Archive

Durrett

4.8. Optional stopping theorem 22 Jan, 2021
4.5. Square integrable martingales 22 Jan, 2021
4.6.3. Riez's decomposition 21 Jan, 2021
4.6.2. Levy's theorem 21 Jan, 2021
4.6.1. Uniform integrability and convergence in $L^1$ 21 Jan, 2021
4.4. Martingale inequalities and convergence in $L^p$ 28 Dec, 2020
4.3. Application of martingales 28 Dec, 2020
4.2. Martingales and a.s. convergence 27 Dec, 2020
4.1. Conditional expectation 27 Dec, 2020
3.9. Infinitely divisible distributions 25 Dec, 2020
3.10. Limit theorems in ℝᵈ 23 Dec, 2020
3.6. Poisson convergence 23 Dec, 2020
3.4. Central limit theorem 23 Dec, 2020
3.3. Characteristic functions 22 Dec, 2020
3.2.2. Vague convergence and uniform tightness 22 Dec, 2020
3.2.1. Weak convergence 22 Dec, 2020
2.S1. Convergence concepts 21 Dec, 2020
2.5. Convergence of random series 21 Dec, 2020
2.4. Strong law of large numbers 21 Dec, 2020
2.3. Borel-Cantelli lemmas 20 Dec, 2020
2.2. Weak laws of large numbers 20 Dec, 2020
2.1. Independence 20 Dec, 2020
1.7. Product space 20 Dec, 2020
1.6. $L^p$ space 19 Dec, 2020
1.5. Convergence theorems and elementary inequalities 19 Dec, 2020
1.4. The Lebesgue integral 19 Dec, 2020
1.3. Random variables 18 Dec, 2020
1.2. Distributions 18 Dec, 2020
1.1. Basics on measure theory 18 Dec, 2020

Empirical processes in m-estimation

3.4.3. Uniform Law of Convex Hulls 12 Jul, 2021
3.4.2. Uniform Law of Vapnik-Chervonenkis Subgraph Classes 10 Jul, 2021
3.4.1. Examples of Sufficiencies of the Uniform Law 9 Jul, 2021
3.3. Uniform Law Under Random Entropy 9 Jul, 2021
3.2. Essential Techniques 8 Jul, 2021
3.1. Uniform Law Under Finite Bracketing Entropy 7 Jul, 2021
2.3. Entropy Inequalities 7 Jul, 2021
2.2. Entropy 6 Jul, 2021
2.1. Empirical Process 2 Jul, 2021
1.3. Consistency of MLE 1 Jul, 2021
1.2. Mean Estimation in the Binary Choice Problem 1 Jul, 2021
1.1. Binary Choice Problem 30 Jun, 2021

Real and complex analysis

4. Hilbert Space Theory 11 Apr, 2021
3. $L^p$ Space 11 Apr, 2021
2. Construction of Lebesgue Measure 22 Mar, 2021
1. Measurable Space and Integration 4 Mar, 2021

The elements of statistical learning

3. Shrinkage Estimators 17 Mar, 2021
2. Linear classifiers 16 Mar, 2021
1. Overview of Supervised Learning 3 Mar, 2021

Adaptive sequential decision making

2. Explore-Then-Commit algorithm 5 Mar, 2021
1. Introduction to Multi-armed Bandit 5 Mar, 2021

Applied

$k$-mer Sequence Motif는 얼마나 자주 등장할까 25 Oct, 2018
요인분석으로 내게 맞는 스마트폰 카메라 찾기 29 Dec, 2017
2017 대선 후보 지지층 군집분석 28 Apr, 2017

Asymptotics

3.4.3. Uniform Law of Convex Hulls 12 Jul, 2021
3.4.2. Uniform Law of Vapnik-Chervonenkis Subgraph Classes 10 Jul, 2021
3.4.1. Examples of Sufficiencies of the Uniform Law 9 Jul, 2021
3.3. Uniform Law Under Random Entropy 9 Jul, 2021
3.2. Essential Techniques 8 Jul, 2021
3.1. Uniform Law Under Finite Bracketing Entropy 7 Jul, 2021
2.3. Entropy Inequalities 7 Jul, 2021
2.2. Entropy 6 Jul, 2021
2.1. Empirical Process 2 Jul, 2021
1.3. Consistency of MLE 1 Jul, 2021
1.2. Mean Estimation in the Binary Choice Problem 1 Jul, 2021
1.1. Binary Choice Problem 30 Jun, 2021
Asymptotics is strange 21 Apr, 2021

