Dual Problem

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: Optimization Using Lagrangian Functions in Machine Learning (2) Extended Lagrangian Method

Overview of optimization methods and algorithms using extended Lagrangian function methods in machine learning for digital transformation, artificial intelligence, and machine learning tasks proximity point algorithm, strongly convex, linear convergence, linearly constrained convex optimization problems, strong duality theorem, steepest descent method, Moreau envelope, conjugate function, proximity mapping, dual problem, dual ascent method, penalty function method, barrier function method

2023.05.23

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: 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: Overview of nu-Support Vector Machines by Statistical Mathematics Theory

Overview of nu-support vector machines by statistical mathematics theory utilized in digital transformation, artificial intelligence, and machine learning tasks (kernel functions, boundedness, empirical margin discriminant error, models without bias terms, reproducing nuclear Hilbert spaces, prediction discriminant error, uniform bounds Statistical Consistency, C-Support Vector Machines, Correspondence, Statistical Model Degrees of Freedom, Dual Problem, Gradient Descent, Minimum Distance Problem, Discriminant Bounds, Geometric Interpretation, Binary Discriminant, Experience Margin Discriminant Error, Experience Discriminant Error, Regularization Parameter, Minimax Theorem, Gram Matrix, Lagrangian Function).

2023.02.23

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集合論:Set theory

Protected: Batch Stochastic Optimization – Stochastic Dual Coordinate Descent

Stochastic dual coordinate descent algorithms as batch-type stochastic optimization utilized in digital transformation, artificial intelligence, and machine learning tasks Nesterov's measurable method, SDCA, mini-batch, computation time, batch proximity gradient method, optimal solution, operator norm, maximum eigenvalue , Fenchel's dual theorem, principal problem, dual problem, proximity mapping, smoothing hinge loss, on-line type stochastic optimization, elastic net regularization, ridge regularization, logistic loss, block coordinate descent method, batch type stochastic optimization

2023.01.11

アルゴリズム:Algorithms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: 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

Geometric approach to data

Geometric approaches to data utilized in digital transformation, artificial intelligence, and machine learning tasks (physics, quantum information, online prediction, Bregman divergence, Fisher information matrix, Bethe free energy function, the Gaussian graphical models, semi-positive definite programming problems, positive definite symmetric matrices, probability distributions, dual problems, topological, soft geometry, topology, quantum information geometry, Wasserstein geometry, Lupiner geometry, statistical geometry)

2022.12.25

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: Structured Support Vector Machines

SVM structure learning and parsing using the deletion plane method algorithm on support vector machines utilized for digital transformation, artificial intelligence, and machine learning tasks, and protein similarity sequence search

2022.08.08

Rアルゴリズム:Algorithms幾何学:Geometry微分積分:Calculus最適化:Optimization機械学習:Machine Learning画像認識技術異常検知・変化検知確率・統計:Probability and Statistics線形代数:Linear Algebra自然言語処理:Natural Language Processing音声信号認識技術

Protected: Regression Analysis with Support Vector Machines (1)Approach to linear regression problems

Regression problems with linear functions using dual problems with Lagrangian functions with support vector machines utilized in digital transformation, artificial intelligence, and machine learning tasks

2022.05.20

微分積分:Calculus最適化:Optimization機械学習:Machine Learning確率・統計:Probability and Statistics自然言語処理:Natural Language Processing