グラフ理論

Protected: Unsupervised Learning with Gaussian Processes (2) Extension of Gaussian Process Latent Variable Model

Extension of Gaussian process latent variable models as unsupervised learning by Gaussian processes, an application of stochastic generative models utilized in digital transformation, artificial intelligence, and machine learningtasks ,infinite warp mixture models, Gaussian process dynamics models, Poisson point processes, log Gaussian Cox processes, latent Gaussian processes, elliptic slice sampling

2022.12.05

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深層学習:Deep 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

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

Protected: Spatial statistics of Gaussian processes, with application to Bayesian optimization

Spatial statistics of Gaussian processes as an application of stochastic generative models used in digital transformation, artificial intelligence, and machine learning tasks, and tools ARD, Matern kernelsfor Bayesian optimization GPyOpt and GPFlow and GPyTorch

2022.11.07

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

Hierarchical Temporal Memory and Clojure

Deep learning with hierarchical temporal memory and sparse distributed representation with Clojure for digital transformation (DX), artificial intelligence (AI), and machine learning (ML) tasks

2022.11.02

Clojurepython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微分積分:Calculus時系列データ解析最適化: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

Network analysis using Clojure (1) Width-first/depth-first search, shortest path search, minimum spanning tree, subgraphs and connected components

Network analysis using Clojure/loop for digital transformation , artificial intelligence and machine learning tasks, width-first/depth-first search, shortest path search, minimum spanning tree, subgraph and connected components

2022.10.31

Clojureアルゴリズム:Algorithmsグラフ理論セマンテックウェブ技術:Semantic web Technologyマルチエージェントシステム微分積分: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

Integration of logic and rules with probability/machine learning

Integration of logic and rules with machine learning (inductive logic programming, statistical relational learning, knowledge-based model building, Bayesian nets, probabilistic logic learning, hidden Markov models) used for digital transformation, artificial intelligence, and machine learning tasks.

2022.10.30

Symbolic Logicアルゴリズム:Algorithmsエキスパートシステム:expertsystemグラフ理論セマンテックウェブ技術:Semantic web Technology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深層学習:Deep Learning確率・統計:Probability and Statistics関係データ学習

Protected: Structural learning of graphical models

On learning graph structures from data in Bayesian networks and Markov probability fields (Max-Min Hill Climbing (MMHC), Chow-Liu's algorithm, maximizing the score function, PC (Peter Spirtes and Clark Clymoir) Algorithm, GS (Grow-Shrink) algorithm, SGS (Spietes Glymour and Scheines) algorithm, sparse regularization, independence condition)

2022.10.26

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: Calculation method for Gaussian processes based on a lattice arrangement of auxiliary points

Gaussian process method calculations based on lattice-like auxiliary point arrangements in Gaussian process models Kronecker method, Teblitz method, local kernel interpolation, KISS-GP method, an application of stochastic generative models used in digital transformation, artificial intelligence, machine learning

2022.10.24

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