Python SKLearn:逻辑回归概率 [英] Python SKLearn: Logistic Regression Probabilities

问题描述

我正在使用Python SKLearn模块执行逻辑回归.我有一个因变量矢量Y(从M个类中的1个取值)和独立变量矩阵X(具有N个特征).我的代码是

I am using the Python SKLearn module to perform logistic regression. I have a dependent variable vector Y (taking values from 1 of M classes) and independent variable matrix X (with N features). My code is

        LR = LogisticRegression()
        LR.fit(X,np.resize(Y,(len(Y))))

我的问题是，LR.coef_和LR.intercept_代表什么.我最初以为它们保留值intercept(i)和coef(i,j) s.t.

My question is, what does LR.coef_ and LR.intercept_ represent. I initially thought they held the values intercept(i) and coef(i,j) s.t.

log(p(1)/(1-p(1))) = intercept(1) + coef(1,1)*X1 + ... coef(1,N)*XN
.
.
.
log(p(M)/(1-p(M))) = intercept(M) + coef(M,1)*X1 + ... coef(M,N)*XN

其中，p(i)是具有特征[X1, ... ,XN]的观察在类i中的概率.但是当我尝试转换时

where p(i) is the probability that observation with features [X1, ... ,XN] is in class i. However when I try to convert

V = X*LR.coef_.transpose()
U = V + LR.intercept_
A = np.exp(U)
A/(1+A)

，因此A是p(1) ... p(M)中观察值的p(1) ... p(M)矩阵.该值应与

so that A is the matrix of p(1) ... p(M) for the observations in X. This should be the same value as

LR.predict_proba(X)

但是它们很接近，但又有所不同.为什么是这样?

however they are close, but different. Why is this?

推荐答案

coef_和intercept_属性表示您的想法，因为您忘记了归一化，所以概率计算已关闭:

The coef_ and intercept_ attributes represent what you think, your probability calculations are off because you forgot to normalize: after

P = A / (1 + A)

你应该做

P /= P.sum(axis=1).reshape((-1, 1))

再现 scikit-learn算法.

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