逻辑回归算法原理还是比较容易理解的，根据计算的结果实现一下：
手写的推导过程如下：
然后我们开始写实现的过程
1、写出判断模型准确性的函数，这个比较容易理解
import numpy as np
from math import sqrt
def accuracy_score(y_true, y_predict):
"""计算y_true和y_predict之间的准确率"""
assert len(y_true) == len(y_predict), \
"the size of y_true must be equal to the size of y_predict"
return np.sum(y_true == y_predict) / len(y_true)2、写出来训练数据集和测试数据集的分割函数，这个也可以直接用sklearn中写好的包
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"""
assert X.shape[0] == y.shape[0], \
"the size of X must be equal to the size of y"
assert 0.0 <= test_ratio <= 1.0, \
"test_ration must be valid"
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
3、写出函数的fit过程，求解用的是批量梯度下降法，这个过程和线性回归比较类似
import numpy as np
class LogisticRegression:
def __init__(self):
"""初始化模型"""
self.coef_ = None
self.intercept_ = None
self._theta = None
#有下划线是私有函数
def _sigmod(self,t):
return 1./(1.+np.exp(-t))
def fit(self,X_train,y_train,eta=0.01,n_iters=1e4):
"""根据模型训练数据集X_train,y_train,使用梯度下降法训练Logistic Regression"""
assert X_train.shape[0] == y_train.shape[0],\
"the size of X_train must be equal to the size of y_trian"
#计算损失函数
def J(theta,X_b,y):
y_hat = self._sigmod(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._sigmod(X_b.dot(theta))-y) / len(X_b)
def gradient_descent(X_b, y, inital_theta, eta, n_inters=1e4, epsilon=1e-8):
theta = initial_theta
i_inter = 0
while i_inter < n_inters:
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
i_inter += 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
4、写出来预测的概率和预测的分类结果
#预测的概率函数
def predict_proba(self,X_predict):
"""给定待预测数据集X_predict,返回X_predict的结果向量"""
assert self.intercept_ is not None and self.coef_ is not None,\
"Must fit before predixt"
assert X_predict.shape[1] == len(self.coef_),\
"the feature number of X_predict must be equal to X_train"
X_b = np.hstack([np.ones((len(X_predict),1)), X_predict])
return self._sigmod(X_b.dot(self._theta))
#预测结果的函数
def predict(self,X_predict):
"""给定预测数据集X_predict,返回表示X_predict的结果向量"""
assert self.intercept_ is not None and self.coef_ is not None,\
"Must fit before predixt"
assert X_predict.shape[1] == len(self.coef_),\
"the feature number of X_predict must be equal to X_train"
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()"5、然后用iris数据集验证下我们写的函数
import numpy as np
import matplotlib.pyplot as plt
from sklearn import datasets
from sklearn.model_selection import train_test_split
iris = datasets.load_iris()
X = iris.data
y = iris.target
X = X[y<2, :2]
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()
X_train,X_test,y_train,y_test = train_test_split(X,y)
log_reg = LogisticRegression()
log_reg.fit(X_train,y_train)
log_reg.score(X_test,y_test)
结果如下：
6、我们输出一下概率和每个的分类结果
7、总结
自己实现一下算法还是很有好处的，虽然中间有的函数也不知道为什么这样调用什么的，但是编程就是多写，写的多了应该就能有进步。
还有，自己实现一下(也是看着教程写的)有助于理解公式和sklearn的设计方式，细节性的东西比较容易把握到，比起公式的抽象，编程实现更能把两者结合起来。