Bandit

2. Explore-Then-Commit algorithm 5 Mar, 2021
1. Introduction to Multi-armed Bandit 5 Mar, 2021

Bayesian

Understanding Latent Dirichlet Allocation (5) Smooth LDA 17 Feb, 2021
Understanding Latent Dirichlet Allocation (4) Gibbs Sampling 16 Feb, 2021
Understanding Latent Dirichlet Allocation (3) Variational EM 15 Feb, 2021
Understanding Latent Dirichlet Allocation (2) The Model 14 Feb, 2021

Bioinformatics

Quantile Normalization 19 Jul, 2019
FASTA 압축기 만들기 20 Jun, 2018

Decision theory

The slowest run vs. the fastest walk: which is faster? 22 May, 2020
Logistic, cross-entropy loss의 확률론적 의미 3 May, 2018

Empirical process

3.4.3. Uniform Law of Convex Hulls 12 Jul, 2021
3.4.2. Uniform Law of Vapnik-Chervonenkis Subgraph Classes 10 Jul, 2021
3.4.1. Examples of Sufficiencies of the Uniform Law 9 Jul, 2021
3.3. Uniform Law Under Random Entropy 9 Jul, 2021
3.2. Essential Techniques 8 Jul, 2021
3.1. Uniform Law Under Finite Bracketing Entropy 7 Jul, 2021
2.3. Entropy Inequalities 7 Jul, 2021
2.2. Entropy 6 Jul, 2021
2.1. Empirical Process 2 Jul, 2021
1.3. Consistency of MLE 1 Jul, 2021
1.2. Mean Estimation in the Binary Choice Problem 1 Jul, 2021
1.1. Binary Choice Problem 30 Jun, 2021

Exploratory analysis

요인분석으로 내게 맞는 스마트폰 카메라 찾기 29 Dec, 2017

Generative model

Understanding Restricted Boltzmann Machine 14 Jul, 2021

Information theory

Understanding Restricted Boltzmann Machine 14 Jul, 2021
Mutual information and Channel Capacity 13 Jul, 2021
The Shannon Entropy 12 Jul, 2021
A metric derived from KL divergence 5 May, 2020

Kernel

4. Multivariate Kernel Density Estimation 19 Mar, 2021
3. Bandwidth Selection 18 Mar, 2021
2. Univariate Kernel Density Estimation 13 Mar, 2021
1. Brief Introduction to Nonparametric function estimation 3 Mar, 2021

Linear model

Limitation of $R^2$ 28 Apr, 2020

Machine learning

Understanding Restricted Boltzmann Machine 14 Jul, 2021
Understanding ELMo 24 Feb, 2021
Understanding Latent Dirichlet Allocation (5) Smooth LDA 17 Feb, 2021
Understanding Latent Dirichlet Allocation (4) Gibbs Sampling 16 Feb, 2021
Understanding Latent Dirichlet Allocation (3) Variational EM 15 Feb, 2021
Understanding Latent Dirichlet Allocation (2) The Model 14 Feb, 2021
Understanding FastText 9 Feb, 2021
Understanding Skip Gram 8 Feb, 2021
Understanding Neural Probabilistic Language Model 4 Feb, 2021
Setting up M1 Mac for both TensorFlow and PyTorch 29 Jan, 2021
Weakly-Supervised Localization: 뉴럴넷은 어디를 바라보고 있는가 17 Jun, 2018
Batch Normalization 이해하기 28 May, 2018
Convolutional Neural Network (CNN) 이해하기 27 May, 2018
인공신경망 이해하기 (4) 학습 과정 - 디테일 20 Apr, 2018
인공신경망 이해하기 (3) 학습 과정 - 개요 19 Apr, 2018
인공신경망 이해하기 (2) 퍼셉트론과 신경망 17 Apr, 2018
인공신경망 이해하기 (1) 선형 분류기 17 Apr, 2018

