为什么逻辑回归称为回归? [英] Why is logistic regression called regression?

问题描述

根据我所了解的，线性回归预测的结果可以具有连续值，而逻辑回归预测的结果是离散的.在我看来，逻辑回归类似于分类问题.那么，为什么叫回归?

According to what I have understood, linear regression predicts the outcome which can have continuous values, whereas logistic regression predicts outcome which is discrete. It seems to me that logistic regression is similar to a classification problem. So, why is it called regression?

还有一个相关的问题:线性回归和逻辑回归之间有什么区别?

There is also a related question: What is the difference between linear regression and logistic regression?

推荐答案

线性回归和逻辑回归之间有严格的联系.

There is a strict link between linear regression and logistic regression.

通过线性回归，您正在寻找k _i 个参数:

With linear regression you're looking for the k_i parameters:

h = k ₀ +Σ k _i ˙ X _i = K ^t ˙ X

h = k₀ + Σ k_i ˙ X_i = K^t ˙ X

使用逻辑回归可以达到相同的目标，但是等式是:

With logistic regression you've the same aim but the equation is:

h = g(K ^t ˙ X)

h = g(K^t ˙ X)

g是 Sigmoid函数的地方:

g(w)= 1/(1 + e ^-w )

所以:

h = 1/(1 + e ^{-K t ˙ X} )

h = 1 / (1 + e^{-Kt ˙ X})

您需要将K拟合到您的数据中.

and you need to fit K to your data.

假设存在二元分类问题，则输出h是示例x在分类任务中为正匹配的估计概率:

Assuming a binary classification problem, the output h is the estimated probability that the example x is a positive match in the classification task:

P(Y = 1)= 1/(1 + e ^{-K t ˙ X} )

P(Y = 1) = 1 / (1 + e^{-Kt ˙ X})

当概率大于0.5时，我们可以预测匹配".

When the probability is greater than 0.5 then we can predict "a match".

在以下情况下，概率大于0.5:

The probability is greater than 0.5 when:

g(w)> 0.5

g(w) > 0.5

并且在以下情况下是正确的

and this is true when:

w = K ^t ˙ X≥ 0

w = K^t ˙ X ≥ 0

超平面:

K ^t ˙ X = 0

K^t ˙ X = 0

是决策边界.

总结:

• 逻辑回归是使用相同线性回归基本公式的广义线性模型，但它是回归得出绝对结果的可能性.

• logistic regression is a generalized linear model using the same basic formula of linear regression but it is regressing for the probability of a categorical outcome.

这是一个非常删节的版本.您可以在这些视频(机器学习的第三周，由Andrew Ng提供.

This is a very abridged version. You can find a simple explanation in these videos (third week of Machine Learning by Andrew Ng).

您还可以查看 http://www.holehouse.org/mlclass/06_Logistic_Regression .html 中有关课程的一些注释.

You can also take a look at http://www.holehouse.org/mlclass/06_Logistic_Regression.html for some notes on the lessons.

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