深度学习02——线性回归问题

1. 实现一个线性回归的问题 

# 实现一个线性回归的问题
# y = wx + b

step1: 计算损失函数loss的值

 

# 实现一个线性回归的问题
# y = wx + b
# step1: 计算损失函数loss的值
def compute_error_for_line_given_points(b, w, points):  #points表示数据的数量
    totalError = 0   #初始化损失函数的值
    for i in range(0, len(points)):
        x = points[i, 0]
        y = points[i, 1]
        # computer mean-squared-error
        totalError += (y - (w * x + b)) ** 2   #求loss的累积和
    # average loss for each point
    return totalError / float(len(points))

step2:计算梯度与更新

 

# step2:计算梯度与更新
def step_gradient(b_current, w_current, points, learningRate):
    b_gradient = 0
    w_gradient = 0
    N = float(len(points))
    for i in range(0, len(points)):
        x = points[i, 0]
        y = points[i, 1]
        # grad_b = 2(wx+b-y)
        b_gradient += (2/N) * ((w_current * x + b_current) - y)
        # grad_w = 2(wx+b-y)*x
        w_gradient += (2/N) * x * ((w_current * x + b_current) - y)
    # update w'
    new_b = b_current - (learningRate * b_gradient)
    new_w = w_current - (learningRate * w_gradient)
    return [new_b, new_w]

step3:更新权值w

 

 

#更新权值w
def gradient_descent_runner(points, starting_b, starting_w, learning_rate, num_iterations):
    b = starting_b
    w = starting_w
    # update for several times
    for i in range(num_iterations):
        b, w = step_gradient(b, w, np.array(points), learning_rate)
    return [b, w]

 step4:主函数

def run():
	
    points = np.genfromtxt("data.csv", delimiter=",")   #读取数据
    learning_rate = 0.0001  #学习率
    initial_b = 0 # initial y-intercept guess
    initial_w = 0 # initial slope guess
    num_iterations = 1000 
    print("Starting gradient descent at b = {0}, w = {1}, error = {2}"
          .format(initial_b, initial_w,
                  compute_error_for_line_given_points(initial_b, initial_w, points))
          )
    print("Running...")
    [b, w] = gradient_descent_runner(points, initial_b, initial_w, learning_rate, num_iterations)
    print("After {0} iterations b = {1}, w = {2}, error = {3}".
          format(num_iterations, b, w,
                 compute_error_for_line_given_points(b, w, points))
          )

if __name__ == '__main__':
    run()

线性回归问题的全部代码：

import numpy as np

# 实现一个线性回归的问题
# y = wx + b
# step1: 计算损失函数loss的值
def compute_error_for_line_given_points(b, w, points):  #points表示数据的数量
    totalError = 0   #初始化损失函数的值
    for i in range(0, len(points)):
        x = points[i, 0]
        y = points[i, 1]
        # computer mean-squared-error
        totalError += (y - (w * x + b)) ** 2   #求loss的累积和
    # average loss for each point
    return totalError / float(len(points))


# step2:计算梯度与更新
def step_gradient(b_current, w_current, points, learningRate):
    b_gradient = 0
    w_gradient = 0
    N = float(len(points))
    for i in range(0, len(points)):
        x = points[i, 0]
        y = points[i, 1]
        # grad_b = 2(wx+b-y)
        b_gradient += (2/N) * ((w_current * x + b_current) - y)
        # grad_w = 2(wx+b-y)*x
        w_gradient += (2/N) * x * ((w_current * x + b_current) - y)
    # update w'
    new_b = b_current - (learningRate * b_gradient)
    new_w = w_current - (learningRate * w_gradient)
    return [new_b, new_w]

#更新权值w
def gradient_descent_runner(points, starting_b, starting_w, learning_rate, num_iterations):
    b = starting_b
    w = starting_w
    # update for several times
    for i in range(num_iterations):
        b, w = step_gradient(b, w, np.array(points), learning_rate)
    return [b, w]


def run():
	
    points = np.genfromtxt("data.csv", delimiter=",")   #读取数据
    learning_rate = 0.0001  #学习率
    initial_b = 0 # initial y-intercept guess
    initial_w = 0 # initial slope guess
    num_iterations = 1000
    print("Starting gradient descent at b = {0}, w = {1}, error = {2}"
          .format(initial_b, initial_w,
                  compute_error_for_line_given_points(initial_b, initial_w, points))
          )
    print("Running...")
    [b, w] = gradient_descent_runner(points, initial_b, initial_w, learning_rate, num_iterations)
    print("After {0} iterations b = {1}, w = {2}, error = {3}".
          format(num_iterations, b, w,
                 compute_error_for_line_given_points(b, w, points))
          )

if __name__ == '__main__':
    run()