prox operator

Protected: Mathematical Properties and Optimization of Sparse Machine Learning with Atomic Norm

Mathematical properties and optimization of sparse machine learning with atomic norm for digital transformation, artificial intelligence, and machine learning tasks L∞ norm, dual problem, robust principal component analysis, foreground image extraction, low-rank matrix, sparse matrix, Lagrange multipliers, auxiliary variables, augmented Lagrangian functions, indicator functions, spectral norm, robust principal component analysis, Frank-Wolfe method, alternating multiplier method in duals, L1 norm constrained squared regression problem, regularization parameter, empirical error, curvature parameter, atomic norm, prox operator, convex hull, norm equivalence, dual norm

2023.05.24

アルゴリズム:Algorithmsグラフ理論スパースモデリングスパースモデリング幾何学:Geometry微分積分:Calculus最適化:Optimization機械学習:Machine Learning確率・統計:Probability and Statistics線形代数:Linear Algebra

Protected: Sparse Machine Learning with Overlapping Sparse Regularization

Sparse machine learning with overlapping sparse regularization for digital transformation, artificial intelligence, and machine learning tasks main problem, dual problem, relative dual gap, dual norm, Moreau's theorem, extended Lagrangian, alternating multiplier method, stopping conditions, groups with overlapping L1 norm, extended Lagrangian, prox operator, Lagrangian multiplier vector, linear constraints, alternating direction multiplier method, constrained minimization problem, multiple linear ranks of tensors, convex relaxation, overlapping trace norm, substitution matrix, regularization method, auxiliary variables, elastic net regularization, penalty terms, Tucker decomposition Higher-order singular value decomposition, factor matrix decomposition, singular value decomposition, wavelet transform, total variation, noise division, compressed sensing, anisotropic total variation, tensor decomposition, elastic net

2023.05.04

アルゴリズム:Algorithmsグラフ理論スパースモデリングスパースモデリング幾何学:Geometry微分積分:Calculus最適化:Optimization機械学習:Machine Learning確率・統計:Probability and Statistics線形代数:Linear Algebra

Protected: Sparse learning based on group L1 norm regularization

Sparse machine learning based on group L1-norm regularization for digital transformation, artificial intelligence, and machine learning tasks relative dual gap, dual problem, gradient descent, extended Lagrangian function, dual extended Lagrangian method, Hessian, L1-norm regularization, and group L1-norm regularization, dual norm, empirical error minimization problem, prox operator, Nesterov's acceleration method, proximity gradient method, iterative weighted reduction method, variational representation, nonzero group number, kernel weighted regularization term, concave conjugate, regenerative kernel Hilbert space, support vector machine, kernel weight Multi-kernel learning, basis kernel functions, EEG signals, MEG signals, voxels, electric dipoles, neurons, multi-task learning

2023.04.06

アルゴリズム:Algorithmsグラフ理論スパースモデリングスパースモデリング微分積分:Calculus最適化:Optimization機械学習:Machine Learning確率・統計:Probability and Statistics線形代数:Linear Algebra集合論:Set theory

Protected: Optimization methods for L1-norm regularization for sparse learning models

Optimization methods for L1-norm regularization for sparse learning models for use in digital transformation, artificial intelligence, and machine learning tasks (proximity gradient method, forward-backward splitting, iterative- shrinkage threshholding (IST), accelerated proximity gradient method, algorithm, prox operator, regularization term, differentiable, squared error function, logistic loss function, iterative weighted shrinkage method, convex conjugate, Hessian matrix, maximum eigenvalue, second order differentiable, soft threshold function, L1 norm, L2 norm, ridge regularization term, η-trick)

2023.03.10

アルゴリズム:Algorithmsグラフ理論スパースモデリングスパースモデリング幾何学:Geometry微分積分:Calculus最適化:Optimization機械学習:Machine Learning確率・統計:Probability and Statistics線形代数:Linear Algebra