Positive Definite Matrix

Protected: Sparse machine learning based on trace-norm regularization

Sparse machine learning based on trace norm regularization for digital transformation, artificial intelligence, and machine learning tasks PROPACK, random projection, singularity decomposition, low rank, sparse matrix, update formula for proximity gradient, collaborative filtering, singular value solver,. Trace norm, prox action, regularization parameter, singular value, singular vector, accelerated proximity gradient method, learning problem with trace norm regularization, semidefinite matrix, square root of matrix, Frobenius norm, Frobenius norm squared regularization, Torres norm minimization, binary classification problem, multi-task learning group L1 norm, recommendation systems

2023.04.20

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: Quasi-Newton Methods as Sequential Optimization in Machine Learning (2)Quasi-Newton Methods with Memory Restriction

Quasi-Newton method with memory restriction (sparse clique factorization, sparse clique factorization, chordal graph, sparsity, secant condition, sparse Hessian matrix, DFP formula, BFGS formula, KL divergence, quasi-Newton method, maximal clique, positive definite matrix, positive definite matrix completion, positive define matrix composition, graph triangulation, complete subgraph, clique, Hessian matrix, triple diagonal matrix Hestenes-Stiefel method, L-BFGS method)

2023.03.07

アルゴリズム:Algorithms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集合論:Set theory

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: 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: Information Geometry of Positive Definite Matrices (2) From Gaussian Graphical Models to Convex Optimization

Information geometry of positive definite matrices utilized in digital transformation, artificial intelligence, and machine learning tasks From Gaussian graphical models to convex optimization (chordal graphs, triangulation graphs, dual coordinates, Pythagorean theorem, information geometry, geodesics, sample variance-covariance matrix, maximum likelihood Estimation, divergence, knot space, Riemannian metric, multivariate Gaussian distribution, Kullback-Leibler information measure, dual connection, Euclidean geometry, narrowly convex functions, free energy)

2022.11.26

アルゴリズム:Algorithmsグラフ理論幾何学: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: Information Geometry of Positive Definite Matrices (1) Introduction of dual geometric structure

Introduction of dual geometric structures as information geometry for positive definite matrices utilized in digital transformation, artificial intelligence, and machine learning tasks (Riemannian metric, tangent vector space, semi-positive definite programming problem, self-equilibrium, Levi-Civita connection, Riemannian geometry, geodesics, Euclidean geometry, ∇-geodesics, tangent vector, tensor quantity, dual flatness, positive definite matrix set)

2022.11.12

グラフ理論スパースモデリングベイズ推定数理論理学最適化: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

Fundamentals of Continuous Optimization – Calculus and Linear Algebra

Fundamentals of Continuous Optimization - Calculus and Linear Algebra (Taylor's theorem, Hesse matrix, Landau's symbol, Lipschitz continuity, Lipschitz constant, implicit function theorem, Jacobi matrix, diagonal matrix, eigenvalues, nonnegative definite matrix, positive definite matrix, subspace, projection, 1-rank update, natural gradient method, quasi Newton method, Sherman-Morrison formula, norm, Euclidean norm, p-norm, Schwartz inequality, Helder inequality, function on matrix space)

2022.10.28

アルゴリズム:Algorithms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