梯度下降算法未收敛线性回归

Question

我正在尝试实现梯度下降算法，以最大程度地减少最适合ML类的线的参数。 我正在最小化成本函数。 这是我所拥有的：

数据如下：

    year    dipnet days fished  dipnet sockeye harvest
0   1996    10503   102821
1   1997    11023   114619
2   1998    10802   103847
3   1999    13738   149504
4   2000    12354   98262
5   2001    14772   150766
6   2002    14840   180028
7   2003    15263   223580
8   2004    18513   262831
9   2005    20977   295496
10  2006    12685   127630
11  2007    21908   291270
12  2008    20772   234109
13  2009    26171   339993
14  2010    28342   389552
15  2011    32818   537765
16  2012    34374   526992
17  2013    33193   347222
18  2014    36380   379823

和代码...

import numpy as np
import pandas as pd
import matplotlib.pyplot as plt

data = pd.read_csv("D:/Assignment 1/Exercise1/dip-har-eff.csv")
data.head()

    year days fished sockeye harvest
0   1996    10503   102821
1   1997    11023   114619
2   1998    10802   103847
3   1999    13738   149504
4   2000    12354   98262

np_data = data.values
harvest = np_data[:, 2]
days = np_data[:, 1]

plt.scatter(days, harvest)

start = np.array([0,0])         #the starting values for b_0 and b_1
step = .01                      #the gradient multiplier
iterations = 30                 #number of iteration for the algorithm
batch_size = 3                 #the batch size

X = days[0:batch_size]
Y = harvest[0:batch_size]

def del_cost(b_0, b_1):
    error_x = []
    error_y = []
    for i in range(0, batch_size):
        e = (b_1*X[i] + b_0) - Y[i]
        error_x.append(e)
        f = ((b_1*X[i] + b_0) - Y[i])*X[i]
        error_y.append(f)
    d_x = (1/batch_size)*np.sum(error_x)
    d_y = (1/batch_size)*np.sum(error_y)
    return np.array([d_x, d_y])

for i in range(iterations):
    temp = start
    start = start - step*(del_cost(temp[0], temp[1]))
    print(start[0])
    print(start[1])

输出是...

1070.95666667
11550431.6467
-1244672383.04
-1.3417834015e+13
1.44590456124e+15
1.55871598694e+19
-1.67967091608e+21
-1.81072110836e+25
1.9512314035e+27
2.10346911158e+31
-2.26669638292e+33
-2.44354709455e+37
2.63316410506e+39
2.83860712307e+43
-3.05888042899e+45
-3.29753840927e+49
3.55342436154e+51
3.83066732703e+55
-4.12792359372e+57
-4.44998976483e+61
4.79530488393e+63
5.16944104421e+67
-5.57058492188e+69
-6.00520947728e+73
6.47120821783e+75
6.97610061854e+79
-7.51743962004e+81
-8.10396040706e+85
8.73282029238e+87
9.41416672011e+91
-1.01446974121e+94
-1.09362003986e+98
1.17848395063e+100
1.27043085931e+104
-1.36901512729e+106
-1.47582753557e+110
1.590350397e+112
1.7144316818e+116
-1.84747000587e+118
-1.99161210964e+122
2.14615938035e+124
2.31360563233e+128
-2.4931393047e+130
-2.68765739877e+134
2.8962171447e+136
3.12218391597e+140
-3.36446252059e+142
-3.62696242817e+146
3.90841138178e+148
4.21335091378e+152
-4.54030307537e+154
-4.89454365031e+158
5.27435574267e+160
5.68586809762e+164
-6.12708624038e+166
-6.60512977987e+170
7.11768178497e+172
7.67301292606e+176
-8.26843168262e+178
-8.91354588413e+182

我不知道为什么这些参数是1）不断增长而不适应分钟，以及2）每次交替显示符号。 我已经手工检查了前几次迭代的计算，它们是正确的。 我不知道怎么了，请帮忙！

Answer 1

您的step参数太大。 您需要减少很多。 试试0.001或0.0001之类的值

Answer 2

扩展数据也可能会有所帮助。您可以使用scikit learning。

另外，减小步长并查看。