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Modelling cross-sectional tabular data using convolutional neural networks: Prediction of corporate bankruptcy in Poland

Aneta Dzik-Walczak
Aneta Dzik-Walczak
 et 
Maciej Odziemczyk
Maciej Odziemczyk
   | 27 nov. 2021
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Publié en ligne: 27 nov. 2021
Pages: 352 - 377
DOI: https://doi.org/10.2478/ceej-2021-0024
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© 2021 Aneta Dzik-Walczak et al., published by Sciendo
This work is licensed under the Creative Commons Attribution-NonCommercial-NoDerivatives 4.0 International License.

Figure 1

Naive InceptionSource: Own elaboration
Naive InceptionSource: Own elaboration

Figure 2

Optimum InceptionSource: Own elaboration.
Optimum InceptionSource: Own elaboration.

Figure 3

PR and ROC curves for all prediction horizons, test dataSource: Authors’ calculations
PR and ROC curves for all prediction horizons, test dataSource: Authors’ calculations

Figure A1

8 × 8 images, raw data, normalised, validation, one-year horizonSource: Authors’ calculations
8 × 8 images, raw data, normalised, validation, one-year horizonSource: Authors’ calculations

Figure A2

8 × 8 images, outlier-free, normalised, validation, one-year horizonSource: Authors’ calculations
8 × 8 images, outlier-free, normalised, validation, one-year horizonSource: Authors’ calculations

Figure A3

8 × 8 images, outlier-free, power transformation, normalised, validation, one-year horizonSource: Authors’ calculations.u
8 × 8 images, outlier-free, power transformation, normalised, validation, one-year horizonSource: Authors’ calculations.u

Figure A4

20 × 20 images, raw data, normalised, validation, one-year horizonSource: Authors’ calculations
20 × 20 images, raw data, normalised, validation, one-year horizonSource: Authors’ calculations

Figure A5

20 × 20 images, data without outliers, normalised, validation, one-year horizonSource: Authors’ calculations
20 × 20 images, data without outliers, normalised, validation, one-year horizonSource: Authors’ calculations

Figure A6

20 × 20 images, outlier-free, power transformation, normalised, validation, one-year horizonSource: Authors’ calculations
20 × 20 images, outlier-free, power transformation, normalised, validation, one-year horizonSource: Authors’ calculations

Figure A7

Learning curves depending on the variant of preprocessing with early stopping for the MLP model example.Source: Authors’ calculations
Learning curves depending on the variant of preprocessing with early stopping for the MLP model example.Source: Authors’ calculations

Figure A8

Learning curves depending on the variant of preprocessing with early stopping for CNN model examplesSource: Authors’ calculations
Learning curves depending on the variant of preprocessing with early stopping for CNN model examplesSource: Authors’ calculations

MLP and convolutional neural networks: hyperparameters and results for best networks, all horizons

