为什么梯度下降时我们可以解析线性回归 [英] why gradient descent when we can solve linear regression analytically

问题描述

在线性回归空间中使用梯度下降有什么好处?看起来我们可以用分析方法解决问题(找到最小的成本函数的theta0-n)，那么为什么我们仍然要使用梯度下降来做同样的事情?谢谢

what is the benefit of using Gradient Descent in the linear regression space? looks like the we can solve the problem (finding theta0-n that minimum the cost func) with analytical method so why we still want to use gradient descent to do the same thing? thanks

推荐答案

使用正态方程来分析成本函数时，您必须计算:

When you use the normal equations for solving the cost function analytically you have to compute:

其中X是您的输入观察矩阵，y是您的输出向量.此操作的问题是计算n(n ^ 3)的nxn矩阵的逆的时间复杂度，并且随着n的增加，它可能需要很长时间才能完成.

Where X is your matrix of input observations and y your output vector. The problem with this operation is the time complexity of calculating the inverse of a nxn matrix which is O(n^3) and as n increases it can take a very long time to finish.

当n较低(n <1000或n <10000)时，您可以将正则方程视为计算theta的更好选择，但是对于更大的值，梯度下降要快得多，所以唯一的原因是时间:)

When n is low (n < 1000 or n < 10000) you can think of normal equations as the better option for calculation theta, however for greater values Gradient Descent is much more faster, so the only reason is the time :)

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