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Application of Bayesian networks to the prediction of the AMEn: a new methodology in broiler nutrition

Application of Bayesian networks to the prediction of the AMEn: a new methodology in broiler... Application of Bayesian networks to the prediction of the AMEn: a new methodology in broiler nutrition †,1 † † ‡ Tatiane C. Alvarenga, Renato R. Lima, Júlio S. S. Bueno Filho, Sérgio D. Simão, § ‡ ‡ Flávia C. Q. Mariano, Renata R. Alvarenga, and Paulo B. Rodrigues † ‡ Department of Statistics, Federal University of Lavras, 37200-000 Lavras, Minas Gerais, Brazil; Department of Animal Science, Federal University of Lavras, 37200-000 Lavras, Minas Gerais, Brazil; and Department of Science and Technology, Federal University of São Paulo, 12231-280 São José dos Campos, São Paulo, Brazil ABSTRACT:  Designing balanced rations for the random variables. BN uses machine learning broilers depends on precise knowledge of nitro- algorithms, being a methodology of artificial in- gen-corrected apparent metabolizable energy telligence. The bnlearn package in R software was (AMEn) and the chemical composition of the used to predict AMEn from the following covar- feedstuffs. The equations that include the meas- iates: crude protein, crude fiber, ethereal extract, urements of the chemical composition of the mineral matter, as well as food category, i.e., en- feedstuff can be used in the prediction of AMEn. ergy (corn, corn by-products, and others) or pro- In the literature, there are studies that obtained tein (soybean, soy by-products, and others) and prediction equations through multiple regression, the type of animal (chick or cockerel). The data meta-analysis, and neural networks. However, come from 568 feeding experiments carried out other statistical methodologies with promising in Brazil. Additional data from metabolic experi- potential can be used to obtain better predic- ments were obtained from the Federal University tions of energy values. The objective of the pre- of Lavras (UFLA) – Lavras, Minas Gerais, Brazil. sent study was to propose and evaluate the use of The model with the highest accuracy (mean Bayesian networks (BN) to the prediction of the squared error = 66529.8 and multiple coefficients AMEn values of energy and protein feedstuffs of of determination = 0.87) was fitted with the max- vegetable origin used in the formulation of broiler min hill climbing algorithm (MMHC) using 80% rations. In addition, verify that the predictions of and 20% of the data for training and test sets, re- energy values using this methodology are the most spectively. The accuracy of the models was evalu- accurate and, consequently, are recommended to ated based on their values of mean squared error, Animal Science professionals area for the prep- mean absolute deviation, and mean absolute per- aration of balanced feeds. BN are models that centage error. The equations proposed by a new consist of graphical and probabilistic represen- methodology in avian nutrition can be used by the tations of conditional and joint distributions of broiler industry in the determination of rations. Key words: graph models, max-min hill-climbing algorithm, metabolic energy, probability distributions © The Author(s) 2021. Published by Oxford University Press on behalf of the American Society of Animal Science. This is an Open Access article distributed under the terms of the Creative Commons Attribution License (http://creativecommons.org/licenses/by/4.0/), which permits unrestricted reuse, distribu- tion, and reproduction in any medium, provided the original work is properly cited. Transl. Anim. Sci. 2021.5:1-11 doi: 10.1093/tas/txaa215 Corresponding author: tatianecarvalhoalvarenga@gmail. com Received August 28, 2020. Accepted January 20, 2021. 1 Alvarenga et al. INTRODUCTION approaches have not yet been applied to examine broiler nutrition. Production of low-cost high protein chicken To find more accurate results, BN are used to pre- meat through intensively reared broiler chickens has dict the AMEn according to the chemical compos- high economic importance at national and inter- ition of feedstuffs, BN are graphical models, which national levels. The need to formulate diets that are consist of the graphical representation (graph) and increasingly adequate to the demands of broilers is probabilistic (conditional and joint probability necessary for the production system. The productive distributions) of the variables (Scutari and Denis, efficiency of birds is directly related to the adequate 2015; Koller and Friedman, 2009; Lauritzen and supply of dietary energy, which, in turn, depends Spiegelhalter, 1988; Spirtes et al., 2000). In the ap- on the nitrogen-corrected apparent metabolizable plied areas, mainly Agriculture, there are still very energy (AMEn) of the foods. However, one of the few publications, however, Bayesian networks are highest problems actually is the real knowledge of an unprecedented line of research in poultry nutri- the energy composition of feedstuffs, which directly tion and that can be studied by researchers who are interferes with the energy levels of the rations and, interested in predicting the values of metabolizable consequently, on the nutrient balance of the same. energy (Alvarenga et al., 2020). Currently, several