Renlin Li lirenlin

Jａｃｏｂｉａｎ矩阵　用于一阶梯度下降法
Hessian矩阵，　用于二阶牛顿法
高斯牛顿法，　使用J^TJ作为牛顿法中二阶Hessian矩阵的近似，　从而省略了计算Ｈ的过程
http://jacoxu.com/jacobian%E7%9F%A9%E9%98%B5%E5%92%8Chessian%E7%9F%A9%E9%98%B5/

Hessian是对称矩阵 jacobian, Hassian and gradient　关系
https://blog.csdn.net/DSbatigol/article/details/12558891

The gradient is a vector-valued function, as opposed to a derivative, which is scalar-valued.

In some applications it is customary to represent the gradient as a row vector or column vector of its components in a rectangular coordinate system.

muti-variable function
- scalar-valued function: Rn -> R, gradient vector, row matrix or column matrix.
  f(x1, x2 ... xn):

滤波器模型１，　假设了马尔科夫性，　当前状态只跟上一个时候状态有关２，　线性高斯假设　－－》　卡尔曼滤波器模型

线性高斯系统：运动方程，　观测方程都可以由线性来描述，　并假设所有的运动和观测噪声都满足高斯分布
x_k = A_k*x_k-1 + u_k + w_k
z_k = C_k*x_k + v_k
w_k ~ N (0, R)\

MLE：　最大似然概率给定测量结果，　系统模型，　寻求系统模型参数让结果跟观测结果最贴近。

似然函数（也称作似然），是一个关于统计模型参数的函数。也就是这个函数中自变量是统计模型的参数。对于观测结果 x ，在参数集合 θ 上的似然，就是在给定这些参数值的基础上，观察到的结果的概率 P(x|θ) 。也就是说，似然是关于参数的函数，在参数给定的条件下，对于观察到的 x 的值的条件分布。

MAP:　最大后验概率考虑到先验概率的存在 prior probability

theta` = argmax P(theta|x) = P(x|theta) * p(theta) / p(x)

	tree vs graph

	in tree, every node has a single predecessor, could have multiple sucessors.
	in graph, there is no limitation, multiple predecessors, multiple sucessors.

	RPO in graph, ensures all predecessors are visited before the current node is visited. Topologic sorting, forward data flow analysis.
	RPO is the same as pre-order in tree, but different in graph.

	post-order ensures all sucessors are visited before current node is visited. This is the reverse of RPO. backward data analysis.

	.ssh/config
	Host *
	ForwardAgent yes

	eval `ssh-agent -s`
	ssh-add
	ssh -A xx@xxx


	https://stackoverflow.com/questions/17846529/could-not-open-a-connection-to-your-authentication-agent

	position independent executable: executable
	position independent code: shared object/library


	PIE is to support address space layout randomization (ASLR) in executable files.

	static pie: executable without external dependency of shared library or dynamic linker.
	It should be able to self-relocate itself.

	There must be a entry point stub which only use pc relative addressing.

	解析解，又稱為閉式解，是可以用解析表達式來表達的解。在数学上，如果一个方程或者方程组存在的某些解，是由有限次常见运算的組合给出的形式，则称该方程存在解析解。
	二次方程的根就是一个解析解的典型例子。在低年级数学的教学当中，解析解也被称为公式解。

	当解析解不存在时，比如五次以及更高次的代数方程，则该方程只能用数值分析的方法求解近似值。大多數偏微分方程，尤其是非线性偏微分方程，都只有數值解。

	Euclidean space
	Cartesian coordinate system
	manifolds