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I'd like to hear the opinion of an expert for artifical neural networks on a problem that I try to solve. I just started to use articial neural networks and want to train an ANN with 3 inputs and 3 outputs by using 3375 data points. The goal is to map the 3 inputs to the 3 outputs. For that purpose I use a multilayer percetron implemented in tensorflow and keras.

I thought that normally a ANN is especially good in doing such kind of input-output mapping. However, the results are extremely bad. I varied everything many many times with huge differences in the values (batch size, epochs, number of hidden layers, number of neurons, error functions), however the results remain extremely bad (e.g. val_mean_absolute_percentage_error: 2360328448.0000). The mapping is so extermely wrong that it is not at all useful. What suprises me that even using inputs from the training dataset lead to disastrous outputs.

This is why I would like to hear your opinion on that. Am I doing something completely wrong or is my assumption that ANNs are especially good for such input-output mapping in this case just not true? Or maybe there is an issue with the training data? I'd highly appreciate any comments and advice from you because I do not know what else to do.

Here you can see the code:

# For data manipulation
import numpy as np
import pandas as pd

#For plotting
from matplotlib import pyplot as plt

# For building model and loading dataset
import tensorflow as tf
from tensorflow.keras.models import Sequential
from tensorflow.keras.layers import Dense
from tensorflow import keras

#Load the data
dataframe = pd.read_csv("C:/Users/User1/Desktop/ANN_inputs_outputs.csv", sep =";")
dataset = dataframe.values


# Assign the columns of the dataframe to the inputs for arrays for the ANN

X_input_dataset = dataset[:, 1:4]
Y_output_dataset = dataset[:, 4:7]

#Create the model

#Input shape defiens the number of input neurons
input_shape = (3,)


#Sequential model is just one for a vanilla MLP
model = Sequential()

#Add the different layers
model.add(keras.layers.Flatten(input_shape=(3,))),
model.add(Dense(20,  activation='relu'))
model.add(Dense(40,  activation='relu'))
model.add(Dense(20,  activation='relu'))
model.add(Dense(3, activation='linear'))

# Configure the model and start training

model.compile(loss='mean_squared_error', optimizer='adam', metrics=['mean_absolute_percentage_error'])
history = model.fit(X_input_dataset, Y_output_dataset, epochs=100, batch_size=10, verbose=1, validation_split=0.2)

#Plot training results
history_dict = history.history
print(history_dict.keys())


plt.plot(history.history['mean_absolute_percentage_error'])
plt.plot(history.history['val_mean_absolute_percentage_error'])
plt.title('Mean absolute percentage errror')
plt.ylabel('Mean absolute percentage errror')
plt.xlabel('epoch')
plt.legend(['train', 'val'], loc='upper left')
plt.show()

plt.plot(history.history['loss'])
plt.plot(history.history['val_loss'])
plt.title('Loss function')
plt.ylabel('mean absolute error')
plt.xlabel('epoch')
plt.legend(['train', 'val'], loc='upper left')
plt.show()

#predict values
x_new = [(100000,100000,100000), (100000,1000000,500000),
        (100000,100000,100000), (100000,500000,100000),
        (100000,100000,100000), (500000,100000,100000)]

y_new = model.predict(x_new)
print(y_new)

Unfortunately the data is too big such that I can't share it directly via StackExchange (I tried this). This is why I uploaded the csv file to File Dropper CSV_File. If you do not want to download the data from there, please tell me another source/way how I could share the data with you. I do not know if this helps but here you can at least see the first 100 datapoints out of the 3375 (in the full data I varied every input and created all combinations of inputs):