methods are available to assess Among the benefits of using BN are: 1) redu- the energy composition of feedstuffs and, often, cing the costs of in vivo trials to determine AMEn discrepant results are observed. values, 2)  Enhancing the accuracy of predictions The energy values feedstuffs can be obtained of AMEn, 3)  Reducing the variability in tabu- in biological tests, with the execution is time-con- lated values for AMEn, 4)  Expanding the use of suming and of high cost, or by the composition Bayesian networks to areas where machine learn- tables of the feedstuffs (Albino, 1980). Another ing and related methods are starting to be em- way of obtaining the values of AMEn is the pre- ployed, and 5) Capturing conditional dependency diction equations established according to the among random variables in, a broader sense than chemical composition of the feedstuffs, which traditional methods can achieve. In this paper, the is usually easy and quick to obtain (Rodrigues proposal using and evaluate BN, a new method- et  al., 2001, 2002). Zhao et  al. (2008) developed ology in broiler nutrition, to obtain prediction prediction equations using multiple regression equations for AMEn from a meta-analysis of en- to estimate the energy values using the chemical ergy and protein feedstuffs used for determining composition of the feedstuffs; however, their re- broiler rations. sults have been inconsistent or applicable only to one feedstuff group (Alvarenga et  al., 2011). MATERIALS AND METHODS Nascimento et  al. (2009, 2011) and Mariano et  al. (2012) used meta-analyses to better predict Data AMEn. Perai et  al. (2010), Ahmadi et  al. (2007, 2008), and Mariano et al. (2013) used neural net- To obtain the equations via BN, data from the works (NN), and the latter used a larger number meta-analysis were used, referring to the experiments of foods and in vivo trials. conducted in Brazil in the period from 1967 to 2007, NN and Bayesian networks (BN) are suitable resulting in 568 experiments (Nascimento et al., 2009; tools for prediction due to their superior ability to Nascimento et al., 2011), among them which refer to capture and express complex dependencies on covar- the values of AMEn and chemical composition of iates and response variables (Bishop, 2006; Gianola energy (n = 370) and protein (n = 198) feedstuffs, of et al., 2011). BN has been used in medicine, genetics, vegetable origin, commonly used in the formulation robotics, economics, demography forensics, educa- of broiler diets. The data used to validate the pro- tion, human behavior, industrial applications, spe- posed equations were obtained by Alvarenga et  al. cies conservation, and mining (Pourret et al., 2008). (2011). These data come from two in vivo trials to Mariano et al. (2013) focused on predicting AMEn determine the energy value of protein and energy using a NN. Felipe et al. (2015) indicated the pos- feedstuffs, with growing chicks (traditional method sibility of using BN in Animal Science; however, of total excreta collection), respectively in February/ the previous use of BN for Animal Science papers March and July 2008. The trials were carried out in is not restricted to breeding and genomic selection Lavras, state of Minas Gerais, Brazil (21° 14′ 45″S, (Gianola et  al., 2011; Morota et  al., 2013). These 44° 59′ 59″W, 919 m a.s.l.) at the Federal University of Translate basic science to industry innovation Application of Bayesian networks to the prediction of the AMEn Lavras (Alvarenga et al., 2011). For both data used to The variables used to learn the DAG were CP, obtain and validate the equations via BN, the values EE, ash, CF, food category (1 – energy concentrate, of the response variable – AMEn, were estimated with ingredients: 1.1 – corn, 1.2 – corn by-products, by the covariables; crude protein (CP), ether extract 1.3 – others, 2 – protein concentrate, with ingredi- (EE), ash, crude fiber (CF), classification of the feed- ents 2.1 – soybean meal, 2 – soybean by-products, stuffs category (1  – energy concentrate, 2  – protein 3 – others) and type of animal used in the bioassay concentrate), specification of the ingredient in the with two levels: 1 – chicks, 2 – cocks). category (1 – energy concentrate): (1 – corn, 2 – corn The initial step for a BN is to have an algorithm by-products, 3 – others), the ingredient specification to learn the basic graph structure (Scutari, 2010). The in the category (2 – protein concentrate): (1 – soybean, next step is to learn the implicit local distributions for 2 – soybean by-products, 3 – others) and the type of this given structure (Scutari et al., 2014). Nagarajan animal used in the bioassay (1 – chicks, 2 – cockerels). et  al. (2013) discussed three algorithms for learning network structure. The first, constraint-based al- gorithms, are based on conditional independence tests to infer the arrow direction between nodes. The Prediction Models second, score-based algorithms, select among all possible structures the BN with the highest quality, The structure of a directed acyclic graph (DAG) scored by probability-based measures such as Akaike that represents the BN, the nodes are connected, information criterion (AIC) or Bayesian (Schwarz) and all the arrows are directed without cycling (the information criterion (BIC). The third type, hybrid arrow