• Self
  • Intro
  • (PART) 20-02
  • 1 Categorical
    • 1.1 Overview
      • 1.1.1 Data Type and Statistical Analysis
  • 2 Bayesian
    • 2.1 Abstract
      • 2.1.1 변수의 독립성
      • 2.1.2 교환가능성
    • 2.2 Continual Aeassessment Method
    • 2.3 Horseshoe Prior
  • (PART) 21-01
  • 3 Mathematical Stats
    • 3.1 Inference
      • 3.1.1 Rao-Blackwell thm.
      • 3.1.2 Completeness
      • 3.1.3 레만-쉐페 thm.
      • 3.1.4 Rao-Blackwell thm.
    • 3.2 Hypothesis Test
    • 3.3 Power Fucntion
      • 3.3.1 Significance Probability (p-value)
    • 3.4 Optimal Testing Method
    • 3.5 Data Reduction
      • 3.5.1 Sufficiency Principle
    • 3.6 Borel Paradox
    • 3.7 Neyman–Pearson lemma
      • 3.7.1 Overview
      • 3.7.2 Generalized LRT
    • 3.8 개념
  • 4 MCMC
    • 4.1 Importance Sampling
      • 4.1.1 Independent Monte Carlo
    • 4.2 Markov Chain Monte Carlo
      • 4.2.1 MH Algorithm
      • 4.2.2 Random Walk Chains (Most Widely Used)
      • 4.2.3 Basic Gibbs Sampler
      • 4.2.4 Implementation
    • 4.3 Advanced MCMC (wk08)
      • 4.3.1 Data Augmentation
      • 4.3.2 Hit-and-Run Algorithm
      • 4.3.3 Metropolis-Adjusted Langevin Algorithm
      • 4.3.4 Multiple-Try Metropolis Algorithm
      • 4.3.5 Reversible Jump MCMC Algorithm
    • 4.4 Auxiliary Variable MCMC
      • 4.4.1 Introduction
      • 4.4.2 Multimodal Target Distribution
      • 4.4.3 Doubly-intractable Normalizing Constants
    • 4.5 Approximate Bayesian Computation
      • 4.5.1 Simulator-Based Models
      • 4.5.2 ABCifying Monte Carlo Methods
      • 4.5.3 ABC-MCMC Algorithm
    • 4.6 Hamiltonian Monte Carlo
      • 4.6.1 Introduction to Hamiltonian Monte Carlo
    • 4.7 Population Monte Carlo
      • 4.7.1 Adaptive Direction Sampling
      • 4.7.2 Conjugate Gradient MC
      • 4.7.3 Parallel Tempering
      • 4.7.4 Evolutionary MC
      • 4.7.5 Sequential Parallel Tempering
    • 4.8 Stochastic Approximation Monte Carlo
    • 4.9 Review
      • 4.9.1 Wk01
      • 4.9.2 wk03
      • 4.9.3 wk04, 05
    • 4.10 Else
      • 4.10.1 Hw4. Rasch Model
      • 4.10.2 DA) Example: MVN
      • 4.10.3 Bayesian adaptive clinical trial with delayed outcomes
      • 4.10.4 NMAR의 종류
      • 4.10.5 wk10) Bayesian Model Selection
      • 4.10.6 Autologistic model
      • 4.10.7 wk10) Bayesian Model Averaging
  • 5 MVA
    • 5.1 Overview of mva (not ended)
      • 5.1.1 Notation
      • 5.1.2 Summary Statistics
      • 5.1.3 Statistical Inference on Correlation
      • 5.1.4 Standardization
      • 5.1.5 Missing Value Treatment
    • 5.2 Multivariate Nomral (wk2)
      • 5.2.1 Overview
      • 5.2.2 Spectral Decomposition
      • 5.2.3 Properties of MVN
      • 5.2.4 \(\Chi^2\) distribution
      • 5.2.5 Linear Combination of Random Vectors
      • 5.2.6 Multivariate Normal Likelihood
      • 5.2.7 Sampling Distribtion of \(\bar {\pmb y}, S\)
      • 5.2.8 Assessing Normality
      • 5.2.9 Power Transformation
    • 5.3 Inference about Mean Vector (wk3)
      • 5.3.1 Overview
      • 5.3.2 1. Confidence Region
      • 5.3.3 2. Simultaneous CI
      • 5.3.4 3. Note: Bonferroni Multiple Comparison
      • 5.3.5 4. Large Sample Inferences about a Mean Vector
      • 5.3.6 1. Profile Analysis (wk4, 5)
      • 5.3.7 2. Test for Linear Trend
      • 5.3.8 3. Inferences about a Covariance Matrix
    • 5.4 Comparison of Several MV Means (wk5)
      • 5.4.1 Paired Comparison
      • 5.4.2 Comparing Mean Vectors from Two Populations
      • 5.4.3 Profile Analysis (for \(g=2\))
      • 5.4.4 Comparing Several Multivariate Population Means
    • 5.5 Multivariate Multiple Regression (wk6)
      • 5.5.1 Overview
      • 5.5.2 Multivariate Multiple Regression
      • 5.5.3 Example)
    • 5.6 PCA
    • 5.7 Factor
      • 5.7.1 Method of Estimation
      • 5.7.2 Factor Rotation
      • 5.7.3 Varimax Criterion
