線形代数:Linear Algebra

Protected: Representation Theorems and Rademacher Complexity as the Basis for Kernel Methods in Statistical Mathematics Theory

Representation theorems and Rademacher complexity as a basis for kernel methods in statistical mathematics theory used in digital transformation, artificial intelligence, and machine learning tasks Gram matrices, hypothesis sets, discriminant bounds, overfitting, margin loss, discriminant functions, predictive semidefiniteness, universal kernels, the reproducing kernel Hilbert space, prediction discriminant error, L1 norm, Gaussian kernel, exponential kernel, binomial kernel, compact sets, empirical Rademacher complexity, Rademacher complexity, representation theorem

2023.01.26

アルゴリズム:Algorithmsグラフ理論幾何学:Geometry微分積分:Calculus数理論理学:Mathematical logic最適化:Optimization機械学習:Machine Learning確率・統計:Probability and Statistics線形代数:Linear Algebra

Protected: Batch Stochastic Optimization – Stochastic Variance-Reduced Gradient Descent and Stochastic Mean Gradient Methods

Batch stochastic optimization for digital transformation, artificial intelligence, and machine learning tasks - stochastic variance reduced gradient descent and stochastic mean gradient methods (SAGA, SAG, convergence rate, regularization term, strongly convex condition, improved stochastic mean gradient method, unbiased estimator, SVRG, algorithm, regularization, step size, memory efficiency, Nekaterov's acceleration method, mini-batch method, SDCA)

2023.01.25

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集合論:Set theory

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: Approximate computation of various models in machine learning by Bayesian inference

Approximate computation of various models in machine learning using Bayesian inference for digital transformation, artificial intelligence, and machine learning tasks (structured variational inference, variational inference algorithms, mixture models, conjugate prior, KL divergence, ELBO, evidence lower bound, collapsed Gibbs sampling, blocking Gibbs sampling, approximate inference)

2023.01.23

アルゴリズム:Algorithmsグラフ理論ベイズ推定微分積分: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: Application of Neural Networks to Reinforcement Learning Value Function Approximation, which implements value evaluation as a function with parameters.

Application of Neural Networks to Reinforcement Learning used for Digital Transformation, Artificial Intelligence, and Machine Learning tasks Examples of implementing value evaluation with functions with parameters (CartPole, Q-table, TD error, parameter update, Q-Learning, MLPRegressor, Python)

2023.01.19

アルゴリズム:Algorithmsグラフ理論幾何学:Geometry強化学習微分積分: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: Network Analysis Using Clojure (2)Computing Triangles in a Graph Using Glittering

Network analysis using triangle computation in graphs using Clojure/Glittering for digital transformation, artificial intelligence, and machine learning tasks (GraphX, Pregel API, Twitter dataset, custom triangle count algorithm, message send function, message merge function, outer join, RDD, vertex attributes, Apache Spark, Sparkling, MLlib, Glittering, triangle counting, edge-cut strategy, random-vertex-cut strategy, and social networks, graph parallel computing functions, Hadoop, data parallel systems, RDG, Resilient Distributed Graph, Hama, Giraph)

2023.01.18

Clojureアルゴリズム:Algorithmsグラフ理論最適化:Optimization機械学習:Machine Learning線形代数:Linear Algebra集合論:Set theory

Protected: Regret Analysis for Stochastic Banded Problems

Regret analysis for stochastic banded problems utilized in digital transformation, artificial intelligence, and machine learning tasks (sum of equal sequences, gamma function, Thompson extraction, beta distribution, hem probability, Mills ratio, partial integration, posterior sample, conjugate prior distribution, Bernoulli distribution, cumulative distribution function, expected value, DMED measure, UCB measure, Chernoff-Hefding inequality, likelihood, upper bound, lower bound, UCB score, arms)

2023.01.13

アルゴリズム:Algorithms強化学習微分積分: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: Regenerate nuclear Hilbert spaces as a basis for kernel methods in statistical mathematics theory.

Regenerate kernel Hilbert spaces as a basis for kernel methods in statistical mathematics theory used in digital transformation, artificial intelligence, and machine learning tasks orthonormal basis, Hilbert spaces, Gaussian kernels, continuous functions, kernel functions, complete spaces, inner product spaces, equivalence classes, equivalence relations, Cauchy sequences, linear spaces, norms, complete inner products

2023.01.12

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: Batch Stochastic Optimization – Stochastic Dual Coordinate Descent

Stochastic dual coordinate descent algorithms as batch-type stochastic optimization utilized in digital transformation, artificial intelligence, and machine learning tasks Nesterov's measurable method, SDCA, mini-batch, computation time, batch proximity gradient method, optimal solution, operator norm, maximum eigenvalue , Fenchel's dual theorem, principal problem, dual problem, proximity mapping, smoothing hinge loss, on-line type stochastic optimization, elastic net regularization, ridge regularization, logistic loss, block coordinate descent method, batch type stochastic optimization

2023.01.11

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: 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