cannot return to the same node). The DAG algorithms, combine ideas of both. is a directional, connected, and acyclic graph. We The bnlearn package (Scutari, 2010; R Core can observe that the neighbors of a node are the Team, 2020) for R implements the following con- adjacent nodes, which are either parents or sons straint-based algorithms: Grow-Shrink (GS) incre- (Nagarajan et al., 2013). mental association Markov blanket (IAMB) fast Most algorithms used to find graph structure incremental association (Fast-IAMB) interleaved depend on topology because causal relations are as- incremental association (Inter-IAMB); max-min sociated with precedence for conditioning. Some of parents and children (MMPC); semi-interleaved the algorithms use a Markov blanket to the target Hiton-PC (SI-HITON-PC). Each can be used for con- node. The nodes that separate the target node ditional independence tests (Nagarajan et al., 2013). from the remaining structure are parent, child, and The score-based algorithms also implemented nodes that share a child with the target node. For are hill climbing (HC) (Margaritis, 2003) and Tabu prediction, only those variables would be relevant search (TABU). The scoring function can be AIC, to modeling (Koski and Noble, 2009; Scutari and BIC, or others. Hybrid algorithms include max- Denis, 2015). min hill climbing (MMHC) (Tsamardinos et  al., A BN is a graphic representation of a joint prob- 2006) and general 2-phase restricted maximiza- ability distribution (or joint density, Margaritis, tion (RSMAX2). MMHC uses constraint-based 2003). It can be described by the structure of a MMPC to search graph skeletons, estimating DAG. Factorization of the BN, as described by parent–child Markov coverage for each pair of equation 1, is a chain of products of conditional variables in BN. To determine directionality, a probabilities, as one node, given its parents, is con- score-based HC algorithm is used. A more general ditionally independent of its non-descendants implementation of MMHC is performed by the (Pearl, 1988; Koski and Noble, 2009; Scutari and RSMAX2 algorithm. It can use any combination Denis, 2015). This is a convenient representation of constraint-based and score-based algorithms of the joint probability distribution, allowing for (Scutari and Denis, 2015). an inference on the desired research questions. The AMEn predictions were performed using a hy- joint probability distribution is defined as: brid BN with continuous and discrete variables in the same fashion as a multiple linear regression P (X , X , ...X )= P (X | Pa ) , 1 2 p i i (1) i=1 model (Koski and Noble, 2009). To envision the where p is the number of variables, i is the counter process, consider a set X of random variables, par- of samples and n is the number of observations. titioned into two subsets: X for discrete variables For the case of discrete and continuous nodes in and X for continuous variables. The joint prob- which Pa are the parents of X . ability distribution for P(X) can be factorized as: i i Translate basic science to industry innovation Alvarenga et al. a difference of approximately 1%, and RSMAX24 P(X)= P(X , X ) D C (bias = −48.10), presenting a difference of approxi- mately 10% (Figure 1). = P(X |Pa ) P(X |Pa , Pa ), i D j D C i ∈ D i ∈ C Table  1 summarizes the training (80% of the data) and testing sets. The DAG with the best-fit- in which Pa and Pa are joint probabilities for each D C ting yield by the MMHC learning algorithm is of the subsets, respectively. depicted in Figure  2, according to the result of The term P(X ||Pa , Pa ) brings both j D C i ∈ C the BN model presented in Figure 1. It has eight discrete and continuous parent variables that can nodes and 11 arrows in a Markov blanket with be locally represented by linear regressions with seven nodes. The best learning algorithm was parameters from discrete parents. This is equivalent MMHC, i.e., using a constraint-based MMPC to writing: algorithm with conditional independence testing using mutual information. The scored-based (X |Pa , Pa ) ∼ (Nμ , σ ), in which j D C j X |Pa j D method was hill climbing, using the BIC cri- μ =β + β X . 0,X |Pa i,X |Pa |Pa j D j D j c terion. The number of tests used to learn the best DAG was 165. Thus, for the prediction of AMEn, μ refers The joint distribution represented in Figure  2 to the intercept for each level of the discrete vari- can be written as P(AMEn, CP, EE, ash, CF, able's combination (categories for food and animal Category, Ingredient, Animal)  =  P(EE) · P(CF) · types). β and β are the intercept and 0,X |Pa i,X |Pa j D j D P(Category) · P(Animal) · P(CP | Category) · coefficients of the multivariate linear regression, P(Ingredient | Category) · P(ash | CP:CF) · P(AMEn | respectively. X represents the variables CP, ash, i|Pa C CP : EE : ash : CF : Category : Ingredient : Animal). EE, and CF. This means that EE, CF, Category, and Animal are The original data were described by Mariano not dependent on the other variables; however, CP et al. (2013). For this study, the data were randomly is dependent on Category, and ash is dependent by partitioned into a training set (80% of the sample CP and CF. The response variable AMEn is condi- size) and a testing set (using the remaining data). tionally dependent on all studied variables. Thus, The