Ensemble of hybrid Bayesian networks for predicting the AMEn of broiler feedstuffs

To adequately meet the nutritional needs of broilers, it is necessary to know the values of apparent metabolizable energy corrected by the nitrogen balance (AMEn) of the feedstuffs. To determine AMEn values, biological assays, feedstuff composition tables, or prediction equations are used as a function of the chemical composition of feedstuffs, the latter using statistical methodologies such as multiple linear regression, neural networks, and Bayesian networks (BN). BN is a statistical and computational methodology that consists of graphical (graph) and probabilistic models of quantitative and/or qualitative variables. Ensembles of BN in the area of broiler nutrition are expected, as there is no research showing their AMEn prediction performance. The purpose of this article is to propose and use ensembles of hybrid Bayesian networks (EHBNs) and obtain prediction equations for the AMEn of feedstuffs used in broiler nutrition from their chemical compositions. We trained 100, 1,000, and 10,000 EHBN, and in this way, empirical distributions were found for the coefficients of the covariates (crude protein, ether extract, mineral matter, and crude fiber). Thus, the mean, median, and mode of these distributions were calculated to build prediction equations for AMEn. It is observed that the method for obtaining the coefficients of the covariates discussed in this article is an unprecedented proposal in the field of broiler nutrition. The data used to obtain the equations were obtained by meta-analysis, and the data for the validation of the equations were obtained from metabolic tests. The proposed equations were evaluated by precision measures such as the mean square error (MSE), mean absolute deviation (MAD), and mean absolute percentage error (MAPE). The best equations for predicting AMEn were derived from the mean or mode coefficients for the 10,000 EHBN results. In conclusion, the methodology used is a good tool to obtain prediction equations for AMEn as a function of the chemical composition of their feedstuffs. The coefficients were found to differ from those found by other methodologies, such as the usual neural network or multiple linear regressions. The field of broiler nutrition contributed with new equations and with a never-applied methodology and differentiated in obtaining its coefficients by empirical distributions.