Recently I was introduced a new point of view of RKHS by my advisor. I think it's quite interesting and worth sharing. It provides a new understanding of how RKHS is constructed and, it's

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文档·资料·≈ 2 分钟

2023 年 6 月 24 日

Other Activities

I was awarded five-star Zijing volunteer @ Tsinghua Univ in 2023.

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文档·资料·≈ 5 分钟

2023 年 2 月 26 日

Joke Collection

工程师的罐头打开了，纸跟笔没有动，但墙上有很多印。原来工程师把罐头丢到墙上，试验了很多次，终于找到了合适的角度磕开了罐头。物理学家的罐头也被打开了，他的纸上密密麻麻地满了公式和数字，但墙上只有一个印。原来物理学家经过计算找到了完美的角度，一下子就磕开了罐头。

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文档·资料·≈ 2 分钟

2022 年 12 月 24 日

Λέξεις και Φράσεις

Here are the words and phrases I learnt when attending a second foreign language course of Greek.

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数学与统计·≈ 2 分钟

2022 年 12 月 23 日

Brownian Bridge and Basel Problem

This blog originates from a question in the final exam of Applied Stochastic Process this semester. The question focused on the Karhunen-Loève expansion of Brownian Bridge. Soon I was surprised to

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数学与统计·≈ 2 分钟

2022 年 9 月 19 日

Derivation of Poisson Distribution

Here I record two ways to derive Poisson distribution. A Poisson process is the number of events $\{N(t),t\geq 0\}$ in some given time $[0,t]$ , with the following property:

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数学与统计·≈ 10 分钟

2022 年 8 月 15 日

Reading Notes of Replica Symmetric Breaking

Here is my reading note for the book 『Statistical Physics of Spin Glasses and Information Processing: An Introduction』 by Hidetoshi Nishimori. I am still not quite clear about this field so please

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文档·资料·≈ 1 分钟

2022 年 8 月 12 日

R Package File

The file is written in package.r and called by command source('package.r')

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数学与统计·≈ 2 分钟

2022 年 4 月 27 日

Variance of Odds Ratio in Contingency Table

Odds ratio of the contingency table below is an important statistics

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文档·资料·≈ 6 分钟

2022 年 4 月 24 日

LaTeX Head File

Here I document two LaTeX head files I frequently use. By replacing all CAPITALIZED CONTENTS to what you need and compile with xelatex you could obtain a well pre-designed LaTeX document. For help

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数学与统计·≈ 1 分钟

2022 年 4 月 10 日

Best Linear Estimator

Theoretically best linear estimator is crucial in definition of Partial Autocorrelation in time series. It provides an estimation with correlated variable considered.

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数学与统计·≈ 6 分钟

2022 年 4 月 8 日

Theory of Reproducing Kernel Hilbert Space (RKHS) and Application

Before the rise of (deep) neural network, Kernel trick is an important approach used in feature engineering to 'define similarity' and thus is powerful in extracting feature. Based on Reproducing

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数学与统计·≈ 2 分钟

2022 年 3 月 28 日

Basic Constrained Optimize Theory

For optimize problem in convex set $\mathcal{X}$

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数学与统计·≈ 3 分钟

2022 年 3 月 8 日

Cochran Theorem for Variance Decomposition

Cochran's Theorem is the basis of variance composition in ANOVA. Here is a proof that could be understood intuitively, and an linear regression example of how Cochran's thm. is used in ANOVA.

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数学与统计·≈ 5 分钟

2021 年 12 月 10 日

Expectation-Maximization Algorithm in Gaussian Mixture Model

Expectation-Maximization is used in MLE to estimate some model parameter $\theta$ for model $\{x_i\}$ i.i.d. $\sim f(x\vert \theta )$ .

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数学与统计·≈ 1 分钟

2021 年 11 月 15 日

Convergence Order 1.618 of Secant Interpolation Rooting

For some iteration algorithm $x^{(t+1)}=g\left( x^{(t)} \right)$ with final solution denoted $x^*$ , error $\varepsilon ^{(t)}:=x^{(t)}-x^*$ , its convergence order $\alpha$ and converngence rate $c$ :

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数学与统计·≈ 2 分钟

2021 年 10 月 20 日

Positive-Definition of Diagonal Dominant Matrix

Positive semi-definition of Diagonal Dominant Matrix (with non-negative diagonal) is an important property in numeric linear algebra. Here I record two prooves, one following the idea of Gershgorin

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数学与统计·≈ 1 分钟

2021 年 5 月 30 日

Box-Cox Transformation

Usually transformation to numeric data $\mathcal{D}=\{X_i,Y_i\}_{i=1}^n$ is necessary in regression analysis, usually to stablize variance. Box-Cox is the most important method.

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数学与统计·≈ 3 分钟

2021 年 5 月 2 日

Residuals for Influential Diagnosis in Linear Regression

In linear regression, influential diagnosis is important to obtain better model fit and performance. Usually such diagnosis is based on residuals. Here are some important residuals that help locate

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数学与统计·≈ 2 分钟

2021 年 1 月 18 日

Liénard–Wiechert Potential

In dealing with electro-magnetic field of moving charged particle $q$ at $\vec{r}_0(t)$ with velocity $\vec{v}_0(t)$ :

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数学与统计·≈ 2 分钟

2020 年 11 月 30 日

Proof Two Properties of Log-Likelihood

Given data $\mathcal{D}=\{x\}_{i=1}^N$ and statistics model $X\sim \mathscr{F} = \{ f(x;\theta ):\theta \in\Theta \}$ . Maximum Likelihood Estimation (MLE) is an important approach to estimation of $\theta$

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数学与统计·≈ 1 分钟

2020 年 11 月 24 日

Indepency between $\bar{X}$ and $S^2$

Data is given as $\mathcal{D}=\{X_i\}_{i=1}^n$ , with $X_i$ i.i.d. $\sim N(\mu ,\sigma ^2)$ . Two crucial statistics are mean value $\bar{X}$ and variance $S^2_X$ :

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『Just Because!』圣地巡礼

向 Fuego 进发

水蛋蒸肉饼

辣椒炒肉

地中海风味蔬菜汤

伊比利亚 2025 — 圣诞

皮蛋瘦肉粥

芝士焗饭

日本語

Clam Chowder

蛋炒饭

France 2024 巴黎餐馆简评

西欧春游 2024

青椒炒鸡

广式炖牛腩

Mousse au Chocolat

豉汁排骨

Ragù alla Bolognese

Carbonara

辛拉面配香煎鸡排

LaTeX VSCode Snippets

Steak

奶汁烩菜

RKHS in a Dual Space delta function Perspective

Other Activities

Joke Collection

Λέξεις και Φράσεις

Brownian Bridge and Basel Problem

Derivation of Poisson Distribution

Reading Notes of Replica Symmetric Breaking

R Package File

Variance of Odds Ratio in Contingency Table

LaTeX Head File

Best Linear Estimator

Theory of Reproducing Kernel Hilbert Space (RKHS) and Application

Basic Constrained Optimize Theory

Cochran Theorem for Variance Decomposition

Expectation-Maximization Algorithm in Gaussian Mixture Model

Convergence Order 1.618 of Secant Interpolation Rooting

Positive-Definition of Diagonal Dominant Matrix

Box-Cox Transformation

Residuals for Influential Diagnosis in Linear Regression

Liénard–Wiechert Potential

Proof Two Properties of Log-Likelihood

Indepency between Xˉ\bar{X}Xˉ and S2S^2S2

Indepency between $\bar{X}$ and $S^2$