机器学习--线性回归

1. 案列
   数据: 工资和年龄（2个特征)
   目标：预测银行会贷款给我多少钱（标签)
   考虑：工资和年龄都会影响最终银行贷款的结果那么它们各自有多大的影响呢？（参数）

   
   1-1

2. 通俗解释

• X1,X2就是我们的两个特征（年龄，工资）Y是银行最终会借给我们多少钱

• 找到最合适的一条线（想象一个高维）来最好的拟合我们的数据点

  
  2-1

3. 数学

   
   3-1
   3-2
   3-3
   3-4
   3-5
   3-6
   3-7

4. 完整代码实现(使用sklearn中的数据集)

import matplotlib.pyplot as plt
import numpy as np
from sklearn import datasets

class LinearRegression():
    def __init__(self):
        self.w = None

    def fit(self, X, y):
        X = np.insert(X, 0, 1, axis=1)
        print (X.shape)        
        X_ = np.linalg.inv(X.T.dot(X))
        self.w = X_.dot(X.T).dot(y)
        

    def predict(self, X):
        # Insert constant ones for bias weights
        X = np.insert(X, 0, 1, axis=1)
        y_pred = X.dot(self.w)
        return y_pred


def mean_squared_error(y_true, y_pred):
    mse = np.mean(np.power(y_true - y_pred, 2))
    return mse

def main():
    # Load the diabetes dataset
    diabetes = datasets.load_diabetes()

    # Use only one feature
    X = diabetes.data[:, np.newaxis, 2]
    print (X.shape)
    # Split the data into training/testing sets
    x_train, x_test = X[:-20], X[-20:]

    # Split the targets into training/testing sets
    y_train, y_test = diabetes.target[:-20], diabetes.target[-20:]

    clf = LinearRegression()
    clf.fit(x_train, y_train)
    y_pred = clf.predict(x_test)

    # Print the mean squared error
    print ("Mean Squared Error:", mean_squared_error(y_test, y_pred))

    # Plot the results
    plt.scatter(x_test[:,0], y_test,  color='black')
    plt.plot(x_test[:,0], y_pred, color='blue', linewidth=3)
    plt.show()

main()

输入效果图如下: