tensorflow2.0笔记2：Numpy—实现线性回归问题！

Numpy实现—线性回归问题实战

一、思路分析

• 连续性预测

• 找出 $w,b$ 的偏导数,

1.1、步骤1：计算损失函数

#计算损失函数
# y=wx+b
def computer_error_for_line_given_points(b,w,points):
	totalError=0
	for i in range(0,len(points)):
        x=points[i,0] #等同于points[i][0]numpy，程序中的特殊形式,第0列的第i个元素。
        y=points[i,1]

        #computer mean-squared-error
        totalError+=(y-(w*x+b))**2
    # average loss for each point
    return totallError/float(len(points))

1.2、步骤2：损失函数的梯度

#计算梯度，并且更新w，b
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)*((w_current*x+b_current)-y)*x
	
	#update w'的值
	new_b=b_current-learningRate*b_gradient
	new_w=w_current-learningRate*w_gradient
	return [new_b,new_w]

1.3、步骤3：设定w=w’ 和循环

#迭代更新,最终更新出来的w和b	
def gradient_descent_runner(points,starting_b,starting_w,learning_rate,num_iterations):
	b=starting_b
	w=starting_w
	
	# update for servel times
	for i in range(num_iterations):
		b,w=step_gradient(b,w,np.array(points),learning_rate)
	return [b,w]

二、代码综合梳理

import numpy as np

# y=wx+b 计算损失函数
def computer_error_for_line_given_points(b,w,points):
	totalError=0
	for i in range(0,len(points)):
		x=points[i,0] #等同于传统的points[i][0]，numpy程序中的特殊形式第0列，第i个值。
		y=points[i,1]

		#computer mean-squared-error
		totalError+=(y-(w*x+b))**2
	# average loss for each point
	return totalError/float(len(points))

#计算损失函数梯度
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]								  #等同于传统的points[i][0]
		y=points[i,1]							 	  #等同于传统的points[i][1]
		#grad_b=2(wx+b-y)
		b_gradient+=(2/N)*((w_current*x+b_current)-y) #取一个平均值，更贴切。
		#grad_w=2(wx+b-y)*x
		w_gradient+=(2/N)*((w_current*x+b_current)-y)*x
	#update w'的值
	new_b=b_current-learningRate*b_gradient
	new_w=w_current-learningRate*w_gradient
	return [new_b,new_w]

#迭代更新,最终更新出来的w和b	
def gradient_descent_runner(points,starting_b,starting_w,learning_rate,num_iterations):
	b=starting_b
	w=starting_w
	
	# update for servel times
	for i in range(num_iterations):
		b,w=step_gradient(b,w,np.array(points),learning_rate)
	return [b,w]

# 包括数据的加载，参数的初始化
def run():
	points=np.genfromtxt("C:\\Users\\Devinzhang\\Desktop\\data.csv",delimiter=",") #加载数据集，以,分割。
	learning_rate=0.0001		#初始学习率
	initial_b=0					#初始b=0
	initial_w=0			    	#初始w=0
	num_iterations=1000  		#迭代次数
	
	#计算初始的误差	; 使用'{0}','{1}'形式的占位符
	print("Starting gradient descent at b={0},w={1},error={2}"
	.format(initial_b,initial_w,computer_error_for_line_given_points(initial_b,initial_w,points)))
	
	#开始送进去进行迭代
	print("Runing...")
	[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,computer_error_for_line_given_points(b,w,points)))

if __name__ =='__main__':
	run()

2.1、程序运行结果

2.2、实验的数据集

• 数据内容如下：可以自己建立一个data.csv，把数据复制进去。

32.50234527	31.70700585
53.42680403	68.77759598
61.53035803	62.5623823
47.47563963	71.54663223
59.81320787	87.23092513
55.14218841	78.21151827
52.21179669	79.64197305
39.29956669	59.17148932
48.10504169	75.3312423
52.55001444	71.30087989
45.41973014	55.16567715
54.35163488	82.47884676
44.1640495	62.00892325
58.16847072	75.39287043
56.72720806	81.43619216
48.95588857	60.72360244
44.68719623	82.89250373
60.29732685	97.37989686
45.61864377	48.84715332
38.81681754	56.87721319
66.18981661	83.87856466
65.41605175	118.5912173
47.48120861	57.25181946
41.57564262	51.39174408
51.84518691	75.38065167
59.37082201	74.76556403
57.31000344	95.45505292
63.61556125	95.22936602
46.73761941	79.05240617
50.55676015	83.43207142
52.22399609	63.35879032
35.56783005	41.4128853
42.43647694	76.61734128
58.16454011	96.76956643
57.50444762	74.08413012
45.44053073	66.58814441
61.89622268	77.76848242
33.09383174	50.71958891
36.43600951	62.12457082
37.67565486	60.81024665
44.55560838	52.68298337
43.31828263	58.56982472
50.07314563	82.90598149
43.87061265	61.4247098
62.99748075	115.2441528
32.66904376	45.57058882
40.16689901	54.0840548
53.57507753	87.99445276
33.86421497	52.72549438
64.70713867	93.57611869
38.11982403	80.16627545
44.50253806	65.10171157
40.59953838	65.56230126
41.72067636	65.28088692
51.08863468	73.43464155
55.0780959	71.13972786
41.37772653	79.10282968
62.49469743	86.52053844
49.20388754	84.74269781
41.10268519	59.35885025
41.18201611	61.68403752
50.18638949	69.84760416
52.37844622	86.09829121
50.13548549	59.10883927
33.64470601	69.89968164
39.55790122	44.86249071
56.13038882	85.49806778
57.36205213	95.53668685
60.26921439	70.25193442
35.67809389	52.72173496
31.588117	50.39267014
53.66093226	63.64239878
46.68222865	72.24725107
43.10782022	57.81251298
70.34607562	104.2571016
44.49285588	86.64202032
57.5045333	91.486778
36.93007661	55.23166089
55.80573336	79.55043668
38.95476907	44.84712424
56.9012147	80.20752314
56.86890066	83.14274979
34.3331247	55.72348926
59.04974121	77.63418251
57.78822399	99.05141484
54.28232871	79.12064627
51.0887199	69.58889785
50.28283635	69.51050331
44.21174175	73.68756432
38.00548801	61.36690454
32.94047994	67.17065577
53.69163957	85.66820315
68.76573427	114.8538712
46.2309665	90.12357207
68.31936082	97.91982104
50.03017434	81.53699078
49.23976534	72.11183247
50.03957594	85.23200734
48.14985889	66.22495789
25.12848465	53.45439421

2.3、matplotlib可视化

• 自己增加了一小部分代码，让预测曲线以及数据点可视化出来了！
  
• 在run函数最后增加以下代码就可以显示出来了。

	plt.figure(num=3,figsize=(8,5))
	plt.scatter(points[:,0],points[:,1],c="blue")
	plt.plot(points[:,0],w*points[:,0]+b)
	plt.show()

2.4、线性回归的理解

注意：不要以为线性回归拟合出来的都是直线，这个说法错误的，下面这些都是线性回归，比如第二个多项式拟合为曲线也是线性回归。$linear$ $regression$ 中的 $linear$ 指的是参数和变量之间是线性的 $\beta \times x$，这个东西是线性的。