## 线性回归模型简介

Suppose $Y$ is a response variable, $X_p$ is a $p$-dimension covariates, $\epsilon$ is random error. We say $Y$ linearly dependents $X_p$ if $$Y=X_p^T\beta+\epsilon,(*)$$ here $A^T$ is the transpose of matrix $A$. With model(*), we have some tasks to finish: 1) Does model(*) correctly describe the d […]

## 蚁群算法

Italy scholar Dorigo M. et al. proposed Ant colony algorithm at European Conference on Artificial Life, ECAL) in 1991. 1) Basic Ideas Ant Colony Algorithm(ACA) simulates how ants find the food. Why ants can find the shortest way from their nest to the food? Pheromone is the key. Pheromone can be det […]

## 遗传算法

Gene Algorithm(GA) is a very popular intelligent optimization algorithm. It was proposed by professor John H. Holland and his students of University Michigan at 1960s and 1970s. By evolution of populations, solutions represented by individuals promote the fitness to the environment. After enough gen […]

## EM算法

Suppose we have samples ${X_i,i=1,\cdots,n}$ from $p$-dimension normal distribution, and some observations have partial missing values. Without loss of generality, assume missing values occure at indexes $1,\cdots,d$, and $d < p$. Then how do we estimate the mean and variance of the underlying distr […]

## 非参数模型

What is a nonparametric model? Linear regression models has parameters, the coefficients of covariates, and possible an intercept. A nonparametric model looks like $Y=g(T)+\epsilon,(*)$ here $T$ is a univariate, $Y$ is the response, $\epsilon$ is the error. Model(*) is said to be infinite-dimensio […]

## Euler常数γ的推广

Xiu-You Xu* Email:xiuyouxu#gmail.com abstract When $n\rightarrow\infty$, it is well known that $\sum\nolimits_{i=1}^n\frac{1}{i}\sim{\ln{n}+\gamma}$, where $\gamma$ is Euler-Mascheroni Constant. We will talk about the coefficients of the function having $(-lnx)^m$ as $n$th-order derivative, and gene […]