Scikit-Learn库

line_fitter = LinearRegression() 创建模型
line_fitter.fit(temperature, sales) 传入参数
sales_predict = line_fitter.predict(temperature) 预测模型

import codecademylib3_seaborn
from sklearn.linear_model import LinearRegression
import matplotlib.pyplot as plt
import numpy as np

temperature = np.array(range(60, 100, 2))
temperature = temperature.reshape(-1, 1)
sales = [65, 58, 46, 45, 44, 42, 40, 40, 36, 38, 38, 28, 30, 22, 27, 25, 25, 20, 15, 5]

line_fitter = LinearRegression()
line_fitter.fit(temperature, sales)
sales_predict = line_fitter.predict(temperature)

plt.plot(temperature, sales, 'o')
plt.plot(temperature,sales_predict)

plt.show()

原理

预测直线直线上会有loss

import codecademylib3_seaborn
import matplotlib.pyplot as plt
months = [1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12]
revenue = [52, 74, 79, 95, 115, 110, 129, 126, 147, 146, 156, 184]

#slope:
m = 12
#intercept:
b = 35

plt.plot(months, revenue, "o")

y = [m*month + b for month in months]

plt.plot(months,y)

plt.show()

LOSS

计算loss时要使用平方距离如下图 A的loss是 9(3^2) B的loss是1(1^2)

总loss=10 如果发现一条线路使loss小于10 那么这条线路会成为更好的线路

for i in range(len(y)):
  total_loss+=(y_predicted[i]-y[i])**2

减少loss

grandient descent 梯度下降

找到一点斜率向下的方向说明可以减少损失,所以应该渐变向下

公式

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N is the number of points we have in our dataset
m is the current gradient guess 斜率
b is the current intercept guess 截距

找到当截距=b时的梯度的函数

def get_gradient_at_b(x,y,m,b):
    diff=0
    for i in range(len(x)):
      diff+=(y[i]-(m*x[i]+b))
    b_gradient=diff*(-2)/len(x)
    return b_gradient

公式

N is the number of points we have in our dataset
m is the current gradient guess 斜率
b is the current intercept guess 截距

找到当斜率=m时的梯度的函数

def get_gradient_at_m(x, y, m, b):
    diff = 0
    N = len(x)
    for i in len(x):
      diff += x[i]*(y[i]-(m*x[i]+b))
    m_gradient = -2/N * diff
    return m_gradient

得到合适的梯度

def get_gradient_at_b(x, y, b, m):
  N = len(x)
  diff = 0
  for i in range(N):
    x_val = x[i]
    y_val = y[i]
    diff += (y_val - ((m * x_val) + b))
  b_gradient = -(2/N) * diff  
  return b_gradient

def get_gradient_at_m(x, y, b, m):
  N = len(x)
  diff = 0
  for i in range(N):
      x_val = x[i]
      y_val = y[i]
      diff += x_val * (y_val - ((m * x_val) + b))
  m_gradient = -(2/N) * diff  
  return m_gradient

#Your step_gradient function here
def step_gradient(x, y, b_current, m_current):
    b_gradient = get_gradient_at_b(x, y, b_current, m_current)
    m_gradient = get_gradient_at_m(x, y, b_current, m_current)
    b = b_current - (0.01 * b_gradient)
    m = m_current - (0.01 * m_gradient)
    return [b, m]

months = [1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12]
revenue = [52, 74, 79, 95, 115, 110, 129, 126, 147, 146, 156, 184]

# current intercept guess:
b = 0
# current slope guess:
m = 0

b, m = step_gradient(months, revenue, b, m)
print(b, m)

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