Foundations

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: 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: Basics of gradient method (linear search method, coordinate descent method, steepest descent method and error back propagation method)

Fundamentals of gradient methods utilized in digital transformation, artificial intelligence, and machine learning tasks (linear search, coordinate descent, steepest descent and error back propagation, stochastic optimization, multilayer perceptron, adaboost, boosting, Wolf condition, Zotendijk condition, Armijo condition, backtracking methods, Goldstein condition, strong Wolf condition)

2022.12.20

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 Stochastic Bandid Problems

Basics of stochastic bandid problems utilized in digital transformation, artificial intelligence, and machine learning tasks (large deviation principle and examples in Bernoulli distribution, Chernoff-Heffding inequality, Sanov's theorem, Heffding inequality, Kullback-Leibler divergence, probability mass function, hem probability, probability approximation by central limit theorem).

2022.11.11

バンディッド問題強化学習微分積分:Calculus機械学習:Machine Learning確率・統計:Probability and Statistics線形代数:Linear Algebra

Protected: Foundations of Measure Theory for Nonparametric Bayesian Theory

Foundations of measure theory for nonparametric Bayesian theory (independence of random measures, monotone convergence theorem in Laplace functionals, propositions valid with probability 1, Laplace transform of probability distribution, expectation computation by probability distribution, probability distribution, monotone convergence theorem, approximation theorem by single functions, single functions, measurable functions using Borel set families, Borel sets, σ-finite measures, σ-additive families, Lebesgue measures, Lebesgue integrals)

2022.09.27

アルゴリズム:Algorithmsグラフ理論ベイズ推定微分積分:Calculus推論技術:inference Technology最適化:Optimization機械学習:Machine Learning確率・統計:Probability and Statistics線形代数:Linear Algebra

Protected: Stochastic Generative Models and Gaussian Processes(3) Representation of Probability Distributions

Stochastic generative models utilized in digital transformation, artificial intelligence, and machine learning tasks and representation of probability distributions in samples as a basis for Gaussian processes ,weighted sampling, kernel density estimation, distribution estimation using neural nets

2022.09.12

アルゴリズム:Algorithmsグラフ理論ベイズ推定微分積分:Calculus推論技術:inference Technology最適化:Optimization機械学習:Machine Learning確率・統計:Probability and Statistics線形代数:Linear Algebra

Stochastic Generative Models and Gaussian Processes(1) Basis of Stochastic Models

Stochastic generative models for digital transformation, artificial intelligence, and machine learning tasks and fundamentals of stochastic models to understand Gaussian processes (independence, conditional independence, simultaneous probability, peripheralization and graphical models)

2022.08.15

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

Protected: Overview of Bayesian Estimation with Concrete Examples

Calculate the fundamentals of Bayesian estimation (exchangeability, de Finetti's theorem, conjugate prior distribution, posterior distribution, marginal likelihood, etc.) used in probabilistic generative models for digital transformation, artificial intelligence, and machine learning tasks, based on concrete examples (Dirichlet-multinomial distribution model, gamma-gaussian distribution model).

2022.07.20

アルゴリズム:Algorithmsグラフ理論ベイズ推定微分積分:Calculus推論技術:inference Technology最適化:Optimization機械学習:Machine Learning確率・統計:Probability and Statistics線形代数:Linear Algebra

Protected: Fundamentals of Submodular Optimization (5) Lovász Extension and Multiple Linear Extension

Interpretation of submodularity using Lovász extensions and multiple linear extensions as a basis for submodular optimization, an approach to discrete information used in digital transformation, artificial intelligence, and machine learning tasks

2022.04.21

アルゴリズム:Algorithmsグラフ理論スパースモデリング微分積分:Calculus推論技術:inference Technology数理論理学:Mathematical logic最適化:Optimization機械学習:Machine Learning

Protected: Fundamentals of statistical causal search (3) Causal Markov conditions, faithfulness, PC algorithm, GES algorithm

Causal Markov conditions, fidelity and constraint-based approaches and score-based approaches in the foundations of statistical causal search for digital transformation , artificial intelligence and machine learning tasks.

2022.03.04

Symbolic Logicグラフ理論セマンテックウェブ技術:Semantic web Technology推論技術:inference Technology最適化:Optimization検索技術:Search Technology機械学習:Machine Learning確率・統計:Probability and Statistics