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Protected: Confidence Region Methods in Sequential Optimization in Machine Learning

Confidence region methods (dogleg method, norm constraint, model function optimization, approximate solution of subproblems, modified Newton method, search direction, globally optimal solution, Newton method, steepest descent method, confidence region radius, confidence region, descent direction, step width) in continuous optimization in machine learning used for digital transformation, artificial intelligence, machine learning tasks.

2023.03.20

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: Quasi-Newton Method as Sequential Optimization in Machine Learning(1) Algorithm Overview

Quasi-Newton methods as continuous machine learning optimization for digital transformation, artificial intelligence, and machine learning tasks (BFGS formulas, Lagrange multipliers, optimality conditions, convex optimization problems, KL divergence minimization, equality constrained optimization problems, DFG formulas, positive definite matrices, geometric structures, secant conditions, update laws for quasi-Newton methods, Hesse matrices, optimization algorithms, search directions, Newton methods)

2023.02.21

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集合論:Set theory

Protected: Conjugate gradient and nonlinear conjugate gradient methods as continuous optimization in machine learning

Conjugate gradient methods as continuous machine learning optimization for digital transformation, artificial intelligence, and machine learning tasks (moment method, nonlinear conjugate gradient method, search direction, inertia term, Polak-Ribiere method, linear search, Wolf condition, Dai-Yuan method, strong Wolf condition, Fletcher-Reeves method, global convergence, Newton method, rapid descent method, Hesse matrix, convex quadratic function, conjugate gradient method, minimum eigenvalue, maximum eigenvalue, affine subspace, conjugate direction method, coordinate descent method)

2023.02.07

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確率・統計:Probability and Statistics線形代数:Linear Algebra

Protected: Gauss-Newton and natural gradient methods as continuous optimization for machine learning

Gauss-Newton and natural gradient methods as continuous machine learning optimization for digital transformation, artificial intelligence, and machine learning tasks Sherman-Morrison formula, one rank update, Fisher information matrix, regularity condition, estimation error, online learning, natural gradient method, Newton method, search direction, steepest descent method, statistical asymptotic theory, parameter space, geometric structure, Hesse matrix, positive definiteness, Hellinger distance, Schwarz inequality, Euclidean distance, statistics, Levenberg-Merkert method, Gauss-Newton method, Wolf condition

2023.01.24

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深層学習:Deep Learning確率・統計:Probability and Statistics線形代数:Linear Algebra

Protected: Newtonian and Modified Newtonian Methods as Sequential Optimization in Machine Learning

Newton and modified Newton methods (Cholesky decomposition, positive definite matrix, Hesse matrix, Newtonian direction, search direction, Taylor expansion) as continuous machine learning optimization for digital transformation, artificial intelligence and machine learning tasks

2023.01.10

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