Newton Method

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: 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: Statistical Mathematical Theory for Boosting

Statistical and mathematical theory boosting generalized linear model, modified Newton method, log likelihood, weighted least squares method, boosting, coordinate descent method, iteratively weighted least squares method, iteratively reweighted least squares method, IRLS method, weighted empirical discriminant error, parameter update law, Hessian matrix, corrected Newton method, Newton method, Newton method, iteratively reweighted least squares method, IRLS method) used for digital transformation, artificial intelligence, machine learning tasks. iteratively reweighted least square method, IRLS method, weighted empirical discriminant error, parameter update law, Hessian matrix, corrected Newton method, modified Newton method, Newton method, Newton method, link function, logistic loss, logistic loss, boosting algorithm, logit boost, exponential loss, convex margin loss, adaboost, weak hypothesis, empirical margin loss, nonlinear optimization

2023.03.08

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: 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: 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

Continuous optimization in machine learning

Sequential optimization, an important computational method for constructing machine learning algorithms used in digital transformation artificial intelligence and machine learning tasks

2022.08.12

アルゴリズム:Algorithmsグラフ理論微分積分:Calculus最適化:Optimization機械学習:Machine Learning確率・統計:Probability and Statistics線形代数:Linear Algebra