Input_1 Input_2 Input_3 Output_1    Output_2    Output_3
100000  100000  100000  81.63842992 336.0202553 142.6094997
100000  100000  200000  83.91274058 353.0797849 123.2756595
100000  100000  300000  86.49717207 366.4358367 107.3351762
100000  100000  400000  87.94279678 376.396602  95.92878625
100000  100000  500000  89.57430815 384.9555939 85.73828291
100000  100000  600000  92.65738103 396.8354166 70.77538736
100000  100000  700000  96.0171678  408.3277988 55.92321845
100000  100000  800000  100.5642366 420.7969577 38.90699073
100000  100000  900000  109.0237    438.4473815 12.79710349
100000  100000  1000000 114.2438266 446.0243584 0
100000  100000  1100000 114.2438266 446.0243584 0
100000  100000  1200000 114.2438266 446.0243584 0
100000  100000  1300000 114.2438266 446.0243584 0
100000  100000  1400000 114.2438266 446.0243584 0
100000  100000  1500000 114.2438266 446.0243584 0
100000  200000  100000  92.17726716 320.8186761 147.2722417
100000  200000  200000  93.98736653 336.6494039 129.6314145
100000  200000  300000  96.92805106 349.6806425 113.6594914
100000  200000  400000  98.58276913 360.6424603 101.0429556
100000  200000  500000  100.31333   368.9105132 91.04434172
100000  200000  600000  102.6334311 377.1300392 80.50471475
100000  200000  700000  105.7178567 388.244019  66.30630933
100000  200000  800000  108.9149247 398.1848881 53.16837219
100000  200000  900000  115.571269  411.5986127 33.09830325
100000  200000  1000000 127.0748864 430.1972029 2.996095751
100000  200000  1100000 128.2092221 432.0589629 0
100000  200000  1200000 128.2092221 432.0589629 0
100000  200000  1300000 128.2092221 432.0589629 0
100000  200000  1400000 128.2092221 432.0589629 0
100000  200000  1500000 128.2092221 432.0589629 0
100000  300000  100000  100.0917771 307.9756287 152.2007792
100000  300000  200000  102.9726253 323.9279352 133.3676245
100000  300000  300000  105.6062056 335.7776535 118.884326
100000  300000  400000  107.3121984 346.883184  106.0728025
100000  300000  500000  109.4540231 354.663097  96.15106489
100000  300000  600000  111.8786604 361.5557255 86.83379908
100000  300000  700000  114.7944686 371.5938132 73.87990318
100000  300000  800000  118.1373355 380.0257011 62.10514836
100000  300000  900000  122.8548691 390.9478707 46.46544517
100000  300000  1000000 133.347506  406.5063351 20.41434392
100000  300000  1100000 141.6791937 418.5889913 0
100000  300000  1200000 141.6791937 418.5889913 0
100000  300000  1300000 141.6791937 418.5889913 0
100000  300000  1400000 141.6791937 418.5889913 0
100000  300000  1500000 141.6791937 418.5889913 0
100000  400000  100000  109.503933  294.4172255 156.3470265
100000  400000  200000  112.000167  311.1933026 137.0747154
100000  400000  300000  114.2526188 322.9057599 123.1098063
100000  400000  400000  116.4791304 333.664824  110.1242305
100000  400000  500000  118.2910122 342.0030905 99.97408228
100000  400000  600000  120.2127847 349.3045772 90.75082313
100000  400000  700000  122.7641259 356.8196711 80.68438801
100000  400000  800000  126.3291166 365.4701912 68.46887722
100000  400000  900000  130.0423749 374.3468141 55.87899601
100000  400000  1000000 137.5204755 386.0880788 36.65963063
100000  400000  1100000 148.9375577 401.141397  10.18923033
100000  400000  1200000 152.8379613 407.4302237 0
100000  400000  1300000 152.8379613 407.4302237 0
100000  400000  1400000 152.8379613 407.4302237 0
100000  400000  1500000 152.8379613 407.4302237 0
100000  500000  100000  117.4879678 283.3733734 159.4068438
100000  500000  200000  121.0579184 298.9825928 140.2276737
100000  500000  300000  123.3707729 310.3330953 126.5643168
100000  500000  400000  125.8724146 320.3948833 114.0008871
100000  500000  500000  127.9615773 328.059964  104.2466436
100000  500000  600000  129.5606613 335.4906683 95.21685541
100000  500000  700000  131.4170772 343.7065728 85.14453506
100000  500000  800000  135.3015477 351.1570032 73.80963419
100000  500000  900000  137.8813788 359.0228767 63.36392947
100000  500000  1000000 144.8898942 370.7656611 44.61262969
100000  500000  1100000 154.7571144 383.9513348 21.55973576
100000  500000  1200000 164.1907262 396.0774588 0
100000  500000  1300000 164.1907262 396.0774588 0
100000  500000  1400000 164.1907262 396.0774588 0
100000  500000  1500000 164.1907262 396.0774588 0
100000  600000  100000  124.7561636 274.0110713 161.50095
100000  600000  200000  128.42286   288.8038063 143.0415186
100000  600000  300000  131.2377241 299.8006811 129.2297798
100000  600000  400000  133.8838584 309.2976404 117.0866862
100000  600000  500000  135.5491074 317.3956571 107.3234204
100000  600000  600000  137.8437737 324.061017  98.36339426
100000  600000  700000  139.5148534 331.0105966 89.74273491
100000  600000  800000  143.1729967 338.4279821 78.66720613
100000  600000  900000  146.6596817 344.9709227 68.63758054
100000  600000  1000000 150.9572297 353.3162164 55.9947389
100000  600000  1100000 159.4602916 366.5904292 34.21746416
100000  600000  1200000 171.026723  381.1619306 8.079531382
100000  600000  1300000 175.4286096 384.8395754 0
100000  600000  1400000 175.4286096 384.8395754 0
100000  600000  1500000 175.4286096 384.8395754 0
100000  700000  100000  132.1183934 264.1955984 163.9541932
100000  700000  200000  135.9907245 278.9421043 145.3353562
100000  700000  300000  138.9508032 289.1447258 132.1726561
100000  700000  400000  141.3695688 299.1572684 119.7413478
100000  700000  500000  143.2089855 306.5047858 110.5544137
100000  700000  600000  145.4980373 313.8396234 100.9305243
100000  700000  700000  147.7033751 319.6546207 92.91018914
100000  700000  800000  150.8276735 327.3557851 82.08472648
100000  700000  900000  153.528077  333.3811995 73.35890853
100000  700000  1000000 156.9484214 339.9871429 63.3326207
100000  700000  1100000 164.6661346 352.2010019 43.40104855
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The issue seems to be with the Keras mean_absolute_percentage_error

Check this SO Answer - Link

In your case,

  • You have one output=0 in the 3rd col of Y
  • If you run the model for just one Y column, it will work fine for the first two columns

any(dataset[:, 6:7]==0)

Output - True


I just added a One to remove the 0. It is working fine.

