import numpy as np
# 假设线性回归模型y = wx + b
def compute_error_for_line_given_points(b, w, points):
totalError = 0
for i in range(0, len(points)):
x = points[i, 0]
y = points[i, 1]
# 计算损失函数 computer mean-squared-error
totalError += (y - (w * x + b)) ** 2
# 返回最终的损失函数average loss for each point
return totalError / float(len(points))
# 定义梯度下降规则
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]
# 定义梯度下降运行器,调用之前写的梯度下降方法
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]
#加载数据集,运行代码
def run():
points = np.genfromtxt("data.csv", delimiter=",")
learning_rate = 0.0001
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()
注意:data.csv是要导入是数据集,链接如下
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