【笔记】实现逻辑回归算法

实现逻辑回归算法

实现代码

在python chame中创建LogisticRegression.py文件，写入想要实现的功能

其中，可以将原先的LinearRegression复制过来，详情可见以前的关于线性回归的博客，修改类名，不用的功能直接删除，添加上sigmoid函数以及计算结果概率向量的函数，对损失函数的计算，梯度的计算，预测结果进行修改，使用这里的计算思想即可

代码如下：

  import numpy as np
  from metrics import accuracy_score


  class LogisticRegression:

      def __init__(self):
          """初始化Logistic Regression模型"""
          self.coef_ = None
          self.interception_ = 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):
          """根据训练数据集使用梯度算法训练模型"""
          assert X_train.shape[0] == y_train.shape[0], 
              "the size of X_train must be equal to the size of y_train"

          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(X_b)

          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.interception_ = self._theta[0]
          self.coef_ = self._theta[1:]

          return self

      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"""
          assert self.interception_ is not None and self.coef_ is not None, 
              "must fit before predict!"
          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 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"""
          assert self.interception_ is not None and self.coef_ is not None, 
              "must fit before predict!"
          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._sigmoid(X_b.dot(self._theta))


      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()"


      from matplotlib.colors import ListedColormap
      def plot_decision_boundary(model, axis):

          x0 = np.meshgrid(np.linspace(axis[2], axis[3], int((axis[3] - axis[2]) * 100)).reshape())
          x1 = np.meshgrid(np.linspace(axis[0], axis[1], int((axis[1] - axis[0]) * 100)).reshape())
          X_new = np.c_[x0.ravel(), x1.ravel()]

          y_predict = model.predict(X_new)
          zz = y_predict.reshape(x0.shape)
          custom_cmap = ListedColormap(['#EF9A9A', '#FFF59D', '#90CAF9'])

          plt.contourf(x0, x1, zz, linewidth=5, cmap=custom_cmap)

具体使用

（在notebook中）

加载上相应的包，使用鸢尾花数据集，由于其有三种分类，因此只选用y<2的行，且只取前两个特征，并绘制图像

  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]
  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')

图像如下

分割好数据集以后（使用种子666），调用封装好的方法，进行实例化以后对训练数据集进行fit操作

  from model_selection import train_test_split

  X_train,X_test,y_train,y_test = train_test_split(X,y,seed=666)

  from LogisticRegression import LogisticRegression

  log_reg = LogisticRegression()
  log_reg.fit(X_train,y_train)

使用代码计算分类结果

  log_reg.score(X_test,y_test)

结果如下

分类结果中的数据

  log_reg.predict_proba(X_test)

结果如下

其中y_test中为

然后使用概率矩阵以后的真正得到的log_reg.predict(X_test)中的结果如下

以上为实现的逻辑回归算法的简单的应用