training set was used to search for a best-fitted there are 12 regression equations to AMEn, each DAG. Equations derived from the joint posterior coming from a different combination of levels for were compared to a metabolic data assay from the discrete variables. Each separate prediction Alvarenga et  al. (2011). The parameters used for equation uses only levels of quantitative variables the validation of the model were simple correlation (CP, CF, ash, and EE). The proposed prediction coefficient (r), multiple coefficients of determin- equations and their coefficients are presented in ation (R ), mean squared error (MSE), mean abso- Table 2. lute deviation (MAD), mean absolute percentage The observed values (Alvarenga et  al., 2011) error (MAPE), bias (bias) (Mariano et  al., 2014) and predicted (the result of the equations proposed and prediction mean squared error (PMSE) (Felipe by the BN) are plotted in the graph of Figure  4, et al., 2015). and the statistics used in the assessment of the ad- justment are shown in Table  3. The data used in this validation process coming from in vivo trials. RESULTS Regarding the adjustments, the best evaluations Different hybrid structures learning algo- of the statistics were MSE  =  9051.84 for corn rithms were evaluated, obtained from randomi- by-products, MAD  =  81.66, MAPE  =  2.16 and zations in the training data sets (80%, 75%, and bias  =  −64.51 for other protein foods. The com- 70%) and test (20%, 25%, and 30%). The best result parison between the predictions obtained in this re- obtained was through the MMHC learning algo- search with the results of neural networks is shown rithm (Figure  1) with the randomization of 80% in Table 4. of the learning data compared to the sets of 70% and 75%. The fit statistics were: r = 0.94, R  = 0.87, DISCUSSION MSE  =  66529.8, MAD  =  191.2, MAPE  =  7.52, bias  =  −43.09 and PMSE  =  257.93. The selected This study aimed to propose and evaluate the algorithm MMHC provided better statistics, ex- use of BN and to find equations to the predic- cept for RSMAX21 learning (MAPE = 7.45), with tion of the AMEn values of energy and protein Translate basic science to industry innovation Application of Bayesian networks to the prediction of the AMEn Figure 1. Evaluation of the performance and accuracy of the models for nitrogen-corrected apparent metabolizable energy (AMEn) estimated using Bayesian networks. r: correlation coefficient; R : multiple coefficient of determination; MMHC: max-min hill climbing; RSMAX2: 2-phase restricted maximization; Learning respectively, constraint-based and score-based: 1 – semi-interleaved Hiton Parents and Children (SI.HITON.PC) and hill climbing (HC); 2 – interleaved incremental association (INTER.IAMB) and HC; 3 – fast incremental association (FAST.IAMB) and HC; 4 – incremental association Markov blanket (IAMB) and HC; 5 – Grow-Shrink (GS) and HC. feedstuffs of vegetable origin used in the formula- processing methods and the lack of standardiza- tion of broiler rations. It is known, animal foods tion of national products. have quite different chemical compositions from From this objective used machine learning vegetables, they have no fiber, soluble carbohy- algorithms to learn the graphic structure of the drates are extremely low, they have a high-fat network as well as the probabilistic relationships content, and others. This variation in chemical between the variables, it was possible to prove and energy composition is even greater when it the functionalities of this new promising meth- comes to animal by-products, due to the different odology in broiler nutrition. The algorithm that Translate basic science to industry innovation Alvarenga et al. Table 1. Summaries for variables in the training (80%) and testing (20%) sets. Original data from Nascimento et al. (2009, 2011) Statistics AMEn (kcal/kg) CP (%) EE (%) Ash (%) CF (%) Training set Minimum 1,170 1.470 0.030 0.300 0.020 Median 3,501 14.130 3.480 2.110 3.020 Mean 3,176 23.360 4.872 3.560 4.928 Maximum 4,386 71.440 26.210 12.610 26.500 Testing set Minimum 1,148 1.700 0.030 0.560 0.320 Median 3,275 15.270 3.150 3.010 3.985 Mean 3,050 23.360 4.135 3.826 5.683 Maximum 4,160 68.810 25.540 11.050 27.630 AMEn: nitrogen-corrected apparent metabolizable energy; CP: crude protein; EE: ether extract; CF: crude fiber. composition of food in the ration considered (for some discussion on this, please refer to Moreira et al. (2002) and Brunelli et al. (2006). A metabolic trial was performed in chicks only. Thus, equations for cocks were not validated. Predictions and real- izations based on data from (Alvarenga et al., 2011) are plotted in Figure  4. AMEn values are close to the identity line, indicating good accuracy of the proposed equations. Equations proposed by the BN and those from the NN (Mariano et al., 2013) were validated with these in vivo trials with chicks (Alvarenga Figure 2. Directed acyclic graph (DAG) for study variables. et al., 2011). The results can be found in Table  4. Predicted energy values that are closer to the real- showed the best performance was MMHC as the ized description are described in boldface. From literature mentions in Felipe et al. (2015). It was this table, we conclude that the BN predicted closer observed that the equations differed in the values in 20 out