Statistical Mathematics Theory

Protected: Discriminant Conformal Losses in Multi-Valued Discriminant by Statistical Mathematics Theory and its Application to Various Loss Functions

Discriminant conformal loss of multi-valued discriminant and its application to various loss functions by statistical mathematics theory utilized in digital transformation, artificial intelligence, and machine learning tasks discriminant model loss, discriminant conformal, narrow order preserving properties, logistic model, maximum likelihood estimation, nonnegative convex function, one-to-other loss, constrained comparison loss, convex nonnegative-valued functions, hinge loss, pairwise comparison loss, multivalued surport vector machine, monotone nonincreasing function, predictive discriminant error, predictive ψ-loss, measurable function

2023.04.04

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: Evaluation of Rademacher Complexity and Prediction Discrimination Error in Multi-Valued Discrimination Using Statistical Mathematics Theory

Rademacher Complexity and Prediction Discriminant Error in Multivalued Discrimination by Statistical Mathematics Theory Used in Digital Transformation, Artificial Intelligence and Machine Learning Tasks Convex quadratic programming problems, mathematical programming, discriminant machines, prediction discriminant error, Bayesian error, multilevel support vector machines, representation theorem,. Rademacher complexity, multilevel marginals, regularization terms, empirical loss, reproducing nuclear Hilbert spaces, norm constraints, Lipschitz continuity, predictive Φp-multilevel marginals loss, empirical Φ-multilevel marginals loss, uniform bounds, discriminant functions, discriminant

2023.03.23

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: Overview of nu-Support Vector Machines by Statistical Mathematics Theory

Overview of nu-support vector machines by statistical mathematics theory utilized in digital transformation, artificial intelligence, and machine learning tasks (kernel functions, boundedness, empirical margin discriminant error, models without bias terms, reproducing nuclear Hilbert spaces, prediction discriminant error, uniform bounds Statistical Consistency, C-Support Vector Machines, Correspondence, Statistical Model Degrees of Freedom, Dual Problem, Gradient Descent, Minimum Distance Problem, Discriminant Bounds, Geometric Interpretation, Binary Discriminant, Experience Margin Discriminant Error, Experience Discriminant Error, Regularization Parameter, Minimax Theorem, Gram Matrix, Lagrangian Function).

2023.02.23

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集合論:Set theory

Protected: Overview of C-Support Vector Machines by Statistical Mathematics Theory

Support vector machines based on statistical mathematics theory used in digital transformation, artificial intelligence, and machine learning tasks C-support vector machines (support vector ratio, Markov's inequality, probability inequality, prediction discriminant error, one-out-of-two cross checking method, LOOCV, the discriminant, complementarity condition, main problem, dual problem, optimal solution, first order convex optimization problem, discriminant boundary, discriminant function, Lagrangian function, limit condition, Slater constraint assumption, minimax theorem, Gram matrix, hinge loss, margin loss, convex function, Bayes error, regularization parameter)

2023.02.09

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: 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: Kernel functions as the basis of kernel methods in statistical mathematics theory.

Kernel functions (Gaussian kernels, polynomial kernels, linear kernels, kernel functions, regression functions, linear models, regression problems, discriminant problems) as the basis for kernel methods in statistical mathematics theory used in digital transformation, artificial intelligence and machine learning tasks.

2022.12.22

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: Overview of Discriminant Adaptive Losses in Statistical Mathematics Theory

Overview of Discriminant Conformal Losses in Statistical Mathematics Theory (Ramp Losses, Convex Margin Losses, Nonconvex Φ-Margin Losses, Discriminant Conformal, Robust Support Vector Machines, Discriminant Conformity Theorems, L2-Support Vector Machines, Squared Hinge Loss, Logistic Loss, Hinge Loss, Boosting, Exponential Losses, Discriminant Conformity Theorems for Convex Margin Losses, Bayes Rules, Prediction Φ-loss, Prediction Discriminant Error, Monotonic Nonincreasing Convex Function, Empirical Φ-loss, Empirical Discriminant Error)

2022.12.08

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: Complexity of Hypothesis Sets in Statistical Mathematics Theory

Complexity of sets of hypotheses in statistical mathematical theory used in digital transformation, artificial intelligence, and machine learning tasks Rademacher complexity, VC dimension, large number factor, law of large uniform numbers, decision stocks, set of linear discriminators, set of linear functions, Cauchy-Schwartz inequality, Jensen inequality, Masar's complement, Talagrande's complement, empirical Rademacher complexity, Sauer's complement, Radon's theorem

2022.11.24

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: Basic Framework of Statistical Mathematics Theory

Basic framework of statistical mathematics theory used in digital transformation, artificial intelligence, and machine learning tasks regularization, approximation and estimation errors, Höfding's inequality, prediction discriminant error, statistical consistency, learning algorithms, performance evaluation, ROC curves, AUC, Bayes rules, Bayes error, prediction loss, empirical loss

2022.11.09

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