Computation

Protected: Example of Machine Learning with Bayesian Inference: Variational Inference for Poisson Mixture Models

Examples of machine learning with Bayesian inference utilized for digital transformation, artificial intelligence, and machine learning tasks: variational inference for Poisson mixed models (Gibbs sampling, variational inference, algorithm, ELBO, computation, variational inference algorithm, latent variable parameters, posterior distribution, Dirichlet distribution, gamma distribution)

2023.02.20

アルゴリズム:Algorithmsグラフ理論ベイズ推定幾何学: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: Information Geometry of Positive Definite Matrices (3)Calculation Procedure and Curvature

Procedures and curvature of computation of positive definite matrices as informative geometry utilized in digital transformation, artificial intelligence, and machine learning tasks

2022.12.10

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: Bayesian Learning and Conjugacy

Conjugacy of various probability functions (Gaussian, Bernoulli, Poisson, Dirichlet, and Gamma distributions) and prior distributions for Bayesian learning calculations in stochastic generative models utilized in digital transformation, artificial intelligence, and machine learning tasks

2022.10.13

アルゴリズム:Algorithms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

Protected: Computational Methods for Gaussian Processes(2)Variational Bayesian Method and Stochastic Gradient Method

Calculations using variational Bayesian and stochastic gradient methods for Gaussian process models, an application of stochastic generative models utilized in digital transformation, artificial intelligence, and machine learning tasks Kullback-Leibler information content, Jensen inequality, evidence lower bound function, mini-batch method, evidence lower bound, variational posterior distribution, evidence variational lower bound

2022.10.10

アルゴリズム:Algorithmsグラフ理論スパースモデリング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: Specific examples of graphical models

Computation of specific graphical models such as Boltzmann Machines, Mean Field Approximation, Bethe Approximation, Hidden Markov Models, Bayesian Hidden Markov Models, etc. as probabilistic generative models utilized in digital transformation, artificial intelligence and machine learning tasks.

2022.09.14

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: Application of Variational Bayesian Algorithm to Matrix Decomposition Models with Missing Values

Application of variational Bayesian algorithm to matrix factorization models with missing values as a stochastic generative model computation for use in digital transformation, artificial intelligence, and machine learning tasks

2022.08.31

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: Computation of graphical models without hidden variables

Maximum likelihood, Bayesian, and variational computations of graphical models without hidden variables in probabilistic generative models utilized in digital truss formation, artificial intelligence, and machine learning tasks, learning by the pseudolikelihood function, Bethe approximation, parameter estimation by TRW upper bound, variational methods, entropy functions, IPF algorithm, MAP estimators

2022.08.17

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: 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: Computing the Peripheral Probability Distribution 2 – Bethe Approximation

Variational methods using the Bethe approximation to compute marginal probability distributions in probability propagation methods for probability estimation using graphical models utilized in digital transformation, artificial intelligence, and machine learning tasks.

2022.07.13

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

Protected: Overview of Gaussian Processes(3)Gaussian Process Regression Model

Computation and optimization of regression models and predictive distributions using Gaussian processes, which are dimensionless stochastic generative models used in digital transformation, artificial intelligence, and machine learning tasks

2022.07.11

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