of 36 cases and that the NN was closer of the parameters due to countless DAG options in the other 16 cases. The equations for obtain- (Koski and Noble, 2009). However, according ing the energy values of corn, corn by-products, to the lowest values of errors found in the val- and other protein by means of BN had a better idation using the test data (20%) in the Bayesian performance compared to the estimates obtained network model obtained the equations available by NN (Mariano et  al., 2013). These equations in Table  3. In addition to the validation from (Table  2) are for the corn (AMEn  =  3658.16  − the test data, the validation in the data of meta- 2.41 CP − 11.25 EE + 83.41 ash + 16.76 CF), bolic tests, only for chicks' equations, confirmed corn by-products (AMEn  =  4209.57  − 34.56 CP the efficiency of the obtained equations being + 32.84 EE − 25.15 ash − 142.57 CF) and others indicated for the elaboration of balanced diets protein (AMEn = 2327.69 + 24.23 CP + 77.72 EE for broilers. The results continue to be proven − 167.06 ash − 22.28 CF), the BN was remark- through the predicted and realized values for ably better, but for soybeans, the opposite result AMEn, as shown below. was found. For comparison, in Nascimento et  al. (2009), It is known that the common statistical ap- Mariano et  al. (2012), and Mariano et  al. (2013), proach to obtain the AMEn values is that of the best architecture achieved R  = 0.83, 0.74, and ordinary least squares of multiple regression al- 0.86, respectively. In this research, the BN model though there are few types of research of machine managed to explain 87% of the AMEn variation. learning found for this purpose, these being NN. Predicted and realized values for AMEn are de- However, the authors advocate the use of com- picted in Figure  3. Errors in prediction, such as putational methodologies, such as BN to predict those we found, are attributed to the chemical AMEn and demonstrate that the use of BN for Translate basic science to industry innovation Application of Bayesian networks to the prediction of the AMEn Table 2.  Prediction equations for nitrogen-corrected apparent metabolizable energy (AMEn) estimated using Bayesian networks AMEn (kcal/kg) Coefficients Category Animals Type food Intercept CP EE Ash CF Energy Chicks Corn 3658.16 −2.41 −11.25 +83.41 + 16.76 Corn by-products 4209.57 −34.56 +32.84 −25.15 −142.57 Other Corn products 4335.88 −50.91 +35.40 −67.35 −87.06 Protein Chicks Soybean 3684.83 −19.84 −71.15 +18.14 −8.93 Soybean by-products 2951.05 +0.09 +37.96 +5.04 −17.60 Other soybean products 2327.69 +24.23 +77.72 −167.06 −22.28 Energy Cocks Corn 3321.82 +51.31 + 39.42 −377.11 +113.92 Corn by-products 4716.45 −227.63 +144.47 - - Other Corn products 4133.39 −89.45 +100.32 −5.50 −96.37 Protein Cocks Soybean 4143.45 −3.18 −43.45 −213.55 +6.71 Soybean by-products 518.54 +26.25 +47.10 +184.42 +69.0 Other soybean products 6033.28 −15.02 −105.81 −556.50 +91.23 AMEn: nitrogen-corrected apparent metabolizable energy; CP: crude protein; EE: ether extract; CF: crude fiber. Table 3. Accuracy of prediction equations using data from in vivo trials (Alvarenga et al., 2011) Equation MSE MAD MAPE bias Corn 27314.73 143.28 3.98 −104.56 Soybean 71737.46 254.97 10.74 −254.97 Corn by-products 9051.84 82.85 3.44 81.26 Soybean by-products 131069.90 299.25 10.84 −227.12 Other energy food 64831.12 213.58 7.42 −184.02 Other protein food 16473.99 81.66 2.16 −64.51 MSE: mean squared error; MAD: mean absolute deviation; MAPE: mean absolute percentage error; PMSE: prediction mean squared error. between random variables in a broader sense and of relationships between discrete and continuous variables simultaneously in the model. Especially in the era of information, that computational meth- odologies have been experiencing have been more indicated by the listed properties. Emphasizes, to the AMEn values determined with chicks are found in Table 4, and that the values of AMEn for corn with BN (3,701.423 kcal/kg), NN (3,682.410 kcal/kg) and according to Rodrigues et  al. (2001) using ordinary least squares of multiple regression, for the same feedstuff, the AMEn value was 3,699 kcal/kg, which declares the promising use of BN in bringing these values closer to the methods estab- lished by the literature. According to the results found in this research, indicating good accuracy of the proposed equations via new machine learning methodology in poultry Figure 3. Relationship between the observed and predicted for nitrogen-corrected apparent metabolizable energy (AMEn) values of nutrition, authors in the literature show superiority different feedstuffs using test data. in non-traditional models in the prediction of en- ergy values. Ahmadi et al. (2007, 2008), Perai et al. (2010), and Mariano et  al. (2013), demonstrated areas where machine learning and related methods that the NN model outperformed the traditional are beginning to be employed; it has the benefits models or accurately predicted performance based that traditional methods cannot achieve, espe- on dietary metabolizable energy. cially the BN. BN capture conditional dependence Translate basic science to industry innovation Alvarenga et al. Table 4.  