【Python】机器学习之单变量线性回归练习(计算Cost Function)

注:练习来自于吴恩达机器学习

 

翻译后的题目:

你是一个餐厅的老板,你想在其他城市开分店,所以你得到了一些数据(数据在本文最下方),数据中包括不同的城市人口数和该城市带来的利润。第一列是城市的人口数,第二列是在这个城市开店所带来的利润数。

现在,假设θ0和θ1都是0,计算CostFunction,即计算损失函数

 

首先,本题线性回归的公式应该是这样的:

H(θ) = θ0 + θ1*X

 

简单的来说,本题中,θ0和θ1都为0,即求H(θ) = 0的损失值,

 

然后我们再给出损失的定义:

损失,通俗的来讲,即你预测值和给定值的差

 

这样就得出了损失函数J(θ)的定义:

 

 

m为数据的总条数,即m代表有几条数据。

 

第一步,导包

import numpy as np
import pandas as pd
import matplotlib.pyplot as plt

 

第二步,把数据读入,然后把图打出来看一下:

path = 'ex1data1.txt'
data = pd.read_csv(path, header=None, names=['Population', 'Profit'])
data.plot(kind='scatter', x='Population', y='Profit', figsize=(12, 8))
plt.show()

 

图:

 

 

第三步,定义一下costFunction

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

 

第四步,然后把X从data分出来,Y从data分出来,在X的左边再加一列1,

分出来后的结果为,X为97行2列,Y为97行1列,θ为1行2列,

costFunction是计算矩阵X*矩阵θ的转置得到的值来和真实的Y值比较,计算Cost

data.insert(0, 'Ones', 1)
rows = data.shape[0]
cols = data.shape[1]
X = data.iloc[:, 0:cols - 1]
Y = data.iloc[:, cols - 1:cols]
theta = np.mat('0,0')
X = np.mat(X.values)
Y = np.mat(Y.values)


cost = computeCost(X, Y, theta)
print(cost)

 

标准答案:

32.072733877455676

 

 

 

附数据集ex1data1.txt

6.1101,17.592
5.5277,9.1302
8.5186,13.662
7.0032,11.854
5.8598,6.8233
8.3829,11.886
7.4764,4.3483
8.5781,12
6.4862,6.5987
5.0546,3.8166
5.7107,3.2522
14.164,15.505
5.734,3.1551
8.4084,7.2258
5.6407,0.71618
5.3794,3.5129
6.3654,5.3048
5.1301,0.56077
6.4296,3.6518
7.0708,5.3893
6.1891,3.1386
20.27,21.767
5.4901,4.263
6.3261,5.1875
5.5649,3.0825
18.945,22.638
12.828,13.501
10.957,7.0467
13.176,14.692
22.203,24.147
5.2524,-1.22
6.5894,5.9966
9.2482,12.134
5.8918,1.8495
8.2111,6.5426
7.9334,4.5623
8.0959,4.1164
5.6063,3.3928
12.836,10.117
6.3534,5.4974
5.4069,0.55657
6.8825,3.9115
11.708,5.3854
5.7737,2.4406
7.8247,6.7318
7.0931,1.0463
5.0702,5.1337
5.8014,1.844
11.7,8.0043
5.5416,1.0179
7.5402,6.7504
5.3077,1.8396
7.4239,4.2885
7.6031,4.9981
6.3328,1.4233
6.3589,-1.4211
6.2742,2.4756
5.6397,4.6042
9.3102,3.9624
9.4536,5.4141
8.8254,5.1694
5.1793,-0.74279
21.279,17.929
14.908,12.054
18.959,17.054
7.2182,4.8852
8.2951,5.7442
10.236,7.7754
5.4994,1.0173
20.341,20.992
10.136,6.6799
7.3345,4.0259
6.0062,1.2784
7.2259,3.3411
5.0269,-2.6807
6.5479,0.29678
7.5386,3.8845
5.0365,5.7014
10.274,6.7526
5.1077,2.0576
5.7292,0.47953
5.1884,0.20421
6.3557,0.67861
9.7687,7.5435
6.5159,5.3436
8.5172,4.2415
9.1802,6.7981
6.002,0.92695
5.5204,0.152
5.0594,2.8214
5.7077,1.8451
7.6366,4.2959
5.8707,7.2029
5.3054,1.9869
8.2934,0.14454
13.394,9.0551
5.4369,0.61705
ex1data1.txt

 

posted @ 2019-10-04 14:11  秦羽纶  阅读(...)  评论(... 编辑 收藏