TensorFlow2_200729系列---3、梯度下降求简单线性回归实例
一、总结
一句话总结：
梯度下降：梯度下降是对loss函数做的，对loss的w和b，比如w = w - learningRate*loss对w的梯度
画动态图：在动态图中更新y轴数据即可，如果需要更新text标注，那就也更新
import numpy as np from matplotlib import pyplot as plt from matplotlib import animation from matplotlib import pylab %pylab fig,ax=plt.subplots() # 画散点图 x = data.iloc[:,0] y = data.iloc[:,-1] ax.scatter(x,y) # 画直线图 line,=ax.plot(x,0*x+0) # 存这个text1，方便动画的时候修改 text1 = ax.text(30,110,"w=0.0000,b=0.0000", fontdict={'size':16,'color':'r'}) def animate(i): text1.set_text('w=%.4f,b=%.4f' %(bw_list[i][1],bw_list[i][0])) line.set_ydata(bw_list[i][1]*x+bw_list[i][0]) return line, def init(): line.set_ydata(0*x+0) return line, ani=animation.FuncAnimation(fig=fig,func=animate,frames=999,init_func=init,interval=5,blit=False) ani.save('line_model.gif', writer='imagemagick', fps=30) plt.show()
1、梯度下降为什么会在极值点那里收敛？
因为极值点处斜率（梯度）为0，这样学习率*梯度也是0
2、梯度下降中为什么乘上步长？
不乘上步长，有些情况下，导数太大了
3、matplotlib画动态图如何更新文本标注？
text1 = ax.text(30,110,"w=0.0000,b=0.0000", fontdict={'size':16,'color':'r'})
text1.set_text('w=%.4f,b=%.4f' %(bw_list[i][1],bw_list[i][0]))
4、matplotlib画动态图？
主要是初始化函数和更新函数，在更新函数中更新y数据：line.set_ydata(bw_list[i][1]*x+bw_list[i][0])
5、本题梯度下降核心代码（和公式推导一样）？
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)
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]
6、本题损失函数最小二乘法实例？
totalError += (y - (w * x + b)) ** 2
# 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] # computer mean-squared-error totalError += (y - (w * x + b)) ** 2 # average loss for each point return totalError / float(len(points))
二、梯度下降求简单线性回归实例
博客对应课程的视频位置：
In [1]:
import numpy as np
# data = []
# for i in range(100):
# x = np.random.uniform(3., 12.)
# # mean=0, std=0.1
# eps = np.random.normal(0., 0.1)
# y = 1.477 * x + 0.089 + eps
# data.append([x, y])
# data = np.array(data)
# print(data.shape, data)
# 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]
# computer mean-squared-error
totalError += (y - (w * x + b)) ** 2
# average loss for each point
return totalError / float(len(points))
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]
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