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

Dzik-Walczak, Aneta; Odziemczyk, Maciej

doi:10.2478/ceej-2021-0024

Figures & Tables

Optimum InceptionSource: Own elaboration.

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

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

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

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

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

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

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

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 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
	#F_2in/#F_2out	1/4	1/4		1/4	1/4
	#F_3in/#F_3out	1/4	1/4		1/4	1/4
	#F_4out	4	4		4	4
	Activation	ReLU	ReLU		ReLU	ReLU
	inception module	+	+	−	+	+
	#F₁	8	8		8	8
	#F_2in/#F_2out	4/8	4/8		4/8	4/8
	#F_3in/#F_3out	4/8	4/8		4/8	4/8
	#F_4out	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

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

Figures & Tables

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

Hyperparameters and results for the best models, all horizons

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