如何解决Elman神经网络中的过拟合问题？

Question

I'm training elman network with neurolab python library and my net doesn't work properly.

• Training input vectors: http://pastebin.com/urQX2eEA
• Training target vector: http://pastebin.com/1JQh1xZv
• Sample vector to test a network: http://pastebin.com/jprZhBHa

But while training it is showing too big errors:

Epoch: 100; Error: 23752443150.672318;
Epoch: 200; Error: 284037904.0305649;
Epoch: 300; Error: 174736152.57367808;
Epoch: 400; Error: 3318952.136089243;
Epoch: 500; Error: 299017.4471083774;
Epoch: 600; Error: 176600.0906688521;
Epoch: 700; Error: 176599.32080188877;
Epoch: 800; Error: 185178.21132511366;
Epoch: 900; Error: 177224.2950528976;
Epoch: 1000; Error: 176632.86797784362;
The maximum number of train epochs is reached

As a result network fails on testing sample. Original MICEX:

1758,97
1626,18
1688,34
1609,19
1654,55
1669
1733,17
1642,97
1711,53
1771,05

Predicted MICEX:

[ 1237.59155306]
 [ 1237.59155306]
 [ 1237.59155306]
 [ 1237.59155306]
 [ 1237.59155306]
 [ 1237.59155306]
 [ 1237.59155306]
 [ 1237.59155306]
 [ 1237.59155306]
 [ 1237.59155306]

Here is my code:

import neurolab as nl
import numpy as np

# Create train samples
MICEX = [421.08,455.44,430.3,484,515.17,468.85,484.73,514.71,551.72,591.09,644.64,561.78,535.4,534.84,502.81,549.28,611.03,632.97,570.76,552.22,575.74,635.38,598.04,593.88,603.89,639.98,700.65,784.28,892.5,842.52,944.55,1011,1171.44,1320.83,1299.19,1486.85,1281.5,1331.39,1380.24,1448.72,1367.24,1426.83,1550.71,1693.47,1656.97,1655.19,1698.08,1697.28,1570.34,1665.96,1734.42,1677.02,1759.44,1874.73,1850.64,1888.86,1574.33,1660.42,1628.43,1667.35,1925.24,1753.67,1495.33,1348.92,1027.66,731.96,611.32,619.53,624.9,666.05,772.93,920.35,1123.38,971.55,1053.3,1091.98,1197.2,1237.18,1284.95,1370.01,1419.42,1332.64,1450.15,1436.04,1332.62,1309.31,1397.12,1368.9,1440.3,1523.39,1565.52,1687.99,1723.42,1777.84,1813.59,1741.84,1666.3,1666.59,1705.18,1546.05,1366.54,1498.6,1499.62,1402.02,1510.91,1594.32,1518.29,1474.14,1312.24,1386.89,1406.36,1422.38,1459.01,1423.46,1405.19,1477.87,1547.18,1487.46,1440.02,1386.69,1343.99,1331.24,1377.6,1364.54,1463.13,1509.62,1479.35,1503.39,1454.05,1444.71,1369.29,1306.01,1432.03,1476.38,1379.61,1400.71,1411.07,1488.47,1533.68,1396.61,1647.69]

