Sparse Machine Learning

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: Definition and Examples of Sparse Machine Learning with Atomic Norm

Definitions and examples in sparse machine learning with atomic norm used in digital transformation, artificial intelligence, and machine learning tasks nuclear norm of tensors, nuclear norm, higher-order tensor, trace norm, K-order tensor, atom set, dirty model, dirty model, multitask learning, unconstrained optimization problem, robust principal component analysis, L1 norm, group L1 norm, L1 error term, robust statistics, Frobenius norm, outlier estimation, group regularization with overlap, sum of atom sets, element-wise sparsity of vectors, groupwise sparsity of group-wise sparsity, matrix low-rankness

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スモールデータ幾何学: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 machine learning based on trace-norm regularization

Sparse machine learning based on trace norm regularization for digital transformation, artificial intelligence, and machine learning tasks PROPACK, random projection, singularity decomposition, low rank, sparse matrix, update formula for proximity gradient, collaborative filtering, singular value solver,. Trace norm, prox action, regularization parameter, singular value, singular vector, accelerated proximity gradient method, learning problem with trace norm regularization, semidefinite matrix, square root of matrix, Frobenius norm, Frobenius norm squared regularization, Torres norm minimization, binary classification problem, multi-task learning group L1 norm, recommendation systems

2023.04.20

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