Machine Learning Fundamentals-Unary Linear Regression-01

Regression analysis

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Unary linear regression

• Regression analysis is used to establish an equation to simulate how two
or more variables are related.
• The variable to be predicted is called: dependent variable,
output.
• The variable used to make predictions is called: Independent
variable, input
• One-variable linear regression contains one independent variable and one dependent variable
• The relationship between the above two variables is simulated by a straight line
• If more than two independent variables are included, it is called multiple regression Analysis
(multiple regression)
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Cost Function

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Gradient Descent

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Gradient descent method-unary linear regression code

import numpy as np
import matplotlib.pyplot as plt

# 载入数据
data = np.genfromtxt("data.csv", delimiter=",")
x_data = data[:,0]
y_data = data[:,1]
plt.scatter(x_data,y_data)
plt.show()

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# 学习率learning rate
lr = 0.0001
# 截距
b = 0 
# 斜率
k = 0 
# 最大迭代次数
epochs = 50

# 最小二乘法
def compute_error(b, k, x_data, y_data):
    totalError = 0
    for i in range(0, len(x_data)):
        totalError += (y_data[i] - (k * x_data[i] + b)) ** 2
    return totalError / float(len(x_data)) / 2.0

def gradient_descent_runner(x_data, y_data, b, k, lr, epochs):
    # 计算总数据量
    m = float(len(x_data))
    # 循环epochs次
    for i in range(epochs):
        b_grad = 0
        k_grad = 0
        # 计算梯度的总和再求平均
        for j in range(0, len(x_data)):
            b_grad += (1/m) * (((k * x_data[j]) + b) - y_data[j])
            k_grad += (1/m) * x_data[j] * (((k * x_data[j]) + b) - y_data[j])
        # 更新b和k
        b = b - (lr * b_grad)
        k = k - (lr * k_grad)
        # 每迭代5次，输出一次图像
        if i % 5==0:
            print("epochs:",i)
            plt.plot(x_data, y_data, 'b.')
            plt.plot(x_data, k*x_data + b, 'r')
            plt.show()
    return b, k

print("Starting b = {0}, k = {1}, error = {2}".format(b, k, compute_error(b, k, x_data, y_data)))
print("Running...")
b, k = gradient_descent_runner(x_data, y_data, b, k, lr, epochs)
print("After {0} iterations b = {1}, k = {2}, error = {3}".format(epochs, b, k, compute_error(b, k, x_data, y_data)))

# 画图
# plt.plot(x_data, y_data, 'b.')
# plt.plot(x_data, k*x_data + b, 'r')
# plt.show()

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sklearn-unary linear regression code

from sklearn.linear_model import LinearRegression
import numpy as np
import matplotlib.pyplot as plt

# 载入数据
data = np.genfromtxt("data.csv", delimiter=",")
x_data = data[:,0]
y_data = data[:,1]
plt.scatter(x_data,y_data)
plt.show()
print(x_data.shape)

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x_data = data[:,0,np.newaxis]
y_data = data[:,1,np.newaxis]
# 创建并拟合模型
model = LinearRegression()
model.fit(x_data, y_data)

# 画图
plt.plot(x_data, y_data, 'b.')
plt.plot(x_data, model.predict(x_data), 'r')
plt.show()

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