Energy levels predicted from Bayesian networks (BN) and neural networks (NN, MARIANO et al., 2013) and bias found to result in vivo trials with chicks (Alvarenga et al., 2011) Prediction 1 2 Food sample Alvarenga et al. (2011) BN NN BN NN Corn 3,747 3701.423 3682.410 −45.577 −64.590 3,699 3718.852 3749.960 19.852 50.960 3,813 3723.068 3691.330 −89.931 −121.670 3,572 3783.902 3738.140 211.902 166.140 Soybean 2,373 2524.779 2532.720 151.778 159.720 2,326 2703.916 2505.290 377.916 179.290 2,355 2641.964 2500.180 286.963 145.180 2,396 2677.614 2498.430 281.613 102.430 2,478 2654.566 2513.110 176.566 35.110 Corn by-products 3,624 3628.778 3841.340 4.777 217.340 3,676 3573.398 3803.920 −102.601 127.920 2,184 2086.068 1931.880 −97.432 −251.620 Soybean by-products 3,159 3214.654 2527.200 55.653 −631.800 3,779 3661.684 3580.770 −117.315 −198.230 2,809 2992.756 2431.950 183.756 −377.050 3,772 3938.579 3918.470 166.578 146.470 2,387 2935.302 2342.300 548.302 −44.700 3,971 3753.066 3519.050 −217.934 −451.950 3,288 3617.693 3580.420 329.693 292.420 2,314 2935.302 2351.800 621.302 37.800 3,818 3753.066 3519.050 −64.934 −298.950 3,173 3617.693 3580.420 444.693 407.420 2,339 2935.302 2351.800 596.302 12.800 3,793 3753.066 3519.050 −39.934 −273.950 3,330 3617.693 3580.420 287.693 250.420 2,309 2935.302 2351.800 626.302 42.800 3,890 3753.066 3519.050 −136.934 −370.950 3,267 3617.693 3580.420 350.693 313.420 Energy 3,598 3569.507 3498.87 −28.492 −99.130 3,529 3515.214 3505.98 −13.786 −23.020 3,862 3771.244 3537.47 −90.756 −324.530 2,682 2839.403 2798.87 157.403 116.870 1,941 2342.840 1939.12 401.840 −1.880 3,362 3669.743 3512.24 307.492 149.990 Protein 3,934 3957.047 4049.53 23.046 115.53 3,904 3979.133 4072.38 74.880 168.13 1 2 BN: Prediction BN – Observed by Alvarenga et al. (2011); NN: Prediction NN – Observed by Alvarenga et al. (2011); Prediction NN: Obtained by Mariano et al. (2013). The results demonstrated in Perai et al. (2010) et  al. (2015) that reinforces innovations in estima- that the NN model predicts the nitrogen-corrected tion methods are necessary to obtain better esti- true metabolizable energy (TMEn) values of meat mates of the energy values of feed for broilers. and bone meat samples based on their chemical Felipe et al. (2015) compared different meth- composition outperformed the traditional models. odologies to predict total egg production in Accurately predicted metabolizable energy, methio- quails from different strains. The model with nine, and lysine using NN (Ahmadi et  al., 2007) the combination of the BN and NN resulted in as well, predicted the TMEn values of feather and a better performance to predict total egg pro- poultry offal meal based on their chemical compos- duction. Töpner et  al. (2017) used BN in a corn ition (Ahmadi et al., 2008) are corroborant with the experiment to analyze the relationships between research and application of machine learning meth- characteristics at genomic and residual levels. ods in poultry nutrition. In addition to Alvarenga The BN obtained in this were classified in terms Translate basic science to industry innovation Application of Bayesian networks to the prediction of the AMEn Figure 4. Predicted and realized values for nitrogen-corrected apparent metabolizable energy (AMEn) of different feedstuffs: corn (A), soy- bean (B), corn by-products (C), soybean by-products (D), other energy feeds (E), and other protein feeds (F) using data from chick in vivo trials (Alvarenga et al., 2011). of adjustability and predictive ability through fiber and neutral detergent fiber; missing vari- structural equations. They concluded that when ables or incomplete in the set data used and illustrating the connections of characteristics evaluate the effect of these values in the AMEn concerning their genomic and residual nature, values. Increase the representativeness of the vari- they become clearer, which makes it useful for ables through the Bayesian Fuzzy Evolutionary predicting multiple traits and indirect selection. Networks. They confirm the potential of the BN in health sciences, economics, agriculture among others, CONCLUSIONS that previously were unprecedented in the field of broiler nutrition. After all, Alvarenga et  al. (2015) have shown In future studies, the dataset including other that these prediction equations are important for experimental studies will be updated. It will be increasing the accuracy of diet formulation, al- to develop an innovative technological product lowing producers to correct energy values based on based on the BN methodological proposal, with the variations in the chemical composition of feed- the objective of obtaining prediction equations to stuffs. In conclusion, the MMHC algorithm and a assist broiler nutritionists. Research the behavior partition with 80% of data to the training set seems of AMEn values in different probability distribu- to perform better in determining the DAG and re- tions for the variables, to obtain prediction equa- spective BN. The BN was accurate and as good tions. Impute by BN the values of acid detergent a method as the previous NN, depending on the Translate basic science to industry innovation Alvarenga et al. in European quails based on earlier expressed phenotypes. food category. The predicting equations estimated Poult. Sci. 94:772–780. doi:10.3382/ps/pev031 from a BN can be used to calculate energy levels Gianola,  D., H.  Okut, K.  A.  Weigel, and G.  J.  