python学习：一元线性回归-梯度下降

落日映苍穹つ 2022-02-02 06:11 313阅读 0赞

## 数据 ##

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**以实现简单的一元回归来熟悉一下python的语法**

import numpy as np  
import matplotlib.pyplot as plt

# 最小二乘法构建损失函数 #

def loss(instance, label, x1, x2):
    	loss_sum = 0
    	size = len(instance)
    	m = float(size)
    	for i in range(0, size):
        	predict = x1 * instance[i] + x2
        	loss_sum += (predict - label[i]) ** 2
    	return loss_sum / (2.0 * m)

# 梯度下降同时更新两个参数, parameter := parameter - lr \* 损失函数对其求偏导 #

def gradient_descent_runner(instance, label, x1, x2, learn_rate, total_epochs):
    	size = len(instance)
    	m = float(size)
    	for i in range(0, total_epochs):
        	k_grad = 0
        	b_grad = 0
        	for j in range(0, size):
            	predict = x1 * instance[j] + x2
            	k_grad += (1 / m) * (predict - label[j]) * instance[j]
            	b_grad += (1 / m) * (predict - label[j])
        	x1 = x1 - (learn_rate * k_grad)
        	x2 = x2 - (learn_rate * b_grad)
    	return x2, x1

# 跑一个示例 #

def main():
     	# 载入数据
    	data = np.genfromtxt("../data/data.csv", delimiter=",")
    	x_data = data[:, 0]
    	y_data = data[:, 1]
    	plt.scatter(x_data, y_data)
    	plt.show()
    	
    	# lr: 学习率, b, k, epochs
    	lr = 0.000001
    	b = 0
    	k = 0
    	epochs = 1000
    	print("Starting b = {0}, k = {1}, error = {2}".format(b, k, loss(x_data, y_data, k, b)))
    	print("Running...")
    	b, k = gradient_descent_runner(x_data, y_data, k, b, lr, epochs)
    	print(b, k)
    	print("After {0} iterations b = {1}, k = {2}, error = {3}".format(epochs, k, b, loss(x_data, y_data, k, b)))
    
    	b, k = gradient_descent_runner(x_data, y_data, b, k, lr, epochs)
    	plt.plot(x_data, y_data, 'b.')
    	plt.plot(x_data, k * x_data + b, 'r')
    	plt.show()
    
    
    if __name__ == '__main__':
    	main()

![学习率有点低][watermark_type_ZmFuZ3poZW5naGVpdGk_shadow_10_text_aHR0cHM6Ly9ibG9nLmNzZG4ubmV0L3UwMTQ2MjgxNDY_size_16_color_FFFFFF_t_70]

[watermark_type_ZmFuZ3poZW5naGVpdGk_shadow_10_text_aHR0cHM6Ly9ibG9nLmNzZG4ubmV0L3UwMTQ2MjgxNDY_size_16_color_FFFFFF_t_70]: /images/20220202/8dc13edcb01e4853872a8bb929388448.png