Brent = [26.8,28.16,28.59,30.05,28.34,27.94,28.76,30.48,29.51,33.01,32.36,35.12,36.98,33.51,41.6,39.33,47.08,48.78,44.03,40.24,45.87,50.14,53.05,49.33,49.83,54.85,59.7,66.68,62.56,58.35,53.41,58.87,65.43,60.05,64.94,72,69,73.28,75.16,69.64,61.37,56.97,64.42,60.13,57.21,60.66,68.42,67.28,68.82,73.26,78.05,73.53,81.75,91.14,88,93.85,91.98,100.04,100.51,112.71,128.27,140.3,123.96,115.17,98.96,65.6,53.49,45.59,45.93,45.84,48.68,50.64,65.8,69.42,71.52,69.32,68.92,75.09,78.36,77.93,71.18,78.03,82.17,87.35,74.6,74.66,78.26,74.42,82.11,83.26,85.45,94.59,100.56,112.1,117.17,126.03,116.68,111.8,117.54,114.49,102.15,109.19,110.37,107.22,111.16,123.04,122.8,119.47,101.62,97.57,104.62,114.92,112.14,108.4,111.17,111.11,114.56,111,109.89,101.74,100.15,101.5,107.7,114.45,108.2,108.9,110.11,110.9,105.79,108.65,107.7,108.14,109.49,112.4,105.52,103.11,94.8,85.96,68.34,57.54,52.95]
DJIA = [8850.26,8985.44,9233.8,9415.82,9275.06,9801.12,9782.46,10453.92,10488.07,10583.92,10357.7,10225.57,10188.45,10435.48,10139.71,10173.92,10080.27,10027.47,10428.02,10783.01,10489.94,10766.23,10503.76,10192.51,10467.48,10274.97,10640.91,10481.6,10568.7,10440.07,10805.87,10717.5,10864.86,10993.41,11109.32,11367.14,11168.31,11150.22,11185.68,11381.15,11679.07,12080.73,12221.93,12463.15,12621.69,12268.63,12354.35,13062.91,13627.64,13408.62,13211.99,13357.74,13895.63,13930.01,13371.72,13264.82,12650.36,12266.39,12262.89,12820.13,12638.32,11350.01,11378.02,11543.96,10850.66,9325.01,8829.04,8776.39,8000.86,7062.93,7608.92,8168.12,8500.33,8447,9171.61,9496.28,9712.28,9712.73,10344.84,10428.05,10067.33,10325.26,10856.63,11008.61,10136.63,9774.02,10465.94,10014.72,10788.05,11118.49,11006.02,11577.51,11891.93,12226.34,12319.73,12810.54,12569.79,12414.34,12143.24,11613.53,10913.38,11955.01,12045.68,12217.56,12632.91,12952.07,13212.04,13213.63,12393.45,12880.09,13008.68,13090.84,13437.13,13096.46,13025.58,13104.14,13860.58,14054.49,14578.54,14839.8,15115.57,14909.6,15499.54,14810.31,15129.67,15545.75,16086.41,16576.66,15698.85,16321.71,16457.66,16580.84,16717.17,16826.6,16563.3,17098.45,17042.9,17390.52,17828.24,17823.07,17164.95]
CAC_40 = [2991.75,3084.1,3210.27,3311.42,3134.99,3373.2,3424.79,3557.9,3638.44,3725.44,3625.23,3674.28,3669.63,3732.99,3647.1,3594.28,3640.61,3706.82,3753.75,3821.16,3913.69,4027.16,4067.78,3908.93,4120.73,4229.35,4451.74,4399.36,4600.02,4436.45,4567.41,4715.23,4947.99,5000.45,5220.85,5188.4,4930.18,4965.96,5009.42,5165.04,5250.01,5348.73,5327.64,5541.76,5608.31,5516.32,5634.16,5930.77,6104,6054.93,5751.08,5662.7,5715.69,5841.08,5667.5,5614.08,4871.8,4790.66,4707.07,4996.54,5014.28,4425.61,4392.36,4485.64,4027.15,3487.07,3262.68,3217.97,2962.37,2693.96,2803.94,3159.85,3273.55,3138.93,3426.27,3657.72,3794.96,3601.43,3684.75,3936.33,3737.19,3708.8,3974.01,3816.99,3507.56,3442.89,3643.14,3476.18,3715.18,3833.5,3610.44,3804.78,4005.5,4110.35,3989.18,4106.92,4006.94,3980.78,3672.77,3256.76,2981.96,3242.84,3154.62,3159.81,3298.55,3447.94,3423.81,3212.8,3005.48,3196.65,3291.66,3413.07,3354.82,3429.27,3557.28,3641.07,3732.6,3723,3731.42,3856.75,3948.59,3738.91,3992.69,3933.78,4143.44,4299.89,4295.21,4295.95,4165.72,4408.08,4391.5,4487.39,4519.57,4422.84,4246.14,4381.04,4426.76,4233.09,4390.18,4263.55,4604.25]
SSEC = [1576.26,1486.02,1476.74,1421.98,1367.16,1348.3,1397.22,1497.04,1590.73,1675.07,1741.62,1595.59,1555.91,1399.16,1386.2,1342.06,1396.7,1320.54,1340.77,1266.5,1191.82,1306,1181.24,1159.15,1060.74,1080.94,1083.03,1162.8,1155.61,1092.82,1099.26,1161.06,1258.05,1299.03,1298.3,1440.22,1641.3,1672.21,1612.73,1658.64,1752.42,1837.99,2099.29,2675.47,2786.34,2881.07,3183.98,3841.27,4109.65,3820.7,4471.03,5218.82,5552.3,5954.77,4871.78,5261.56,4383.39,4348.54,3472.71,3693.11,3433.35,2736.1,2775.72,2397.37,2293.78,1728.79,1871.16,1820.81,1990.66,2082.85,2373.21,2477.57,2632.93,2959.36,3412.06,2667.74,2779.43,2995.85,3195.3,3277.14,2989.29,3051.94,3109.11,2870.61,2592.15,2398.37,2637.5,2638.8,2655.66,2978.83,2820.18,2808.08,2790.69,2905.05,2928.11,2911.51,2743.47,2762.08,2701.73,2567.34,2359.22,2468.25,2333.41,2199.42,2292.61,2428.49,2262.79,2396.32,2372.23,2225.43,2103.63,2047.52,2086.17,2068.88,1980.12,2269.13,2385.42,2365.59,2236.62,2177.91,2300.59,1979.21,1993.8,2098.38,2174.66,2141.61,2220.5,2115.98,2033.08,2056.3,2033.31,2026.36,2039.21,2048.33,2201.56,2217.2,2363.87,2420.18,2682.83,3234.68,3210.36]