Rosa. 2011. for broilers. Predicting complex quantitative traits with Bayesian neural networks: a case study with Jersey cows and wheat. ACKNOWLEDGMENTS BMC Genet. 12:87. doi:10.1186/1471-2156-12-87 Koller,  D., and N.  Friedman. 2009. Probabilistic graphical Thanks to the Brazilian funding agencies models: principles and techniques. Cambridge: MIT Coordenação de Aperfeiçoamento de Pessoal de Press; p. 1233 Nível Superior (CAPES) and Fundação de Amparo Koski, T., and J. M. Noble. 2009. Bayesian networks: an intro- duction. Chichester: John Wiley & Sons Ltd; p. 347. à Pesquisa do Estado de Minas Gerais (FAPEMIG) Lauritzen, S. L., and D. J. Spiegelhalter. 1988. Local computa- for the partial support of this work. tions with probabilities on graphical structures and their Conflict of interest statement. No conflict of applications to expert systems. J. R. Stat. Soc. 50:157–224. interest, financial, or otherwise are declared by the http://www.jstor.com/stable/2345762 authors. Margaritis, D. 2003. Learning bayesian network model struc- ture from data [PhD thesis, Doctor of Philosophy]. Pittsburgh (PA): Carnegie Mellon University. LITERATURE CITED Mariano,  F.  C.  M.  Q., R.  R.  Lima, R.  R.  Alvarenga, P.  B.  Rodrigues, and W.  S.  Lacerda. 2014. Neural net- Ahmadi, H., A. Golian, M. Mottaghitalab, and N. Nariman- work committee to predict the AMEn of poultry feed- Zadeh. 2008. Prediction model for true metabolizable en- stuffs. Neural Comput. Appl. 25:1903–1911. doi:10.1007/ ergy of feather meal and poultry offal meal using group s00521-014-1680-3 method of data handling-type neural network. Poult. Sci. Mariano,  F.  C.  M.  Q., R.  R.  Lima, P.  B.  Rodrigues, 87:1909–1912. doi:10.3382/ps.2007-00507 R.  R.  Alvarenga, and G.  A.  J.  Nascimento. 2012. Ahmadi,  H.  A., M.  Mottaghitalab, and N.  Nariman-Zadeh. Equações de predição de valores energéticos de ali- 2007. Group method of data handling-type neural net- mentos obtidas utilizando meta-análise e componentes work prediction of broiler performance based on dietary principais. Ciênc. Rural. 42:1634–1640. doi:10.1590/ metabolizable energy, methionine, and lysine. J. Appl. S0103-84782012005000061 Poult. Res. 16:494–501. doi:10.3382/japr.2006-00074 Mariano,  F .  C.  M.  Q., C.  A.  Paixão, R.  R.  Lima, R.  R.  Alvarenga, Alvarenga, T. C., R. R. Lima, J. S. S. B. Filho, P. B. Rodrigues, P. B. Rodrigues, and G. A. J. Nascimento. 2013. Prediction R.  R.  Alvarenga, and F.  C.  M.  Q.  Mariano. 2020. of the energy values of feedstuffs for broilers using Inovação na predição dos valores energéticos de alimen- meta-analysis and neural networks. Animal 7:1440–1445. tos para aves: um estudo bibliométrico sobre as redes doi:10.1017/S175173111300071 bayesianas. Rev. Bras. Biom. 38:274–289. doi:10.28951/ Moreira,  I., C.  R.  Ribeiro, A.  C.  Furlan, C.  Scapinello, and rbb.v38i3.429 M.  Kutschenko. 2002. Utilization of defatted maize Alvarenga,  R.  R., P.  B.  Rodrigues, M.  G.  Zangeronimo, germ meal on growing-finishing pigs feeding digestibility R.  T.  F.  Freitas, R.  R.  Lima, A.  G.  Bertechini, and and performance. Braz. J.  Anim. Sci. 31:2238–2246. E.  J.  Fassani. 2011. Energetic values of feedstuffs for doi:10.1590/S1516-35982002000900012 broilers determined with in vivo assays and predic- Morota,  G., K.  Masanori, G.  J.  M.  Rosa, A.  W.  Kent, and tion equations. Anim. Feed Sci. Technol. 168:257–266. D.  Gianola. 2013. Predicting complex traits using a di doi:10.1016/j.anifeedsci.2011.04.092 usion kernel on genetic markers with an application to Alvarenga,  R.  R., P.  B.  Rodrigues, M.  G.  Zangeronimo, dairy cattle and wheat data. Genet. Sel. Evol. 45:1–15. E. C. Oliveira, F. C. Mariano, E. M. Lima, A. A. Garcia, doi:10.1186/1297-9686-45-17 Jr, L. P. Naves, and N. B. Nardelli. 2015. Validation of Nagarajan, R., M. Scutari, S. Lèbre. 2013. Bayesian networks prediction equations of energy values of a single in- in R with applications in systems biology. New York: gredient or their combinations in male broilers. Asian- Springer; p. 157. Australas. J.  Anim. Sci. 28:1335–1344. doi:10.5713/ Nascimento,  G.  A.  J., P.  B.  Rodrigues, R.  T.  F.  Freitas, ajas.14.0339 A. G. Bertechini, R. R. Lima, and L. E. A. Pucci. 2009. Albino,  L.  F.  T. 1980. Determinação de valores de energia Equações de predição para estimar os valores energéticos metabolizável e triptofano de alguns alimentos para de alimentos concentrados de origem vegetal para aves aves em diferentes idades. 55f. Dissertação (Mestrado utilizando a metanálise. Revis. Bras. Zootec. 38:1265– em Zootecnia). Viçosa (MG): Universidade Federal de 1271. doi:10.1590/S1516-35982009000700015 Viçosa. Nascimento,  G.  A.  J., P.  B.  Rodrigues, R.  T.  F.  Freitas, Bishop, C. M. 2006. Pattern recognition and machine learning. R.  V.  Reis  Neto, R.  R.  Lima, and I.  B.  Allamann. 2011. New York: Springer; p. 738. Equações de predição para estimar valores da energia Brunelli, S. R., J. W. Pinheiro, C. A. Silva, N. A. N. Fonseca, metabolizável de alimentos concentrados energéti- D.  D.  Oliveira, G.  E.  Cunha, and L.  F.  A.  Souza. 2006. cos para aves utilizando meta-análise. Arq. Bras. Feeding increasing defatted maize germ meal levels Med. Vet. Zootec. 63:222–230. doi:10.1590/S0102- to broiler chickens. Braz. J.  