogates for stochastic manifolds with diverse data.
problem Handling statistical surrogates for stochastic manifolds with heterogeneous data.
method A transient anisotropic kernel is introduced to improve statistical surrogates for stochastic manifolds with heterogeneous data.
result The transient anisotropic kernel provides a better representation of statistical dependencies in the learned probability measure.
OKSVM optimizes RBF kernel hyperparameter for SVMs, improving classification performance.
problem Intrinsic dependence of RBF kernel hyperparameter on SVM performance.
method Gradient descent method for automatic hyperparameter learning and SVM weights adjustment.
result OKSVM outperforms classical SVM regardless of initial RBF hyperparameter values.
New framework models complex spatial data with basis functions and graphical vectors.
problem Modeling highly-multivariate spatial processes with varying resolutions.
method Extends graphical lasso to multivariate Gaussian processes with independent graphical vectors at different resolutions, using an orthogonal basis and fusion penalty.
result Linear complexity and parsimonious conditional independence structure in multilevel graphical model.
This paper optimizes PCE for efficient surrogate modeling in engineering.
problem Efficiently selecting polynomial regressors for surrogate modeling in computationally expensive models.
method Three state-of-the-art basis-adaptive sparse PCE methods are compared and analyzed.
result Automatic selection of the best solver and basis-adaptive scheme improves surrogate model accuracy.
Study shows Calabi-Yau metrics converge to a specific form under certain conditions.
problem Degeneration of Calabi-Yau metrics and their limits.
method Optimal transport problem and minimisation of Kontorovich functional.
result Limit data of Calabi-Yau metrics can be encoded into a unique minimiser.
Radial Basis Functions Neural Networks (RBFNNs) are tools widely used in regression problems. One of their principal drawbacks is that the formulation corresponding to the training with the supervision of both the centers and the weights is a highly non-convex optimization problem, which leads to some fundamentally dif…
A new optimizer for deep learning improves accuracy and reduces training time.
problem Training deep neural networks for classification tasks.
method Hybrid Newton/Gradient Descent (NGD) method exploiting convexity of cross-entropy loss.
result Improves validation error and provides qualitative differences in hidden layer basis functions.
We consider the problem of designing a sparse Gaussian process classifier (SGPC) that generalizes well. Viewing SGPC design as constructing an additive model like in boosting, we present an efficient and effective SGPC design method to perform a stage-wise optimization of a predictive loss function. We introduce new me…
Global optimization problems whose objective function is expensive to evaluate can be solved effectively by recursively fitting a surrogate function to function samples and minimizing an acquisition function to generate new samples. The acquisition step trades off between seeking for a new optimization vector where the…
This paper develops efficient surrogate models for optimization of complex dynamical systems.
problem Computational expense in solving complex dynamical systems through numerical simulation.
method Combination of proper orthogonal decomposition and radial basis functions for constructing low-dimensional surrogate models.
result Surrogate models reduce computational time for optimization problems while maintaining accuracy.
For nonconvex optimization in machine learning, this article proves that every local minimum achieves the globally optimal value of the perturbable gradient basis model at any differentiable point. As a result, nonconvex machine learning is theoretically as supported as convex machine learning with a handcrafted basis …
Study shows optimal rates for independence testing via U-statistic permutation tests.
problem Developing a valid test of independence for pairs with additional smoothness constraints.
method Defining a measure of dependence, using a permutation test based on a basis expansion and U-statistic estimator.
result Proves minimax optimality of the test in separation rates for certain cases.
Recently, path norm was proposed as a new capacity measure for neural networks with Rectified Linear Unit (ReLU) activation function, which takes the rescaling-invariant property of ReLU into account. It has been shown that the generalization error bound in terms of the path norm explains the empirical generalization b…
Basis adaptation in Homogeneous Chaos spaces rely on a suitable rotation of the underlying Gaussian germ. Several rotations have been proposed in the literature resulting in adaptations with different convergence properties. In this paper we present a new adaptation mechanism that builds on compressive sensing algorith…
A new method for learning manifolds efficiently using canonical basis functions.
problem Learning manifolds in high-dimensional data with efficient and distinct latent dimensions.
method Proposes a novel optimization objective to enforce a transformation matrix with a few prominent and non-degenerate basis functions.
result Demonstrates that minimizing the off-diagonal manifold metric elements ℓ1-norm results in a more efficient latent space representation. Compressive sensing (CS) has been studied and applied in structural health monitoring for wireless data acquisition and transmission, structural modal identification, and spare damage identification. The key issue in CS is finding the optimal solution for sparse optimization. In the past years, many algorithms have bee…
Recently there has been renewed interest in the mapping-class group of a compact surface of genus g≥2 and also in its finite order elements. A finite order element of the mapping-class group will be a conformal automorphisms on some Riemann surface of genus g. Here we give the details of the proof that there is…
Motivated by the gap between theoretical optimal approximation rates of deep neural networks (DNNs) and the accuracy realized in practice, we seek to improve the training of DNNs. The adoption of an adaptive basis viewpoint of DNNs leads to novel initializations and a hybrid least squares/gradient descent optimizer. We…
Adapts POD basis for parametric ROMs using pGP.
problem Updating POD basis for accurate system behavior over parameter space.
method Formulates problem as supervised statistical learning, uses pGP to learn mapping between parameter space and Grassmann manifold.
result Proposes pGP for optimal estimation of POD basis parameters and quantifies uncertainty.
