Hesse Matrix

Protected: Optimization for the main problem in machine learning

Optimization for main problems in machine learning used in digital transformation, artificial intelligence, and machine learning tasks (barrier function method, penalty function method, globally optimal solution, eigenvalues of Hesse matrix, feasible region, unconstrained optimization problem, linear search, Lagrange multipliers for optimality conditions, integration points, effective constraint method)

2023.05.02

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: Thompson Sampling, linear bandit problem on a logistic regression model

Thompson sampling, linear bandit problem on logistic regression models utilized in digital transformation, artificial intelligence, and machine learning tasks (Thompson sampling, maximum likelihood estimation, Laplace approximation, algorithms, Newton's method, negative log posterior probability, gradient vector, Hesse matrix, Laplace approximation, Bayesian statistics, generalized linear models, Lin-UCB measures, riglet upper bound)

2023.04.07

アルゴリズム:Algorithmsグラフ理論スパースモデリングバンディッド問題幾何学: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

Protected: Unconstrained optimization for continuous optimization in machine learning

Unconstrained Optimization for Continuous Optimization in Machine Learning for Digital Transformation, Artificial Intelligence, and Machine Learning tasks machine epsilon, stopping conditions without scaling, stopping conditions with scaling, Taylor's theorem, stopping conditions for optimization algorithms, Hesse matrix

2022.11.22

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: 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