from numpy import *
import matplotlib.pyplot as plt

1.导入数据

# 1.导入数据
# 模型 y = wx + b
points = genfromtxt('linear_regress_lsm_data.csv', delimiter=',')
length = len(points)
print('point count %d'%length)
x = array(points[:, 0])
y = array(points[:, 1])
plt.scatter(x, y)
plt.show

point count 100





<function matplotlib.pyplot.show(close=None, block=None)>

2.损失函数

# 2.损失函数
def compute_cost(points, w, b):
    total_cost = 0
    length = len(points)
    for i in range(length):
        x = points[i, 0]
        y = points[i, 1]
        total_cost = (y - w * x - b) ** 2
    return total_cost / float (length)
    

3.模型超参

# 学习率(步长),初始点,迭代次数
learning_rate = 0.0001
init_b = 0
init_w = 0
num_iteration = 10

4.梯度下降

# 梯度下降
def gradient_descent(points, init_w, init_b, learning_rate, num_iteration):
    b = init_b
    w = init_w
    cost_list = []
    
    for i in range(num_iteration):
        cost_list.append(compute_cost(points, w, b))
        w, b = step_grad_desc(w, b, array(points), learning_rate)
    return [w, b, cost_list]
    
# 一次梯度下降    
def step_grad_desc(cur_w, cur_b, points, learning_rate):
    w_grad = 0
    b_grad = 0
    poi_len = len(points)
    for i in range(poi_len):
        x = points[i, 0]
        y = points[i, 1]
        w_grad +=(cur_w * x + cur_b - y) * x 
        b_grad += cur_w * x + cur_b - y
    
    new_w = cur_w - learning_rate * w_grad * (2 / float(poi_len))
    new_b = cur_b - learning_rate * b_grad * (2 / float(poi_len))
    return new_w, new_b

5.训练

w, b, cost_list = gradient_descent(points, init_w, init_b, learning_rate, num_iteration)
print("w= ", w)
print("b= ", b)
print("cost= ", compute_cost(points, w, b))

w=  1.4774173755483797
b=  0.02963934787473238
cost=  2.656735381402925

6.看损失函数随着迭代下降

plt.plot(cost_list)
plt.show()
# 5次左右到极小值

7.画拟合曲线

plt.scatter(x, y)
y_predict = w * x + b
plt.plot(x, y_predict, c = 'y')
plt.show

<function matplotlib.pyplot.show(close=None, block=None)>