Paper proposes a method to recover point configurations from noisy distance data.
problem Recovering point configurations from noisy distance data.
method Robust Euclidean Distance Geometry via Dual Basis (RoDEoDB) algorithm.
result Exact recovery guarantees for point configuration and Gram matrix under mild conditions.
New optimization algorithm for mixed-variable problems improves efficiency.
problem Optimizing functions with both continuous and categorical variables.
method Combines radial basis function and metric stochastic response surface methods with modifications for categorical variables and parallel processing.
result Numerical experiments show the effectiveness of the proposed modifications.
Study optimizes pension scheme risk-sharing for longevity bonds.
problem Managing longevity basis risk in pension schemes with income-drawdown guarantees.
method Stochastic optimal control, dynamic programming, HJB equations.
result Sharing longevity risk increases both manager and member utilities.
In this paper, we study the problem of compressed sensing using binary measurement matrices and ℓ1-norm minimization (basis pursuit) as the recovery algorithm. We derive new upper and lower bounds on the number of measurements to achieve robust sparse recovery with binary matrices. We establish sufficient conditi…
Method learns radial basis function distributions from samples.
problem Learning radial basis function distributions from training samples.
method Projected particle Langevin optimization method with distributionally robust optimization.
result Empirical measure of Langevin particles converges to a reflected Itô diffusion-drift process.
Max-norm regularizer has been extensively studied in the last decade as it promotes an effective low-rank estimation for the underlying data. However, such max-norm regularized problems are typically formulated and solved in a batch manner, which prevents it from processing big data due to possible memory budget. In th…
Two new algorithms reduce online kernel regression's computational cost while maintaining optimal regret bounds.
problem Trade-off between regret and computational cost in online kernel regression.
method AOGD-ALD and NONS-ALD algorithms dynamically maintain nearly orthogonal basis to approximate kernel mapping and control approximate error.
result Achieves nearly optimal regret bounds at sublinear computational complexity.
In recent years, spectral clustering has become a standard method for data analysis used in a broad range of applications. In this paper we propose a new class of algorithms for multiway spectral clustering based on optimization of a certain "contrast function" over the unit sphere. These algorithms, partly inspired by…
Dual Bayesian Affine Estimators for Wiener-type state-space models
problem Estimating parameters in Wiener-type state-space models
method Fixed-point architecture combining two affine estimators
result Dual basis-parameter estimator achieves comparable parameter MSE to purely affine estimator
Improved reinforcement method for optimal control problems.
problem Optimal control problems with limited computational cost.
method Reinforced least squares Monte Carlo method for stochastic control problems.
result Significant improvement in method's efficiency and accuracy.
This paper proposes a new method to adapt ROMs for new parameter settings.
problem ROMs lack robustness when applied to new parameter settings.
method Regression trees on Grassmann Manifold to learn the mapping between parameters and POD bases.
result The proposed method is capable of establishing the mapping between parameters and POD bases, thus adapting ROMs for new parameters.
Study on hedging and valuation of basis risk in incomplete markets with partial information.
problem Hedging and valuation of European and American claims in an incomplete market with correlated assets and partial information.
method Stochastic control and partial information scenario, forward indifference valuation, dual representation, PDE approach.
result Derivation of optimal hedging strategy and forward indifference price representation for claims.
CARE method estimates precision matrix for compositional data, achieving optimality in high dimensions.
problem Challenges in inferring conditional dependence relationships in high-dimensional compositional data.
method Composition adaptive regularized estimation (CARE) method for sparse basis precision matrix.
result CARE estimator achieves minimax optimality in high dimensions, performing as well as if the basis were observed.
Finsler space is differentiable manifold for which Minkowski space is the fiber of the tangent bundle. To understand structure of the reference frame in Finsler space, we need to understand the structure of orthonormal basis in Minkowski space. In this paper, we considered the definition of orthonormal basis in Minkows…
A method for optimal Bayesian filtering using progressive particle flow and optimal transport maps.
problem Optimizing Bayesian filtering with deterministic particles to avoid degeneration.
method Progressive flow of particles through a sequence of sub-steps, each using an optimal transport map to replace non-equally weighted particles with equally weighted ones.
result The method avoids particle degeneration and simplifies the filtering process by not requiring inversions or monotonicity constraints.
K-Means and RBF networks are shown to be equivalent under certain conditions.
problem Discrete clustering vs. continuous optimization in machine learning.
method Established variational and gradient-based equivalence between K-Means and RBF networks.
result Gradient-based updates of RBF centers recover K-Means centroid update rule.
New neural network models for functional data.
problem Handling non-linear functional data.
method Functional Direct Neural Network (FDNN) and Functional Basis Neural Network (FBNN) with gradient-based optimization.
result Demonstrated effectiveness in complex functional models.
New basis confirms Thurston's conjecture and reveals knot configurations.
problem Understanding cluster algebras and their bases from surfaces.
method Topological construction of band basis and comparison with Kazhdan-Lusztig type basis.
result Common triangular basis matches band basis in quantum cluster algebras.
Finsler space is differentiable manifold for which Minkowski space is the fiber of the tangent bundle. To understand structure of the reference frame in Finsler space, we need to understand the structure of orthonormal basis in Minkowski space. In this paper, I considered the definition of orthonormal basis in Minkowsk…