      • 5.7.4 Factor Scores
    • 5.8 Discrimination and Classification
      • 5.8.1 Bayes Rule
      • 5.8.2 Classification with Two mv \(N\) Populations
      • 5.8.3 Evaluating Classification Functions
      • 5.8.4 Classification with several Populations (wk13)
      • 5.8.5 Other Discriminant Analysis Methods
    • 5.9 Clustering, Distance Methods, and Ordination
      • 5.9.1 Overview
      • 5.9.2 Hierarchical Clustering
      • 5.9.3 K-means Clustering
      • 5.9.4 군집의 평가방법
      • 5.9.5 Clustering using Density Estimation (wk14)
      • 5.9.6 Multidimensional Scaling (MDS)
  • 6 Linear
    • 6.1 Overview & SVD
      • 6.1.1 Spectral Decomposition
      • 6.1.2 Singular value Decomposition: General-version
      • 6.1.3 Singular value Decomposition: Another-version
      • 6.1.4 Quadratic Forms
      • 6.1.5 Partitioned Matrices
      • 6.1.6 Geometrical Aspects
      • 6.1.7 Column, Row and Null Space
    • 6.2 Introduction
      • 6.2.1 What
      • 6.2.2 Random Vectors and Matrices
      • 6.2.3 Multivariate Normal Distributions
      • 6.2.4 Distributions of Quadratic Forms
    • 6.3 Estimation
      • 6.3.1 Identifiability and Estimability
      • 6.3.2 Estimation: Least Squares
      • 6.3.3 Estimation: Best Linear Unbiased
      • 6.3.4 Estimation: Maximum Likelihood
      • 6.3.5 Estimation: Minimum Variance Unbiased
      • 6.3.6 Sampling Distributions of Estimates
      • 6.3.7 Generalized Least Squares(GLS)
    • 6.4 One-Way ANOVA
      • 6.4.1 One-Way ANOVA
      • 6.4.2 More About Models
      • 6.4.3 Estimating and Testing Contrasts
      • 6.4.4 Cochran’s Theorem
    • 6.5 Testing
      • 6.5.1 More About Models: Two approaches for linear model
      • 6.5.2 Testing Models
      • 6.5.3 A Generalized Test Procedure
      • 6.5.4 Testing Linear Parametric Functions
      • 6.5.5 Theoretical Complements
      • 6.5.6 A Generalized Test Procedure
      • 6.5.7 Testing Single Degrees of Freedom in a Given Subspace
      • 6.5.8 Breaking SS into Independent Components
      • 6.5.9 General Theory
      • 6.5.10 Two-Way ANOVA
      • 6.5.11 Confidence Regions
      • 6.5.12 Tests for Generalized Least Squares Models
    • 6.6 Generalized Least Squares
      • 6.6.1 A direct solution via inner products
    • 6.7 Flat
      • 6.7.1 1.Flat
      • 6.7.2 2. Solutions to systems of linear equations
    • 6.8 Unified Approach to Balanced ANOVA Models
  • (PART) 21-02
  • 7 Network Stats
    • 7.1 Introduction
      • 7.1.1 Types of Network Analysis
      • 7.1.2 Network Modeling and Inference
      • 7.1.3 Network Processes
    • 7.2 Descriptive Statistics of Networks
      • 7.2.1 Vertex and Edge Characteristics
      • 7.2.2 Characterizing Network Cohesion
      • 7.2.3 Graph Partitioning
      • 7.2.4 Assortativity and Mixing
    • 7.3 Data Collection and Sampling
      • 7.3.1 Sampling Designs
      • 7.3.2 Coping Strategies
      • 7.3.3 Big Data Solves Nothing
    • 7.4 Mathematical Models for Network Graphs
      • 7.4.1 Classical Random Graph Models
      • 7.4.2 Generalized Random Graph Models
      • 7.4.3 Network Graph Models Based on Mechanisms
      • 7.4.4 Assessing Significance of Network Graph Characteristics
    • 7.5 Introduction to ERGM
      • 7.5.1 Exponential Random Graph Models
      • 7.5.2 Difficulty in Parameter Estimation
    • 7.6 Parameter Estimation of ERGM
      • 7.6.1 Current Methods for ERGM
      • 7.6.2 Approximation-based Algorithm
      • 7.6.3 Auxiliary Variable MCMC-based Approaches
      • 7.6.4 Varying Trunction Stochastic Approximation MCMC
      • 7.6.5 Conclusion
    • 7.7 ERGM for Dynamic Networks
      • 7.7.1 Temporal ERGM (TERGM, T ERGM)
      • 7.7.2 Separable Temporal ERGM (STERGM, ST ERGM)
    • 7.8 Latent Network Models
      • 7.8.1 Latent Position Model
      • 7.8.2 Latent Position Cluster Model
