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 […]
051 月
蚁群算法
归类于未分类 3 条评论
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 […]
051 月
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 […]
051 月
EM算法
归类于数学 EM算法已关闭评论
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 […]
051 月
非参数模型
归类于数学 非参数模型已关闭评论
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 […]
051 月
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 […]