Brent_sample = [62.48, 55.1, 66.8, 65.19, 63.14, 51.85, 53.12, 48.44, 49.5, 44.5]
DJIA_sample = [18132.7, 17776.12, 17840.52, 18010.68, 17619.51, 17689.86, 16528.03, 16284.7, 17663.54, 17719.92]
CAC_40_sample = [4922.99, 5031.47, 5042.84, 5084.08, 4812.24, 5081.73, 4652.34, 4453.91, 4880.18, 4951.83]
SSEC_sample = [3310.3, 3747.9, 4441.66, 4611.74, 4277.22, 3663.73, 3205.99, 3052.78, 3382.56, 3445.4]



MICEX = np.asarray(MICEX)
Brent = np.asarray(Brent)
DJIA = np.asarray(DJIA)
CAC_40 = np.asarray(CAC_40)
SSEC = np.asarray(SSEC)

Brent_sample = np.asarray(Brent_sample)
DJIA_sample = np.asarray(DJIA_sample)
CAC_40_sample = np.asarray(CAC_40_sample)
SSEC_sample = np.asarray(SSEC_sample)

size = len(MICEX)

inp = np.vstack((Brent, DJIA, CAC_40, SSEC)).T
tar = MICEX.reshape(size, 1)
smp = np.vstack((Brent_sample, DJIA_sample, CAC_40_sample, SSEC_sample)).T

# Create network with 2 layers and random initialized
net = nl.net.newelm(
        [[min(inp[:, 0]), max(inp[:, 0])],
         [min(inp[:, 1]), max(inp[:, 1])],
         [min(inp[:, 2]), max(inp[:, 2])],
         [min(inp[:, 3]), max(inp[:, 3])]
         ],
        [46, 1],
        [nl.trans.TanSig(), nl.trans.PureLin()]  # SatLinPrm(0.00000001, 421.08, 1925.24)
                )
# Set initialized functions and init
net.layers[0].initf = nl.init.InitRand([-0.1, 0.1], 'wb')
net.layers[1].initf = nl.init.InitRand([-0.1, 0.1], 'wb')
net.init()

# Changing training method
# net.trainf = nl.train.train_cg

# Train network
error = net.train(inp, tar, epochs=1000, show=100, goal=0.02)

# Simulate network
out = net.sim(smp)
print(smp)
print('MICEX predictions for the next 10 periods:\n', out)

Does anybody know a solution of this problem?

Answer 1

First of all this is not overfitting . You are underfitting , you do not even converge for training cases. Can't you just increase number of epochs? Let the net converge.