【头歌】梯度下降法解决线性回归

第1关：数据载入与分析

#encoding=utf8
import os
import pandas as pd

if __name__ == "__main__":
    path = os.getcwd() + '/ex1data1.txt'
    #利用pandas读入数据data，并将数据属性分别命名为'Population'和'Profit'
    #********* begin *********#
    data=pd.read_csv(path,header=None,names=['Population','Profit'])
    #********* end *********#
    print(data.shape)

第2关：计算损失函数

#encoding=utf8
import numpy as np

def computeCost(X, y, theta):
    #根据公式编写损失函数计算函数
    #********* begin *********#
    inner = np.power(((X * theta.T) - y), 2)
    cost=np.sum(inner) / (2 * len(X))
    
    #********* end *********#
    return round(cost,10)

第3关：进行梯度下降得到线性模型

#encoding=utf8
import numpy as np

def computeCost(X, y, theta):
    inner = np.power(((X * theta.T) - y), 2)
    return np.sum(inner) / (2 * len(X))

def gradientDescent(X, y, theta, alpha, iters):
    temp = np.matrix(np.zeros(theta.shape))
    parameters = int(theta.ravel().shape[1])
    cost = np.zeros(iters)
    
    for i in range(iters):
        error = (X * theta.T) - y
        
        for j in range(parameters):
            #********* begin *********#
            term = np.multiply(error, X[:,j])
            temp[0,j] = theta[0,j] - ((alpha / len(X)) * np.sum(term)) 
            #********* end *********#
        theta = temp
        cost[i] = computeCost(X, y, theta)
        
    return theta, cost

第4关：建立完整线性回归模型

#encoding=utf8

import os
import numpy as np
import pandas as pd

#载入数据并进行数据处理
path = os.getcwd() + '/ex1data1.txt'
#********* begin *********#
data=pd.read_csv(path,header=-1,names=['Population','Profit'])

#********* end *********#
data.insert(0, 'Ones', 1)
cols = data.shape[1]
X = data.iloc[:,0:cols-1]
y = data.iloc[:,cols-1:cols]

#初始化相关参数
X = np.matrix(X.values)
y = np.matrix(y.values)
theta = np.matrix(np.array([0,0]))
alpha = 0.01
iters = 1000

#定义损失函数
def computeCost(X, y, theta):
    #********* begin *********#
    inner = np.power(((X * theta.T) - y), 2)
    cost=np.sum(inner) / (2 * len(X))

    #********* end *********#
    return cost

#定义梯度下降函数
def gradientDescent(X, y, theta, alpha, iters):
    temp = np.matrix(np.zeros(theta.shape))
    parameters = int(theta.ravel().shape[1])
    cost = np.zeros(iters)
    
    for i in range(iters):
        error = (X * theta.T) - y
        
        for j in range(parameters):
            #********* begin *********#
            term = np.multiply(error, X[:,j])
            temp[0,j] = theta[0,j] - ((alpha / len(X)) * np.sum(term))  

            #********* end *********#            
        theta = temp
        cost[i] = computeCost(X, y, theta)        
    return theta, cost

#根据梯度下架算法得到最终线性模型参数
g, cost = gradientDescent(X, y, theta, alpha, iters)

print("模型参数为:", g)