Python 线性回归实现中的问题

我是机器学习的新手，我尝试使用numpy从头开始实现向量化线性回归。我尝试使用y=x测试实现。但我的损失正在增加，我无法理解为什么。如果有人能指出为什么会这样，那就太好了。提前谢谢

将numpy导入为np
类线性累加器（对象）：
定义初始化（自我、数值特性）：
self.num\u features=num\u features
self.w=np.random.randn（num_features，1）.astype（np.float32）
self.b=np.array（0.0）.astype（np.float32）
def前进（自身，x）：
返回np.dot（x，self.w）+self.b
@静力学方法
def损失（y_pred，y_true）：
l=np.平均值（np.幂（y_pred-y_true，2））/2
返回l
def计算梯度（self、x、y_pred、y_true）：
self.dl_dw=np.dot（x.T，y_pred-y_true）/len（x）
self.dl_db=np.mean（y_pred-y_true）
def优化（自身、步长）：
self.w-=步长大小*self.dl\u-dw
self.b-=步长大小*self.dl\u db
def系列（自身、x、y、步进尺寸=1.0）：
y_pred=自前向（x）
l=自我损失（y_pred=y_pred，y_true=y）
自计算梯度（x=x，y_pred=y_pred，y_true=y）
自我优化（步长=步长）
返回l
def评估（自、x、y）：
返回自损（自前向（x），y_真）
check_reg=线性累加器（num_features=1）
x=np.数组（列表（范围（1000））。重塑（-1，1）
y=x
损失=[]
对于范围（100）内的迭代：
损失=检查登记序列（x=x，y=y，步长=0.001）
损失。追加（损失）
如果迭代%1==0：
打印（“迭代：{}”。格式（迭代））
打印（丢失）

输出

Iteration: 0
612601.7859402705
Iteration: 1
67456013215.98818
Iteration: 2
7427849474110884.0
Iteration: 3
8.179099502901393e+20
Iteration: 4
9.006330707513148e+25
Iteration: 5
9.917228672922966e+30
Iteration: 6
1.0920254505132042e+36
Iteration: 7
1.2024725981084638e+41
Iteration: 8
1.324090295064888e+46
Iteration: 9
1.4580083421516024e+51
Iteration: 10
1.60547085025467e+56
Iteration: 11
1.7678478362285333e+61
Iteration: 12
1.946647415292399e+66
Iteration: 13
2.1435307416407376e+71
Iteration: 14
2.3603265498975516e+76
Iteration: 15
2.599049318486855e+81
Iteration: 16
nan
Iteration: 17
nan
Iteration: 18
nan
Iteration: 19
nan
Iteration: 20
nan
Iteration: 21
nan
Iteration: 22
nan
Iteration: 23
nan
Iteration: 24
nan
Iteration: 25
nan
Iteration: 26
nan
Iteration: 27
nan
Iteration: 28
nan
Iteration: 29
nan
Iteration: 30
nan
Iteration: 31
nan
Iteration: 32
nan
Iteration: 33
nan
Iteration: 34
nan
Iteration: 35
nan
Iteration: 36
nan
Iteration: 37
nan
Iteration: 38
nan
Iteration: 39
nan
Iteration: 40
nan
Iteration: 41
nan
Iteration: 42
nan
Iteration: 43
nan
Iteration: 44
nan
Iteration: 45
nan
Iteration: 46
nan
Iteration: 47
nan
Iteration: 48
nan
Iteration: 49
nan
Iteration: 50
nan
Iteration: 51
nan
Iteration: 52
nan
Iteration: 53
nan
Iteration: 54
nan
Iteration: 55
nan
Iteration: 56
nan
Iteration: 57
nan
Iteration: 58
nan
Iteration: 59
nan
Iteration: 60
nan
Iteration: 61
nan
Iteration: 62
nan
Iteration: 63
nan
Iteration: 64
nan
Iteration: 65
nan
Iteration: 66
nan
Iteration: 67
nan
Iteration: 68
nan
Iteration: 69
nan
Iteration: 70
nan
Iteration: 71
nan
Iteration: 72
nan
Iteration: 73
nan
Iteration: 74
nan
Iteration: 75
nan
Iteration: 76
nan
Iteration: 77
nan
Iteration: 78
nan
Iteration: 79
nan
Iteration: 80
nan
Iteration: 81
nan
Iteration: 82
nan
Iteration: 83
nan
Iteration: 84
nan
Iteration: 85
nan
Iteration: 86
nan
Iteration: 87
nan
Iteration: 88
nan
Iteration: 89
nan
Iteration: 90
nan
Iteration: 91
nan
Iteration: 92
nan
Iteration: 93
nan
Iteration: 94
nan
Iteration: 95
nan
Iteration: 96
nan
Iteration: 97
nan
Iteration: 98
nan
Iteration: 99
nan