X_input_dataset = dataset[:, 1:4]
X_input_dataset = (X_input_dataset - X_input_dataset.mean())/X_input_dataset.std()
Y_output_dataset = dataset[:, 4:7]

Y_output_dataset[:,-1] = Y_output_dataset[:,-1]+1.0

enter image description here

You can do,
- Handle the 0
- Use mse as metric and calculate MAPE separately
- Write your own custom Metric

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  • $\begingroup$ Thanks for your answer 10xAI. I have several comment to that. 1) I just replaced the 0-entries in the last comments by 1-entries and standardized the x_input_dataset. Now the loss function is way lower HOWEVER the mean_absolute_percentage_error both on the training and validation set is still extremely high (I did not change anything about the mean_absolute_percentage_error in the metric as I do not really understand your advice). Here are the results of the last epoch "loss: 3.18 - mean_absolute_percentage_error: 9619858.0000 - val_loss: 3.4336 - val_mean_absolute_percentage_error: 4447402.5" $\endgroup$
    – PeterBe
    Mar 9 at 8:59
  • $\begingroup$ 2) The prediction results (and those are the most important for me) are now even worse. They used to be extremely bad but now they are just out of anything. Even random guessing leads to way better predictions results. So I think it is not a matter of how keras implements the mean_absolute_percentage_error because basically the error in my case is not lying. The predictions are extremely bad which is consistent with the values of the error. You said that in your case the results are fine. Did you also check the predictions (not only the training results)? $\endgroup$
    – PeterBe
    Mar 9 at 9:05
  • $\begingroup$ 3) I am questionig whether it really makes sense to standardize such kind of input data. Basically I want to map those 3 inputs to the 3 outputs. The inputs should not be changed. At the end I just want to give the same inputs to the ANN (not scaled or normalized) like (100000, 100000, 100000) and receive the Y outputs from my dataset (81.63842992 336.0202553 142.6094997). I am not quite sure about this but I somehow assume that normalizing and standardizing in my case might sabotage the results. $\endgroup$
    – PeterBe
    Mar 9 at 9:06
  • $\begingroup$ 3) Std. is a good practice otherwise it will take a lot of Epochs and in some case unnecessary LR tuning. For the first two comments, I have shown the output screen, MAPE is going down pretty well and prediction is also fine. Check this NB and see if you have changed this properly $\endgroup$
    – 10xAI
    Mar 9 at 12:30
  • $\begingroup$ Thanks 10xAI for your answer and effort. I really appreciate it. So I have 2 follow up comments. 1) Do you use another 'mean_absolute_percentage_error' or another Keras version because in my case, even using your code, the values are quite high. $\endgroup$
    – PeterBe
    Mar 9 at 13:10
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I did not read the question fully because it was too long, so apologies but from what i see

You need to normalize your dataset, ANN do not work with this type of un-normalized data.

Normalize only the train data and use the train normalization params to normalize your test data

Then NN's are useful when your dataset is huge, i think you are just trying to practice.

Once done with data normalization try to see bias variance tradeoff and adjust your nn with learning rate, number of neurons etc

https://stats.stackexchange.com/questions/7757/data-normalization-and-standardization-in-neural-networks

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  • $\begingroup$ Thanks Varun for your answer. I am questionig whether it really makes sense to standardize such kind of input data. Basically I want to map those 3 inputs to the 3 outputs. The inputs should not be changed. At the end I just want to give the same inputs to the ANN (not scaled or normalized) like (100000, 100000, 100000) and receive the Y outputs from my dataset (81.63842992 336.0202553 142.6094997). I am not quite sure about this but I somehow assume that normalizing and standardizing in my case might sabotage the results. $\endgroup$
    – PeterBe
    Mar 9 at 9:07
  • $\begingroup$ Usually we need to de-normalize the data after prediction, check this link out, stats.stackexchange.com/questions/66820/… about results being sabotaged, i have personally seen that in regression problems you might not get very good results, use adjusted r squared to find goodness of fit, then try something like in place of min max scaling use some other method to scale the values etc. you see my point here? (ml in todays world is still hit and trial), if not that try a more sophisticated Bayesian approach $\endgroup$ Mar 10 at 10:42
  • $\begingroup$ yes, i dont think apart from tree based algorithms, there is any other algorithm that allows you to feed data into it without normalizing it $\endgroup$ Mar 10 at 10:46
  • $\begingroup$ Thanks for your answer Varun. $\endgroup$
    – PeterBe
    Mar 10 at 10:56

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