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.
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.
Every local minimum in non-convex machine learning is globally optimal.
problem Non-convex optimization challenges in machine learning.
method Proves every local minimum achieves globally optimal value of perturbable gradient basis model.
result Theoretical support for non-convex machine learning similar to convex machine learning.
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.
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++.
A new method for efficient ordinal regression.
problem Efficiently modeling ordinal relationships in multi-label learning.
method Incremental Sparse Bayesian Ordinal Regression (ISBOR) approach.
result ISBOR achieves accurate predictions with fewer basis functions.
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.
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.
Study optimal dynamic basis trading strategies with stochastic basis model.
problem Optimal dynamic trading of futures and underlying asset under stochastic basis.
method Model basis evolution as stopped scaled Brownian bridge, solve utility maximization problem with HARA risk preferences.
result Derive exact conditions for optimal trading strategies and solve explicitly.
Paper presents a new method for efficient deep learning with over-complete dictionaries.
problem Learning an over-complete basis for optimal reconstruction without optimization.
method Multiscale Residual Mixture of PCA with a hierarchical approach.
result Exponential decrease of error with depth in a recursive deep approach.
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.
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. Paper proposes an active preference learning method using radial basis functions.
problem Optimization problems where decision-maker can only express preferences.
method Iteratively proposes new comparisons based on learning a surrogate function from preferences and decision vectors.
result Surrogate function fit by radial basis functions, leading to better global optimizer.
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.
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.
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 machine-learning approach solves CS data reconstruction for structural health monitoring.
problem Optimal solution for sparse optimization in compressive sensing.
method Formalizing CS data reconstruction as a supervised-learning task, using l1-norm regularization and a multi-neuron layer.
result High reconstruction accuracy achieved by the machine learning-based approach.
Optimized online learning with kernels for large-scale adversarial data.
problem Efficient online learning for large-scale, potentially adversarial datasets.
method Online variations of kernel Ridge regression using approximated basis functions.
result Optimal regret for a wide range of kernels with low per-round complexity.
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.
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.
Improves deep neural network training and accuracy with adaptive basis approach.
problem Gap between theoretical and practical performance of deep neural networks.
method Adaptive basis viewpoint, novel initializations, hybrid optimizer.
result Dramatic increases in accuracy and convergence rate for various DNN applications.
Paper proposes trading strategies considering stock taxes for better returns.
problem Trading strategies without tax consideration can lead to significant loss.
method Used deep reinforcement learning to learn optimal trading strategies with and without taxes.
result Tax ignorance can cause more than 62% loss in average portfolio returns.
A machine learning method selects optimal orthonormal bases for functional data analysis.
problem Lack of formal criteria for choosing initial orthonormal bases in functional data methods.
method Proposes a machine learning algorithm to learn and place knots for efficient orthogonal spline bases (splinets).
result Demonstrates efficiency, especially for sparse functional data and complex physical systems.
Deep RBVFs improve continuous control in RL.
problem Challenges in finding optimal actions for continuous actions in RL.
method Introduced deep radial-basis value functions (RBVFs) for continuous control.
result RBF-DQN significantly outperforms value-function-only baselines and is competitive with actor-critic algorithms.
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.
GLIS uses IDW and RBF for efficient global optimization.
problem Expensive objective function in optimization problems.
method Combines inverse distance weighting and radial basis functions for acquisition function.
result Competitive and computationally lighter than Bayesian optimization.
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.
Sparse coding--that is, modelling data vectors as sparse linear combinations of basis elements--is widely used in machine learning, neuroscience, signal processing, and statistics. This paper focuses on the large-scale matrix factorization problem that consists of learning the basis set, adapting it to specific data. V…
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
Many applications that use empirically estimated functions face a curse of dimensionality, because the integrals over most function classes must be approximated by sampling. This paper introduces a novel regression-algorithm that learns linear factored functions (LFF). This class of functions has structural properties …
New algorithm improves polynomial chaos approximations using compressive sensing.
problem Improving the efficiency and accuracy of polynomial chaos expansions.
method Develops a two-step optimization procedure combining compressive sensing with basis adaptation.
result Optimal sparsity in polynomial chaos approximations with reduced dimensionality.
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.
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.
Kernel methods are widespread in machine learning; however, they are limited by the quadratic complexity of the construction, application, and storage of kernel matrices. Low-rank matrix approximation algorithms are widely used to address this problem and reduce the arithmetic and storage cost. However, we observed tha…
New capacity measure for ReLU networks reduces generalization error.
problem Improper influence of path norm on ReLU network capacity.
method Basis-path Norm, optimization algorithms.
result Basis-path Norm better explains ReLU network generalization.
Machine learning model predicts DFT total energy to complete basis set limit.
problem Finding a model to extrapolate DFT calculations to complete basis set limit.
method Quantile-random-forest model trained on binary solids data.
result Random-forest model achieves <25% symmetric MAPE for both DFT codes.
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.
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.
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…
Unified model combines neural networks and dictionary learning for clinical predictions from brain data.
problem Predicting clinical severity from brain imaging data.
method Combines neural networks with dictionary learning to model patient-specific and shared features.
result Unified model outperforms state-of-the-art methods in predicting clinical severity.
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…
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.
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.
A neural network predicts coarse-scale basis functions for efficient uncertainty quantification.
problem Efficiently estimating coarse-scale basis functions for multiscale methods.
method Data-driven approach using neural networks fitted to solution samples.
result Significant computational savings for uncertainty quantification tasks.
Option Encoder compresses reinforcement learning options into a policy basis.
problem Redundant options in reinforcement learning frameworks.
method Auto-encoder framework with constrained weights to discover a policy basis.
result Option Encoder reduces the number of options while maintaining performance.
New reinforcement learning operators improve performance and robustness.
problem Improving reinforcement learning algorithms to handle approximation errors.
method Developed a new family of robust stochastic operators.
result Preserves optimality and increases action gap on sample paths.
Predicts the number of polynomial additions in Buchberger's algorithm using machine learning.
problem Predict the number of polynomial additions in Buchberger's algorithm.
method Multiple linear regression and recursive neural network models trained on ideal generator statistics.
result Machine learning can predict the number of polynomial additions in Buchberger's algorithm.