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您的实现没有问题。您的步长太大，无法收敛。你在优化波峰周围跳跃，误差越来越大。 为此编辑步长：

loss=check\u reg.train（x=x，y=y，步长=0.000001）

您将获得：

Iteration: 0
58305.102166924036
Iteration: 1
25952.192344178206
Iteration: 2
11551.585414406314
Iteration: 3
5141.729521746186
Iteration: 4
2288.6353484460747
Iteration: 5
1018.6952280352172
Iteration: 6
453.4320214875039
Iteration: 7
201.82728832044089
Iteration: 8
89.83519431606754
Iteration: 9
39.98665864625944
Iteration: 10
17.798416262435936
Iteration: 11
7.92229454258205
Iteration: 12
3.526272890501929
Iteration: 13
1.5696002444816197
Iteration: 14
0.6986516574778796
Iteration: 15
0.3109875219688626
Iteration: 16
0.13843156434074647
Iteration: 17
0.061616235257299326
Iteration: 18
0.027424318402401473
Iteration: 19
0.012205888201891543
Iteration: 20
0.005434012356344396
Iteration: 21
0.0024188644277583476
Iteration: 22
0.0010770380211645404
Iteration: 23
0.0004796730257022216
Iteration: 24
0.00021339295719587025
Iteration: 25
9.499628306355218e-05
Iteration: 26
4.244764386691682e-05
Iteration: 27
1.8965112443214162e-05
Iteration: 28
8.56069334821767e-06
Iteration: 29
3.848135476439999e-06
Iteration: 30
1.7367004907528985e-06
Iteration: 31
8.07976330965736e-07
Iteration: 32
4.0167090640020525e-07
Iteration: 33
2.253979336583221e-07
Iteration: 34
1.5365746125585947e-07
Iteration: 35
1.2480275459766612e-07
Iteration: 36
1.1147859663321005e-07
Iteration: 37
1.0288427880059631e-07
Iteration: 38
1.0036079530613815e-07
Iteration: 39
9.901975516098116e-08
Iteration: 40
9.901971962009025e-08
Iteration: 41
9.901968407922984e-08
Iteration: 42
9.901964853839991e-08
Iteration: 43
9.901961299760048e-08
Iteration: 44
9.901957745683155e-08
Iteration: 45
9.90195419160931e-08
Iteration: 46
9.901950637538515e-08
Iteration: 47
9.90194708347077e-08
Iteration: 48
9.901943529406073e-08
Iteration: 49
9.901939975344426e-08
Iteration: 50
9.901936421285829e-08
Iteration: 51
9.90193286723028e-08
Iteration: 52
9.901929313177781e-08
Iteration: 53
9.901925759128331e-08
Iteration: 54
9.901922205081931e-08
Iteration: 55
9.90191865103858e-08
Iteration: 56
9.901915096998278e-08
Iteration: 57
9.901911542961026e-08
Iteration: 58
9.901907988926822e-08
Iteration: 59
9.901904434895669e-08
Iteration: 60
9.901900880867564e-08
Iteration: 61
9.901897326842509e-08
Iteration: 62
9.901893772820503e-08
Iteration: 63
9.901890218801546e-08
Iteration: 64
9.901886664785639e-08
Iteration: 65
9.901883110772781e-08
Iteration: 66
9.901879556762973e-08
Iteration: 67
9.901876002756213e-08
Iteration: 68
9.901872448752503e-08
Iteration: 69
9.901868894751843e-08
Iteration: 70
9.901865340754231e-08
Iteration: 71
9.901861786759669e-08
Iteration: 72
9.901858232768157e-08
Iteration: 73
9.901854678779693e-08
Iteration: 74
9.901851124794279e-08
Iteration: 75
9.901847570811914e-08
Iteration: 76
9.901844016832599e-08
Iteration: 77
9.901840462856333e-08
Iteration: 78
9.901836908883116e-08
Iteration: 79
9.901833354912948e-08
Iteration: 80
9.90182980094583e-08
Iteration: 81
9.901826246981762e-08
Iteration: 82
9.901822693020742e-08
Iteration: 83
9.901819139062772e-08
Iteration: 84
9.901815585107851e-08
Iteration: 85
9.90181203115598e-08
Iteration: 86
9.901808477207157e-08
Iteration: 87
9.901804923261384e-08
Iteration: 88
9.90180136931866e-08
Iteration: 89
9.901797815378986e-08
Iteration: 90
9.901794261442361e-08
Iteration: 91
9.901790707508786e-08
Iteration: 92
9.901787153578259e-08
Iteration: 93
9.901783599650782e-08
Iteration: 94
9.901780045726355e-08
Iteration: 95
9.901776491804976e-08
Iteration: 96
9.901772937886647e-08
Iteration: 97
9.901769383971367e-08
Iteration: 98
9.901765830059137e-08
Iteration: 99
9.901762276149956e-08

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希望有帮助

谢谢你的回答。那么我如何计算步长呢？我可以使用经验法则吗？关于这方面有大量的文献和许多可以使用的技术，这里有一些：一个非常简单的方法是将步长作为超参数来调整，并使用一个很好的范围来训练模型。然后使用交叉验证验证哪个模型学习得最好。