Evaluation of Predictive Ability of Bayesian Regularized Neural Network Using Cholesky Factorization of Genetic Relationship Matrices for Additive and Non-additive Genetic Effects

Abstract

This study aimed to explore the effects of additive and non-additive genetic effects on the prediction of complex traits using Bayesian regularized artificial neural network (BRANN). The data sets were simulated for two hypothetical pedigrees with five different fractions of total genetic variance accounted by additive, additive x additive, and additive x additive x additive genetic effects. A feed forward artificial neural network (ANN) with Bayesian regularization (BR) was used to assess the performance of different nonlinear ANNs and compare their predictive ability with those from linear models under different genetic architectures of phenotypic traits. Effective number of parameters and sum of squares error (SSE) in test data sets were used to evaluate the performance of ANNs. Distribution of weights and correlation between observed and predicted values in the test data set were used to evaluate the predictive ability. There were clear and significant improvements in terms of the predictive ability of linear (equivalent Bayesian ridge regression) and nonlinear models when the proportion of additive genetic variance in total genetic variance ( ) increased. On the other hand, nonlinear models outperformed the linear models across different genetic architectures. The weights for the linear models were larger and more variable than for the nonlinear network, and presented leptokurtic distributions, indicating strong shrinkage towards 0. In conclusion, our results showed that: a) inclusion of non-additive effects did not improve the prediction ability compared to purely additive models, b) The predictive ability of BRANN architectures with nonlinear activation function were substantially larger than the linear models for the scenarios considered.