Deep Kernel and Deep Learning for Genome-Based Prediction of Single Traits in Multienvironment Breeding Trials

Abstract

Deep learning (DL) is a promising method for genomic-enabled prediction. However, the implementation of DL is difficult because many hyperparameters (number of hidden layers, number of neurons, learning rate, number of epochs, batch size, etc.) need to be tuned. For this reason, deep kernel methods, which only require defining the number of layers, may be an attractive alternative. Deep kernel methods emulate DL models with a large number of neurons, but are defined by relatively easily computed covariance matrices. In this research, we compared the genome-based prediction of DL to a deep kernel (arc-cosine kernel, AK), to the commonly used non-additive Gaussian kernel (GK), as well as to the conventional additive genomic best linear unbiased predictor (GBLUP/GB). We used two real wheat data sets for benchmarking these methods. On average, AK and GK outperformed DL and GB. The gain in terms of prediction performance of AK and GK over DL and GB was not large, but AK and GK have the advantage that only one parameter, the number of layers (AK) or the bandwidth parameter (GK), has to be tuned in each method. Furthermore, although AK and GK had similar performance, deep kernel AK is easier to implement than GK, since the parameter "number of layers" is more easily determined than the bandwidth parameter of GK. Comparing AK and DL for the data set of year 2015-2016, the difference in performance of the two methods was bigger, with AK predicting much better than DL. On this data, the optimization of the hyperparameters for DL was difficult and the finally used parameters may have been suboptimal. Our results suggest that AK is a good alternative to DL with the advantage that practically no tuning process is required.

Keywords: artificial neural networks; deep kernel; deep learning; genomic selection; genomic × environment interaction; kernel methods.

Figure 1

Box plot of grain yield (ton/ha) for four environments (BED5IR, FLAT5IR, BED2IR, and FLAT2IR) for (A) year 2016–2017 and (B) year 2015–2016.

Figure 2

Mean squared error of the prediction for year 2016–2017 for single environment (G) and multienvironment (E+G+GE) models with kernels GB, GK, and AK and the deep learning (DL) method for environments (A) BED5IR, (B) FLAT5IR, (C) BED2IR, and (D) FLAT2IR.

Figure 3

Mean squared error of the Prediction for year 2015–2016 for single environment (G) and multienvironment (E+G+GE) models with kernels GB, GK, and AK and the deep learning (DL) method for environments (A) BED5IR, (B) FLAT5IR, (C) BED2IR, and (D) FLAT2IR.