【机器学习】'Batch' Gradient Descent 批梯度下降

批梯度下降：指的是每下降一步，使用所有的训练集来计算梯度值。

单变量

# -*- coding:utf-8 -*-
# @Time:4/18/19 9:08 PM
# @Author:CIGA
# @Filename:02_batch_gradient_descent.py
# @Software:PyCharm
"""
批梯度下降batch_gradient_descent
批梯度下降：指的是每下降一步，使用所有的训练集来计算梯度值
单变量
"""

import numpy as np

a = np.random.rand(100, 1)
X = 2 * a
y = 4 + 3 * X + a
"""
a = np.array([[1, 2, 3],[7,8,9]])
 
b=np.array([[4,5,6],[1,2,3]])
 
a
Out[4]: 
array([[1, 2, 3],
       [7, 8, 9]])
 
b
Out[5]: 
array([[4, 5, 6],
       [1, 2, 3]])
 
c=np.c_[a,b]
 
c
Out[7]: 
array([[1, 2, 3, 4, 5, 6],
       [7, 8, 9, 1, 2, 3]])
"""
"""
>>> np.ones((2, 1))
array([[ 1.],
      [ 1.]])
"""
X_b = np.c_[np.ones((100, 1)), X]

# 学习率
learning_rate = 0.1
# 迭代次数
n_iterations = 1000
# 样本个数
m = 100

# 1.初始化theta，w0...wn
"""
import numpy as np
a=np.random.randn(2,1)
a
array([[0.68050012],
       [0.75656742]])
"""
theta = np.random.randn(2, 1)

count = 0

for iteration in range(n_iterations):
    count += 1
    # 2.求梯度
    gradients = 1 / m * X_b.T.dot(X_b.dot(theta) - y)
    # 3.应用公式调整theta值，theta_t + 1 = theta_t - gradients * learning_rate
    theta = theta - learning_rate * gradients

print(theta)

多变量

# -*- coding:utf-8 -*-
# @Time:4/18/19 9:32 PM
# @Author:CIGA
# @Filename:02_batch_gradient_descent_mul.py
# @Software:PyCharm
"""
多变量
"""
import numpy as np

X1 = 2 * np.random.rand(100, 1)
X2 = 4 * np.random.rand(100, 1)
X3 = 6 * np.random.rand(100, 1)

y = 4 + 3 * X1 + 4 * X2 + 5 * X3 + np.random.randn(100, 1)
X_b = np.c_[np.ones((100, 1)), X1, X2, X3]
# print(X_b)

learning_rate = 0.1
# 通常在做机器学习的时候，一般不会等到他收敛，因为太浪费时间，所以会设置一个收敛次数
n_iterations = 1000
m = 100

# 1.初始化theta， w0...wn
theta = np.random.randn(4, 1)
count = 0

# 4.不会设置阈值，之间设置超参数，迭代次数，迭代次数到了，我们就认为收敛了
for iteration in range(n_iterations):
    count += 1
    # 2. 接着求梯度gradient
    gradients = 1 / m * X_b.T.dot(X_b.dot(theta) - y)
    # 3. 应用公式调整theta值， theta_t + 1 = theta_t - gradients * learning_rate
    theta = theta - learning_rate * gradients

print(theta)