Coursera机器学习编程作业Python实现（Andrew Ng）—— 2.1 Logistic Regression

2.1 Logistic Regression

import numpy as np
import pandas as pd
import matplotlib.pyplot as plt
import math

数据读取

data1 = pd.read_csv(\'ex2data1.txt\', header=None, names=[\'Exam 1 score\', \'Exam 2 score\', \'Admission\'])

_, ax = plt.subplots(figsize=(10,6))
data1[data1[\'Admission\']==0].plot(x=\'Exam 1 score\', y=\'Exam 2 score\', kind=\'scatter\', c=\'red\', marker=\'o\', ax=ax, label=\'Not admitted\')
data1[data1[\'Admission\']==1].plot(x=\'Exam 1 score\', y=\'Exam 2 score\', kind=\'scatter\', c=\'blue\',marker=\'x\', ax=ax, label=\'Admitted\')
plt.show()

数据预处理

data1.insert(0, \'ones\', 1)
X = data1.values[:,:-1]
y = data1.values[:,-1]
theta = np.zeros(X.shape[1]

定义sigmoid函数

def sigmoid(x):
    return 1 / (1 + np.exp(-x))

定义代价函数

def costFunction(theta, X, y):
    return np.mean(- y * np.log(sigmoid(np.dot(X, theta))) - (1 - y) * np.log(1 - sigmoid(np.dot(X, theta))))

costFunction(theta, X, y)

0.6931471805599453

定义梯度下降函数

def gradient(theta, X, y):
    return (1/X.shape[0]) * np.dot(X.T, sigmoid(np.dot(X, theta)) - y)

gradient(theta, X, y)

array([ -0.1       , -12.00921659, -11.26284221])

构造优化器求解

import scipy.optimize as opt
res = opt.minimize(fun=costFunction, x0=theta, args=(X, y), jac=gradient, method=\'Newton-CG\')
res

 fun: 0.20349771251305832
     jac: array([1.68639010e-05, 9.03344162e-04, 8.76022414e-04])
 message: \'Optimization terminated successfully.\'
    nfev: 71
    nhev: 0
     nit: 28
    njev: 240
  status: 0
 success: True
       x: array([-25.1527642 ,   0.20616308,   0.20140236])

theta_result = res.x

验证

sigmoid(np.dot(np.array([1, 45, 85]), theta_result))

0.776220348464748

def predict(X, theta):
    return (sigmoid(np.dot(X, theta)) >= 0.5).astype(int)
y_pred = predict(X, theta_result)
from sklearn.metrics import classification_report
print(classification_report(y, y_pred))

precision    recall  f1-score   support

        0.0       0.87      0.85      0.86        40
        1.0       0.90      0.92      0.91        60

avg / total       0.89      0.89      0.89       100

x = [X[:,1].min(), X[:,1].max()]
y = [-(theta_result[0]+theta_result[1]*x[0])/theta_result[2],-(theta_result[0]+theta_result[1]*x[1])/theta_result[2]]
_, ax = plt.subplots(figsize=(10,6))
data1[data1[\'Admission\']==0].plot(x=\'Exam 1 score\', y=\'Exam 2 score\', kind=\'scatter\', c=\'red\', marker=\'o\', ax=ax, label=\'Not admitted\')
data1[data1[\'Admission\']==1].plot(x=\'Exam 1 score\', y=\'Exam 2 score\', kind=\'scatter\', c=\'blue\',marker=\'x\', ax=ax, label=\'Admitted\')
ax.plot(x, y)
plt.show()