Xeon e5 2630

In this study, the breast cancer-related GWAS dataset comprising 528,173 SNPs was used to detect genetic epistasis. All the SNPs with a missing genotype rate < 0.1, MAF > 0.05, a Hardy-Weinberg equilibrium (HWE) p > 0.001, and a pair-wise R² < 0.8 were retained. In total, 498,847 SNPs were used for detecting genetic epistasis (available upon request). The eight most widely cited genetic epistasis detection software packages, including pMDR [20 (link)], GBOOST [21 (link)], PLINK [22 (link)], FastEpistasis [23 (link)], SNPRuler [24 (link)], AntEpiSeeker [25 (link)], Ranger [26 (link)], and BEAM3 [27 (link)], were used to detect SNP-SNP interactions. All eight software packages were run using the default configuration on a machine with an Intel Xeon E5-2630 CPU and an Nvidia Quadro K2000 GPU.

Training was performed on a computer with two Intel Xeon E5-2630 CPU processors, four NVIDIA GTX 1080 Ti Graphical processing units, and 128 GB of DDR4 Random access memory. The project was implemented using the Python programming language and the Google Tensorflow library. We used the rectified linear unit (ReLu) as the activation function, the Adam optimizer, and cross-entropy as the loss function. We used the grid search approach for optimizing the learning rate, dropout, and kernel size of the convolution and pooling layers. We varied learning rates from (0.1, 0.001, 0.0001), and dropout from (0, 0.1, 0.2, 0.3, 0.4, 0.5, 0.6) after each convolution layer and fully connected layer. The kernel sizes of convolution layers were varied from (1 × 1 × 1, 2 × 2 × 2, 3 × 3 × 3, 5 × 5 × 5), and pooling kernel sizes ranged from (1 × 1 × 1, 2 × 2 × 2). Eventually, we set the learning rate at 0.001 and set the dropout after the fully connected layer at 0.2. We employed a convolutional kernel size of 3 × 3 × 3 at each layer, with a 2 × 2 × 2 pooling kernel after each convolutional layer. We set β1 = 0.001, β2 = 0.999; ε = 10⁻⁸.

Each of the three neural networks was trained using the methods of gradient descent and backpropagation. A cross-entropy loss function was used for training, with this loss function selected because of its excellent performance in classification tasks [42 (link)], and a stochastic gradient descent (SGD) optimizer was employed because of its good generalization [43 ]. A cross-entropy loss function was used for FlowNet, but an Adam [44 ] optimization function was deployed for faster convergence. For VaporNet, a Mean Square Error (MSE) loss function was implemented and optimized using Adam. The detailed hyperparameters used for training can be seen in Table 1.
FrameNet was trained first, separately from the other two networks, as it is used to generate the training and offline testing data for the other two networks. The recurrent and classification layers of FlowNet and VaporNet were then trained using sets of this feature data generated by FrameNet.
Training of the models was carried out using a workstation with a 2.3 GHz Intel^® Xeon^® E5-2630 CPU, 128 GB RAM, and an NVIDIA^® Kepler™ K40 M GPU with 12 GB of GPU accelerator memory. All networks were implemented using the PyTorch framework [45 ]. A FrameNet model takes approximately 4 h to train, with VaporNet and FlowNet models being trained in under one hour.