convex function

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

Support vector machines based on statistical mathematics theory used in digital transformation, artificial intelligence, and machine learning tasks C-support vector machines (support vector ratio, Markov's inequality, probability inequality, prediction discriminant error, one-out-of-two cross checking method, LOOCV, the discriminant, complementarity condition, main problem, dual problem, optimal solution, first order convex optimization problem, discriminant boundary, discriminant function, Lagrangian function, limit condition, Slater constraint assumption, minimax theorem, Gram matrix, hinge loss, margin loss, convex function, Bayes error, regularization parameter)

2023.02.09

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: Theory of Noisy L1-Norm Minimization as Machine Learning Based on Sparsity (2)

Theory of noisy L1 norm minimization as machine learning based on sparsity for digital transformation, artificial intelligence, and machine learning tasks numerical examples, heat maps, artificial data, restricted strongly convex, restricted isometric, k-sparse vector, norm independence, subdifferentiation, convex function, regression coefficient vector, orthogonal complementary space

2023.02.06

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: On-line Stochastic Optimization and Stochastic Dual Averaging (SDA) for Machine Learning

On-line stochastic optimization and stochastic dual averaging methods for machine learning (mirror image descent, strongly convex functions, convex functions, convergence rates, polynomial decay averaging, strongly convex regularization) for digital transformation, artificial intelligence and machine learning tasks.

2022.12.21

Uncategorized

Protected: Optimality conditions and algorithm stopping conditions in machine learning

Optimality conditions and algorithm stopping conditions in machine learning used in digital transformation, artificial intelligence, and machine learning scaling, influence, machine epsilon, algorithm stopping conditions, iterative methods, convex optimal solutions, constrained optimization problems, global optimal solutions, local optimal solutions, convex functions, second order sufficient conditions, second order necessary conditions, first order necessary conditions

2022.12.06

アルゴリズム:Algorithms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 as a Basic Matter for Sequential Optimization in Machine Learning

Basics of convex analysis as a fundamental matter of continuous optimization utilized in digital transformation, artificial intelligence, and machine learning tasks subgradient, subdifferential, conjugate function, closed truly convex function, conjugate function, strongly convex function, closed truly convex function, upper and lower bounds on function values, Hesse matrix, epigraph, Taylor's theorem, relative interior, Ahuynh envelope, continuity, convex envelope, convex function, convex set

2022.11.10

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: Submodular Optimization and Machine Learning – Overview

Overview of inferior modular optimization, which is machine learning for discrete variables used in sensor placement optimization.

2021.05.13

微分積分:Calculus最適化:Optimization機械学習:Machine Learning確率・統計:Probability and Statistics