吴恩达机器学习课程需要的基础（吴恩达MachineLearning笔记-linearregression）

吴恩达机器学习课程需要的基础（吴恩达MachineLearning笔记-linearregression）The direction in which the step is taken is determined by the partial derivative of J(θ0​ θ1​).Imagine that we graph our hypothesis function based on its fields θ0 and θ1​ (actually we are graphing the cost function as a function of the parameter estimates). We are not graphing x and y itself but the parameter range of our hypothesis function and the cost resulting from selecting a particular set

linear regression

when the target variable that we're trying to predict is continuous we call the learning problem a regression problem when y can take only a small number of discrete values we call it a classification problem.

The cost function of linear regression is:

Our goal is to minimize the cost function.

随机矩阵

随机矩阵实际上应当分成行随机矩阵（Row stochastic matrix）和列随机矩阵（Column stochastic matrix）。行随机矩阵是指方阵的行和等于1；而列随机矩阵就是其列和等于1的非负矩阵。那么同时满足行和列和都是1的非负矩阵就是双随机矩阵（Double stochastic matrix），单位矩阵就是一种双随机矩阵。

Gradient Descent

Imagine that we graph our hypothesis function based on its fields θ0 and θ1​ (actually we are graphing the cost function as a function of the parameter estimates). We are not graphing x and y itself but the parameter range of our hypothesis function and the cost resulting from selecting a particular set of parameters.

The main steps of Gradient Descent are as follow:

The way we do this is by taking the derivative (the tangential line to a function) of our cost function. The slope of the tangent is the derivative at that point and it will give us a direction to move towards. We make steps down the cost function in the direction with the steepest descent. The size of each step is determined by the parameter α which is called the learning rate.

The direction in which the step is taken is determined by the partial derivative of J(θ0​ θ1​).