Approximate Bayesian neural networks in genomic prediction

Genome-wide marker data are used both in phenotypic genome-wide association studies (GWAS) and genome-wide prediction (GWP). Typically, such studies include high-dimensional data with thousands to millions of single nucleotide polymorphisms (SNPs) recorded in hundreds to a few thousands individuals. Different machine-learning approaches have been used in GWAS and GWP effectively, but the use of neural networks (NN) and deep-learning is still scarce. This study presents a NN model for genomic SNP data. We show, using both simulated and real pig data, that regularization is obtained using weight decay and dropout, and results in an approximate Bayesian (ABNN) model that can be used to obtain model averaged posterior predictions. The ABNN model is implemented in mxnet and shown to yield better prediction accuracy than genomic best linear unbiased prediction and Bayesian LASSO. The mean squared error was reduced by at least 6.5% in the simulated data and by at least 1% in the real data. Moreover, by comparing NN of different complexities, our results confirm that a shallow model with one layer, one neuron, one-hot encoding and a linear activation function performs better than more complex models. The ABNN model provides a computationally efficient approach with good prediction performance and in which the weight components can also provide information on the importance of the SNPs. Hence, ABNN is suitable for both GWP and GWAS.