    • 7.9 Additive and Multiplicative Effects Network Models
      • 7.9.1 Introduction
      • 7.9.2 Social Relations Regression
      • 7.9.3 Multiplicative Effects Models
      • 7.9.4 Inference via Posterior Approximation
      • 7.9.5 Discussion and Example with R
    • 7.10 Stochastic Block Models
      • 7.10.1 Stochastic Block Model
      • 7.10.2 Mixed Membership Block Model (MMBM)
  • 8 High Dimension
    • 8.1 Introduction
    • 8.2 Concentration inequalities
      • 8.2.1 Motivation
      • 8.2.2 From Markov to Chernoff
      • 8.2.3 sub-Gaussian random variables
      • 8.2.4 Properties of sub-Gaussian random variables
      • 8.2.5 Equivalent definitions
      • 8.2.6 Sub-Gaussian random vectors
      • 8.2.7 Hoeffding’s inequality
      • 8.2.8 Maximal inequalities
      • 8.2.9
    • 8.3 Concentration inequalities
      • 8.3.1 Sub-exponential random variables
      • 8.3.2 Bernstein’s condition
      • 8.3.3 McDiarmid’s inequality
      • 8.3.4 Levy’s inequality
      • 8.3.5 Quadratic form
      • 8.3.6 The Johnson–Lindenstrauss Lemma
    • 8.4 Metric entropy and its uses
      • 8.4.1 Metric space
      • 8.4.2 Covering numbers and metric entropy
      • 8.4.3 Packing numbers
      • 8.4.4
      • 8.4.5
      • 8.4.6
    • 8.5 Covariance estimation
      • 8.5.1 Matrix algebra review
      • 8.5.2 Covariance matrix estimation in the operator norm
      • 8.5.3 Bounds for structured covariance matrices
    • 8.6 Matrix concentration inequalities
      • 8.6.1 Matrix calculus
      • 8.6.2 Matrix Chernoff
      • 8.6.3 Sub-Gaussian and sub-exponential matrices
      • 8.6.4 랜덤 매트릭스에 대한 Hoeffding and Bernstein bounds
    • 8.7 Principal Component Analysis
      • 8.7.1 PCA
      • 8.7.2 Matrix Perturbation
      • 8.7.3 Spiked Cov Model
      • 8.7.4 sparse PCA
    • 8.8 Linear Regression
      • 8.8.1 Problem formulation
      • 8.8.2 Least Squares Estimator in high dimensions
      • 8.8.3 Sparse linear regression
    • 8.9 Uniform laws of large numbers
      • 8.9.1 Motivation
      • 8.9.2 A uniform law via Rademacher complexity
      • 8.9.3 Upper bounds on the Rademacher complexity
  • 9 Survival Analysis
    • 9.1 Introduction
    • 9.2
    • 9.3 Counting Processes and Martingales
      • 9.3.1 Conditional Expectation
      • 9.3.2 Martingale
      • 9.3.3 Key Martingales Properties
      • 9.3.4
      • 9.3.5
    • 9.4
    • 9.5 Cox Regression
    • 9.6 Filtration의 개념을 정복하자!
      • 9.6.1 Random Process를 이야기 하기까지의 긴 여정의 요약
      • 9.6.2 Ft-measurable
      • 9.6.3 EPILOGUE
    • 9.7 Concepts
  • (PART) 22-01
  • 10 scikit
    • 10.1 Linear Models
      • 10.1.1 Ordinary Least Squares
  • (APPENDIX) 00-00
  • 11 Concepts
    • 11.1 Autologistics
    • 11.2 Ordered Logit
    • 11.3 Concepts Questions
      • 11.3.1 통계 및 수학
  • 12 About Cluster-GCN
    • 12.0.1 ANN
    • 12.0.2 CNN
    • 12.0.3 Graph Convolution Network
    • 12.0.4 Cluster-GCN
  • 13 CNN
  • 14 CNN
  • 15 CNN
  • 16 01
  • Published with bookdown

Self-Study

Self-Study

Intro

뮤텍스(Mutex)와 세마포어(Semaphore)의 차이
GAN 모델의 이해와 구현
Statistical Learning Theory (1) - VC Bound
Machine Learning 스터디 (10) PAC Learning & Statistical Learning Theory
Sanghyuk Chun - Github
Vapnik SVM
About Support Vector Machine
about AI
VC dimension
Proof For Bernstein Bounds
WeiYa’s Work Yard
Dantzig’s unsolved homework problems
TAIL BOUNDS FOR NON-SYMMETRIC MATRICES
CNN 역전파를 이해하는 가장 쉬운 방법
Network Analysis using R
DL-딥러닝 토이 프로젝트 (AI 판타지 소설가)
CNN, Convolutional Neural Network 요약
생존분석 개념들
Gradient Descent(경사하강법) 와 SGD( Stochastic Gradient Descent) 확률적 경사하강법
R apply 계열 함수 총 정리 1 ( apply / lapply / sapply / vapply )
R apply 계열 함수 총 정리 2 ( lapply / mclapply )
ReLu(Rectified Linear Unit)
Network Modularity (네트워크의 모듈성)
빅데이터 분석 - 소셜 네트워크 분석 2(R 관련 그래프 실습)
Recommender System/추천 시스템
Java - Log4j 사용해 로그기록하기
생존분석 실습