Table 1 Proposed and implemented models. NN denotes that the parameters are not needed for a model. Alpha is the parameter α and is needed only in generalized Poisson regression models. UPDN_1 denotes the univariate Poisson deep neural network with 1 hidden layer, UPDN_2 denotes a UPDN with two hidden layers and so on. MPDN_1 denotes the multivariate Poisson deep neural network with 1hidden layer, MPDN_2 denotes a MPDN with two hidden layers, and so on

Model	Model name	Abbreviation of model	Hidden layer	Alpha
1	Univariate Poisson deep neural network	UPDN_1	1	NN
2	Univariate Poisson deep neural network	UPDN_2	2	NN
3	Univariate Poisson deep neural network	UPDN_3	3	NN
4	Univariate Poisson deep neural network	UPDN_4	4	NN
5	Multivariate Poisson deep neural network	MPDN_1	1	NN
6	Multivariate Poisson deep neural network	MPDN_2	2	NN
7	Multivariate Poisson deep neural network	MPDN_3	3	NN
8	Multivariate Poisson deep neural network	MPDN_4	4	NN
9	Univariate Generalized Poisson Elastic net regression	GPR_0.75	0	0.75
10	Univariate Generalized Poisson Elastic net regression	GPR_0.5	0	0.5
11	Univariate Generalized Poisson Elastic net regression	GPR_0.25	0	0.25
12	Univariate Generalized Poisson Lasso regression	GPR_Lasso	0	1
13	Univariate Generalized Poisson Ridge regression	GPR_Ridge	0	0