线性回归练习1

上周二居家隔离到周六，进度很慢，对之前一部分的课程进行一些笔记总结；
整体算法原理，框架结构已经理解，但是还有一些语句理解的不是很透彻。


#导入数据并绘图
import numpy as np
import pandas as pd
import matplotlib.pyplot as plt
path =  'ex1data1.txt'

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

 

 

######定义代价函数
def computeCost(X, y, theta):
    inner = np.power(((X * theta.T) - y), 2)
    return np.sum(inner) / (2 * len(X))

data.insert(0, 'Ones', 1)#加一行用向量计算
#变量初始化
cols = data.shape[1]
X = data.iloc[:, 0:cols - 1]  # X是所有行，去掉最后一列
y = data.iloc[:, cols - 1:cols]  # X是所有行，最后一列
print(X.head())  # head()是观察前5行
print(y.head())
#转换X，y为numpy矩阵
X = np.matrix(X.values)
y = np.matrix(y.values)
theta = np.matrix(np.array([0, 0]))#初始化为（0,0）


##梯度下降算法
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):
            term = np.multiply(error, X[:, j])
            temp[0, j] = theta[0, j] - ((alpha / len(X)) * np.sum(term))

        theta = temp
        cost[i] = computeCost(X, y, theta)

    return theta, cost
#初始化迭代步数和学习率
alpha = 0.01
iters = 1000

g, cost = gradientDescent(X, y, theta, alpha, iters)#开始迭代

computeCost(X, y, g)#寻找到合适参数后的代价函数值
#绘制拟合图
x = np.linspace(data.Population.min(), data.Population.max(), 100)
f = g[0, 0] + (g[0, 1] * x)

fig, ax = plt.subplots(figsize=(12,8))
ax.plot(x, f, 'r', label='Prediction')
ax.scatter(data.Population, data.Profit, label='Traning Data')
ax.legend(loc=2)
ax.set_xlabel('Population')
ax.set_ylabel('Profit')
ax.set_title('Predicted Profit vs. Population Size')
plt.show()、

 

 

#代价函数随迭代次数的变化图
fig, ax = plt.subplots(figsize=(12,8))
ax.plot(np.arange(iters), cost, 'r')
ax.set_xlabel('Iterations')
ax.set_ylabel('Cost')
ax.set_title('Error vs. Training Epoch')
plt.show()