Machine learning(2-Linear regression with one variable )
作者:互联网
1、Model representation
- Our Training Set [训练集]:
- We will start with this ‘’Housing price prediction‘’ example first of fitting linear functions, and we will build on this to eventually have more complex models
2、Cost function
- 代价函数(平方误差函数):It figures out how to fit the best possible straight line to our data
- So how to choose θi's ?
- and just try:
- The parameters we choose determine the accuracy of the straight line we get relative to our training set
- But there is modeling error 建模误差
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Our goal is to select the model parameters that minimize the sum of squares of modeling errors
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That is to minimize the cost function!
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summary:
2-1、Cost function introduction I
- We look up some plots to understand the cost function
2-2、Cost function introduction II
- Let's take a look at the three-dimensional space diagram of the cost function(also called a convex function 凸函数)
- And here is an example of a contour figure:
- The contour figure is a more convenient way to visualize the cost function
3、Gradient descent
- It turns out gradient descent(梯度下降) is a more general algorithm and is used not only in linear regression. I will introduce how to use gradient descent for minimizing some arbitrary function J
- The formula of the batch gradient descent algorithm :
4、Gradient descent intuition
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Derivative term purpose :get closer to the minimum
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Learning rate α :
- But what if my parameter θ1 is already at a local minimum?
- Gradient descent can converge to a local minimum, even with the learning rate α fixed
5、Gradient descent for linear regression
标签:function,Linear,Gradient,Machine,gradient,linear,cost,variable,descent 来源: https://www.cnblogs.com/wangzheming35/p/14861404.html