Mathematical analysis

Feynmann's technique for Gamma-like integrals 21 Jul, 2021

Multivariate

요인분석으로 내게 맞는 스마트폰 카메라 찾기 29 Dec, 2017

Natural language processing

Understanding ELMo 24 Feb, 2021
Understanding Latent Dirichlet Allocation (5) Smooth LDA 17 Feb, 2021
Understanding Latent Dirichlet Allocation (4) Gibbs Sampling 16 Feb, 2021
Understanding Latent Dirichlet Allocation (3) Variational EM 15 Feb, 2021
Understanding Latent Dirichlet Allocation (2) The Model 14 Feb, 2021
Understanding Latent Dirichlet Allocation (1) Backgrounds 14 Feb, 2021
Understanding FastText 9 Feb, 2021
Understanding Skip Gram 8 Feb, 2021
Understanding Neural Probabilistic Language Model 4 Feb, 2021

Nonparametric

4. Multivariate Kernel Density Estimation 19 Mar, 2021
3. Bandwidth Selection 18 Mar, 2021
2. Univariate Kernel Density Estimation 13 Mar, 2021
1. Brief Introduction to Nonparametric function estimation 3 Mar, 2021

Probability

Negative Version of Hypergeometric Distribution 20 Jul, 2021
4.8. Optional stopping theorem 22 Jan, 2021
4.5. Square integrable martingales 22 Jan, 2021
4.6.3. Riez's decomposition 21 Jan, 2021
4.6.2. Levy's theorem 21 Jan, 2021
4.6.1. Uniform integrability and convergence in $L^1$ 21 Jan, 2021
4.4. Martingale inequalities and convergence in $L^p$ 28 Dec, 2020
4.3. Application of martingales 28 Dec, 2020
4.2. Martingales and a.s. convergence 27 Dec, 2020
4.1. Conditional expectation 27 Dec, 2020
3.9. Infinitely divisible distributions 25 Dec, 2020
3.10. Limit theorems in ℝᵈ 23 Dec, 2020
3.6. Poisson convergence 23 Dec, 2020
3.4. Central limit theorem 23 Dec, 2020
3.3. Characteristic functions 22 Dec, 2020
3.2.2. Vague convergence and uniform tightness 22 Dec, 2020
3.2.1. Weak convergence 22 Dec, 2020
2.S1. Convergence concepts 21 Dec, 2020
2.5. Convergence of random series 21 Dec, 2020
2.4. Strong law of large numbers 21 Dec, 2020
2.3. Borel-Cantelli lemmas 20 Dec, 2020
2.2. Weak laws of large numbers 20 Dec, 2020
2.1. Independence 20 Dec, 2020
1.7. Product space 20 Dec, 2020
1.6. $L^p$ space 19 Dec, 2020
1.5. Convergence theorems and elementary inequalities 19 Dec, 2020
1.4. The Lebesgue integral 19 Dec, 2020
1.3. Random variables 18 Dec, 2020
1.2. Distributions 18 Dec, 2020
1.1. Basics on measure theory 18 Dec, 2020
Application of Dynkin's π-λ theorem 13 May, 2020
Kolmogorov's maximal inequality with shifted starting point 9 May, 2020
Determination of random variables and random number generation 30 Apr, 2020
Borel-Cantelli lemmas are converses of each other 29 Apr, 2020
Irregularity of almost sure convergence 27 Apr, 2020
Strong law of large numbers 25 Apr, 2020
High-dimensional box 24 Apr, 2020

Real analysis

4. Hilbert Space Theory 11 Apr, 2021
3. $L^p$ Space 11 Apr, 2021
2. Construction of Lebesgue Measure 22 Mar, 2021
1. Measurable Space and Integration 4 Mar, 2021

Spline

1. Brief Introduction to Nonparametric function estimation 3 Mar, 2021

Statistical learning

3. Shrinkage Estimators 17 Mar, 2021
2. Linear classifiers 16 Mar, 2021
1. Overview of Supervised Learning 3 Mar, 2021

Thoughts

내 가장 오래된 프로그래밍 기억 1 Jul, 2021
Another semester has gone by 29 Jun, 2021
의식을 이식하기 23 Mar, 2017

Author | Sihyung Park

An M.S. student majoring in Statistics. Hope my works lead to meaningful results.