Evaluation of predictive ability of Cholesky factorization of genetic relationship matrix for additive and non-additive genetic effect using Bayesian regularized neural network

Abstract Text: This study aimed to explore the effects of additive and non-additive genetic effects on the prediction from 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 and predictive ability of different nonlinear ANNs and linear models for genetic architectures. Effective number of parameters (γ) and sum of squares error (SSE) in test data sets were used to evaluate the performance of ANNs. Distribution of weights (w_ij) 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 at each genetic architecture. The weights for the linear models were larger and more variable than for the nonlinear network, where distributions were leptokurtic, indicating strong shrinkage towards 0. In conclusion our results showed that: a) inclusion of non-additive effects did not improved 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.

Keywords:  Artificial neural networks, Bayesian regularization, additive and non-additive genetic effects