L1 Norm

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: Fundamentals of convex analysis in stochastic optimization (1) Convex functions and subdifferentials, dual functions

Convex functions and subdifferentials, dual functions (convex functions, conjugate functions, Young-Fenchel inequality, subdifferentials, Lejandre transform, subgradient, L1 norm, relative interior points, affine envelope, affine set, closed envelope, epigraph, convex envelope, smooth convex functions, narrowly convex functions, truly convex closed functions, closed convex closed functions, execution domain, convex set) in basic matters of convex analysis in stochastic optimization used for Digital Transformation, Artificial Intelligence, Machine Learning tasks.

2023.04.18

アルゴリズム:Algorithmsグラフ理論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: Two-Pair Extended Lagrangian and Two-Pair Alternating Direction Multiplier Methods as Optimization Methods for L1-Norm Regularization

Optimization methods for L1 norm regularization in sparse learning utilized in digital transformation, artificial intelligence, and machine learning tasks FISTA, SpaRSA, OWLQN, DL methods, L1 norm, tuning, algorithms, DADMM, IRS, and Lagrange multiplier, proximity point method, alternating direction multiplier method, gradient ascent method, extended Lagrange method, Gauss-Seidel method, simultaneous linear equations, constrained norm minimization problem, Cholesky decomposition, alternating direction multiplier method, dual extended Lagrangian method, relative dual gap, soft threshold function, Hessian matrix

2023.03.22

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

Protected: Representation Theorems and Rademacher Complexity as the Basis for Kernel Methods in Statistical Mathematics Theory

Representation theorems and Rademacher complexity as a basis for kernel methods in statistical mathematics theory used in digital transformation, artificial intelligence, and machine learning tasks Gram matrices, hypothesis sets, discriminant bounds, overfitting, margin loss, discriminant functions, predictive semidefiniteness, universal kernels, the reproducing kernel Hilbert space, prediction discriminant error, L1 norm, Gaussian kernel, exponential kernel, binomial kernel, compact sets, empirical Rademacher complexity, Rademacher complexity, representation theorem

2023.01.26

アルゴリズム:Algorithmsグラフ理論幾何学:Geometry微分積分:Calculus数理論理学:Mathematical logic最適化:Optimization機械学習:Machine Learning確率・統計:Probability and Statistics線形代数:Linear Algebra

Protected: What triggers sparsity and for what kinds of problems is sparsity appropriate?

What triggers sparsity and for what kinds of problems is sparsity suitable for sparse learning as it is utilized in digital transformation, artificial intelligence, and machine learning tasks? About alternating direction multiplier method, sparse regularization, main problem, dual problem, dual extended Lagrangian method, DAL method, SPAMS, sparse modeling software, bioinformatics, image denoising, atomic norm, L1 norm, trace norm, number of nonzero elements

2023.01.09

アルゴリズム:Algorithms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