Network Horizon (balance) 1 year (6.94%) 2 years (5.25%) 3 years (4.71%) 4 years (3.93%) 5 years (3.86%)
MLP neural networks Architecture
dense layer + + + + +
neurons 60 60 60 60 60
activation tanh tanh tanh tanh tanh
dropout 0.4 0.4 0.4 0.4
regularisation L1 0.00005 L1 0.00005 L2 0.00005 L1 0.00005
dense layer + + + + +
neurons 60 60 60 60 60
activation sigmoid sigmoid sigmoid sigmoid sigmoid
dropout 0.4 0.4 0.4 0.4 0.4
regularisation L1 0.00005 L1 0.00005 L2 0.00005 L1 0.00005
dense layer + + + + +
Neurons 1 1 1 1 1
activation sigmoid sigmoid sigmoid sigmoid sigmoid
early stopping 4,873 3,972 4,892 6,843 7,243
batch size 394 394 394 394 394
Optimiser Adam Adam Adam Adam Adam
Results
AUC-PR 0.717 0.611 0.632 0.629 0.519
overfitting PR 0.238 0.214 0.35 0.282 0.34
AUC-ROC 0.929 0.895 0.9 0.909 0.883
overfitting ROC 0.065 0.079 0.098 0.085 0.106
8×8 convolutional neural networks Architecture
inception module + + − + +
#F1 4 4 4 4
#F2in/#F2out 1/4 1/4 1/4 1/4
#F3in/#F3out 1/4 1/4 1/4 1/4
#F4out 4 4 4 4
Activation ReLU ReLU ReLU ReLU
inception module + + − + +
#F1 8 8 8 8
#F2in/#F2out 4/8 4/8 4/8 4/8
#F3in/#F3out 4/8 4/8 4/8 4/8
#F4out 8 8 8 8
Activation ReLU ReLU ReLU ReLU
Convolution − − + − −
Size 3 × 3
#F 32
Padding same
Stride 1 × 1
Activation ReLU
Convolution − − + − −
Size 3 × 3
#F 64
Padding same
Stride 1 × 1
Activation ReLU
Max pooling − − + − −
Size 2 × 2
Padding Valid
Stride 2 × 2
Convolution − − + − −
Size 1 × 1
#F 32
Stride 1 × 1
Activation ReLU
Average pooling + + − + +
Size 2 × 2 2 × 2 2 × 2 2 × 2 2 × 2
Padding valid valid valid valid
Stride 2 × 2 2 × 2 2 × 2 2 × 2 2 × 2
flatten layer + + + + +
dense layer + + + + +
Neurons 256 256 512 256 256
Activation ReLU ReLU sigmoid ReLU ReLU
Dropout 0.4 0.4 0.4 0.4
regularisation L1 0.000025 L2 0.00005 L2 0.00005 L2 0.0001 L2 0.00005
dense layer − − + + −
neurons 256 128
activation sigmoid ReLU
dropout
regularisation L2 0.00005 L2 0.00005
dense layer + + + + +
neurons 1 1 1 1 1
activation sigmoid sigmoid sigmoid sigmoid sigmoid
early stopping 418 350 112 220 326
batch size 394 394 394 394 394
optimiser Adam Adam RMSprop Adam Adam
Results
AUC-PR 0.547 0.393 0.392 0.342 0.306
overfitting PR 0.219 0.404 0.43 0.414 0.392
AUC-ROC 0.885 0.828 0.84 0.814 0.793
overfitting ROC 0.07 0.147 0.136 0.156 0.169
20 × 20 convolutional neural networks early stopping 189 157 137 155 239
Results
AUC-PR 0.542 0.456 0.401 0.394 0.345
overfitting PR 0.233 0.447 0.489 0.576 0.553
AUC-ROC 0.881 0.846 0.837 0.847 0.811
overfitting ROC 0.074 0.143 0.152 0.151 0.173

Hyperparameters and results for the best models, all horizons

Model Horizon (balance) 1 year (6.94%) 2 years (5.25%) 3 years (4.71%) 4 years (3.93%) 5 years (3.86%)
Logit λ 1 0.08 0 0.05 0.03
Results
AUC-PR 0.497 0.28 0.251 0.221 0.27
overfitting PR 0.05 0.067 0.035 0.07 0.075
AUC-ROC 0.852 0.782 0.762 0.726 0.764
overfitting ROC 0.003 0.022 0.03 0.04 0.036
Random forests max depth 12 12 13 12 8
max number of characteristics 52 58 54 55 33
min observations to divide 4 18 8 10 5
min observations in the leaf 4 17 6 9 4
number of trees 200 200 200 600 100
preprocessing q+n p+n - q+p+n p+n
Results
AUC-PR 0.535 0.337 0.284 0.292 0.264
overfitting PR 0.416 0.412 0.67 0.603 0.564
AUC-ROC 0.89 0.84 0.829 0.817 0.795
overfitting ROC 0.1 0.1367 0.168 0.175 0.192
XGBoost max depth 6 7 5 5 4
learning rate η 0.08 0.03 0.07 0.1 0.07
column fraction 0.8 0.8 1 0.8 0.9
raw fraction 0.9 0.9 0.9 0.9 0.8
loss reduction γ 3 5 0.08 4 2
regularisation L1 0.4 1 1 0.4 0.1
regularisation L2 0.4 0.2 0 1 0.3
preprocessing q+n - q+n - n
estimators median 122 271 209 246 164
Results
AUC-PR 0.596 0.411 0.39 0.392 0.355
overfitting PR 0.392 0.52 0.598 0.571 0.54
AUC-ROC 0.909 0.869 0.864 0.86 0.835
overfitting ROC 0.09 0.124 0.136 0.137 0.145
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