此处用代码展示一下，如何用梯度下降法获取逻辑回归算法的参数。
一、加载sklearn中的鸢尾花数据进行测试
为了数据可视化，我们选择2种类型的鸢尾花，并且只选择2个特征。
import numpy as np
import matplotlib.pyplot as plt
from sklearn import datasets
iris = datasets.load_iris()
X = iris.data
y = iris.target
X = X[y<2, :2] # 只取前两个特征
y = y[y<2]
plt.scatter(X[y==0,0], X[y==0,1], color='red')
plt.scatter(X[y==1,0], X[y==1,1], color='blue')
plt.show()
Output：
二、编写逻辑回归算法
先在playML文件夹中写一个metrics模块，用于计算准确率：
import numpy as np
def accuracy_score(y_true, y_predict):
"""计算y_true和y_predict之间的准确率"""
return np.sum(y_true == y_predict) / len(y_true)
接着在playML文件夹中编写逻辑回归算法：
import numpy as np
from .metrics import accuracy_score # .表示当前目录
class LogisticRegression:
def __init__(self):
"""初始化Logistic Regression模型"""
self.coef_ = None
self.intercept_ = None
self._theta = None
def _sigmoid(self, t):
return 1. / (1. + np.exp(-t))
def fit(self, X_train, y_train, eta=0.01, n_iters=1e4):
"""根据训练数据集X_train, y_train, 使用梯度下降法训练Logistic Regression模型"""
def J(theta, X_b, y):
y_hat = self._sigmoid(X_b.dot(theta))
try:
return - np.sum(y*np.log(y_hat) + (1-y)*np.log(1-y_hat)) / len(y)
except:
return float('inf')
def dJ(theta, X_b, y):
return X_b.T.dot(self._sigmoid(X_b.dot(theta)) - y) / len(y)
def gradient_descent(X_b, y, initial_theta, eta, n_iters=1e4, epsilon=1e-8):
theta = initial_theta
cur_iter = 0
while cur_iter < n_iters:
gradient = dJ(theta, X_b, y)
last_theta = theta
theta = theta - eta * gradient
if (abs(J(theta, X_b, y) - J(last_theta, X_b, y)) < epsilon):
break
cur_iter += 1
return theta
X_b = np.hstack([np.ones((len(X_train), 1)), X_train])
initial_theta = np.zeros(X_b.shape[1])
self._theta = gradient_descent(X_b, y_train, initial_theta, eta, n_iters)
self.intercept_ = self._theta[0]
self.coef_ = self._theta[1:]
return self
def predict_proba(self, X_predict):
"""给定待预测数据集X_predict，返回表示X_predict的结果概率向量"""
X_b = np.hstack([np.ones((len(X_predict), 1)), X_predict])
return self._sigmoid(X_b.dot(self._theta))
def predict(self, X_predict):
"""给定待预测数据集X_predict，返回表示X_predict的结果向量"""
proba = self.predict_proba(X_predict)
return np.array(proba >= 0.5, dtype='int')
def score(self, X_test, y_test):
"""根据测试数据集 X_test 和 y_test 确定当前模型的准确度"""
y_predict = self.predict(X_test)
return accuracy_score(y_test, y_predict)
def __repr__(self):
return "LogisticRegression()"
然后在playML文件夹中编写一个分割数据集的模块：
import numpy as np
def train_test_split(X, y, test_ratio=0.2, seed=None):
"""将数据 X 和 y 按照test_ratio分割成X_train, X_test, y_train, y_test"""
if seed:
np.random.seed(seed)
shuffled_indexes = np.random.permutation(len(X))
test_size = int(len(X) * test_ratio)
test_indexes = shuffled_indexes[:test_size]
train_indexes = shuffled_indexes[test_size:]
X_train = X[train_indexes]
y_train = y[train_indexes]
X_test = X[test_indexes]
y_test = y[test_indexes]
return X_train, X_test, y_train, y_test
三、实现逻辑回归
from playML.model_selection import train_test_split
from playML.LogisticRegression import LogisticRegression
X_train, X_test, y_train, y_test = train_test_split(X, y, seed=666)
log_reg = LogisticRegression()
log_reg.fit(X_train, y_train) # 训练模型
print(log_reg._theta) # 参数
print(log_reg.score(X_test, y_test)) # 预测准确率
print(log_reg.predict_proba(X_test)) # X预测为各个类别的概率的概率值
print(y_test) # 实际值
print(log_reg.predict(X_test)) # 预测值
Output：
log_reg._theta：array([-0.69377193, 3.01796521, -5.04447145]) # 第1个是截距，后2个是相关参数
log_reg.score(X_test, y_test)：1.0 # 因为数据比较少，且只取了2个特征
log_reg.predict_proba(X_test)：array([0.92972035, 0.98664939, 0.14852024, 0.01685947, 0.0369836 ,
0.0186637 , 0.04936918, 0.99669244, 0.97993941, 0.74524655,
0.04473194, 0.00339285, 0.26131273, 0.0369836 , 0.84192923,
0.79892262, 0.82890209, 0.32358166, 0.06535323, 0.20735334])
y_test：array([1, 1, 0, 0, 0, 0, 0, 1, 1, 1, 0, 0, 0, 0, 1, 1, 1, 0, 0, 0])
log_reg.predict(X_test)：array([1, 1, 0, 0, 0, 0, 0, 1, 1, 1, 0, 0, 0, 0, 1, 1, 1, 0, 0, 0])
参考资料：bobo老师机器学习教程