Anim. Sci. 35:1349–1358. doi:10.1590/S1516-35982006000500014 Pearl,  J. 1988. Probabilistic reasoning in intelligent systems: Felipe, V. P., M. A. Silva, B. D. Valente, and G. J. Rosa. 2015. networks of plausible inference. San Francisco: Editor Using multiple regression, Bayesian networks and artifi- Morgan Kaufmann; p. 552. cial neural networks for prediction of total egg production Translate basic science to industry innovation Application of Bayesian networks to the prediction of the AMEn Perai,  A.  H., H.  Nassiri  Moghaddam, S.  Asadpour, Scutari,  M. 2010. Learning bayesian networks with the J. Bahrampour, and G. Mansoori. 2010. A comparison of bnlearn R package. J. Stat. Softw. 35:1–21. doi:10.18637/ artificial neural networks with other statistical approaches jss.v035.i03 for the prediction of true metabolizable energy of meat Scutari, M., and J. B. Denis. 2015. Bayesian networks with ex- and bone meal. Poult. Sci. 89:1562–1568. doi:10.3382/ amples in R. New York: Taylor & Francis Group; p. 221. ps.2010-00639. Scutari,  M., P.  Howell, D.  J.  Balding, and I.  Mackay. 2014. Pourret, O., P. Naim, and B. Marcot. 2008. Bayesian networks: Multiple quantitative trait analysis using bayesian a practical guide to applications. The Atrium, Southern networks. Genetics 198:129–137. doi:10.1534/genetics. Gate, Chichester: John Wiley Sons Ltd. 114.165704 R Core Team (2020). R: a language and environment for stat- Spirtes, P., C. Glymour, and R. Scheines. 2000. Causation, pre- istical computing. Vienna, Austria: R Foundation for diction and search. 2nd ed. Cambridge (MA): The MIT Statistical Computing. Disponível em: http://www.R-pro- Press. ject.org/. Acesso em 15 de maio de 2020. Töpner,  K., G.  J.  M.  Rosa, D.  Gianola, and C.  C.  Schön. Rodrigues, P. B., H. S. Rostagno, L. F. T. Albino, P. C. Gomes, 2017. Bayesian networks illustrate genomic and residual W.  A.  Barboza, and R.  T.  Santana. 2001. Valores trait connections in Maize (Zea mays L.). G3 (Bethesda). energéticos do milheto, do milho e subprodutos do 7:2779–2789. doi:10.1534/g3.117.044263 milho, determinados com frangos de corte e galos adul- Tsamardinos,  I., L.  E.  Brown, and C.  F.  Aliferis. 2006. The tos. Revis. Bras. Zootec.. 30:1767–1778. doi:10.1590/ maxmin hill-climbing Bayesian network structure learn- S1516-35982001000700015 ing algorithm. Mach. Learn. 65:31–78. doi:10.1007/ Rodrigues,  P.  B., H.  S.  Rostagno, and L.  F.  T.  Albino 2002. s10994-006-6889-7 Valores energéticos da soja e subprodutos da soja, Zhao,  F., H.  F.  Zhang, S.  S.  Hou, and Z.  Y.  Zhang. 2008. determinados com frangos de corte e galos adultos. Predicting metabolizable energy of normal corn from its Revis. Bras. Zootec. 31:1771–1782. doi:10.1590/S1516- chemical composition in adult Pekin ducks. Poult. Sci. 35982002000700020 87:1603–1608. doi:10.3382/ps.2007-00494 Translate basic science to industry innovation http://www.deepdyve.com/assets/images/DeepDyve-Logo-lg.png Translational Animal Science Oxford University Press

Application of Bayesian networks to the prediction of the AMEn: a new methodology in broiler nutrition

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Abstract

Application of Bayesian networks to the prediction of the AMEn: a new methodology in broiler nutrition †,1 † † ‡ Tatiane C. Alvarenga, Renato R. Lima, Júlio S. S. Bueno Filho, Sérgio D. Simão, § ‡ ‡ Flávia C. Q. Mariano, Renata R. Alvarenga, and Paulo B. Rodrigues † ‡ Department of Statistics, Federal University of Lavras, 37200-000 Lavras, Minas Gerais, Brazil; Department of Animal Science, Federal University of Lavras, 37200-000 Lavras, Minas Gerais, Brazil; and Department of Science and Technology, Federal University of São Paulo, 12231-280 São José dos Campos, São Paulo, Brazil ABSTRACT:  Designing balanced rations for the random variables. BN uses machine learning broilers depends on precise knowledge of nitro- algorithms, being a methodology of artificial in- gen-corrected apparent metabolizable energy telligence. The bnlearn package in R software was (AMEn) and the chemical composition of the used to predict AMEn from the following covar- feedstuffs. The equations that include the meas- iates: crude protein, crude fiber, ethereal extract, urements of the chemical composition of the mineral matter, as well as food category, i.e., en- feedstuff can be used in the prediction of AMEn. ergy (corn, corn by-products, and others) or pro- In the literature, there are studies that obtained tein (soybean, soy by-products, and others) and prediction equations through multiple regression, the type of animal (chick or cockerel). The data meta-analysis, and neural networks. However, come from 568 feeding experiments carried out other statistical methodologies with promising in Brazil. Additional data from metabolic experi- potential can be used to obtain better predic- ments were obtained from the Federal University tions of energy values. The objective of the pre- of Lavras (UFLA) – Lavras, Minas Gerais, Brazil. sent study was to propose and evaluate the use of The model with the highest accuracy (mean Bayesian networks (BN) to the prediction of the squared error = 66529.8 and multiple coefficients AMEn values of energy and protein feedstuffs of of determination = 0.87) was fitted with the max- vegetable origin used in the formulation of broiler min hill climbing algorithm (MMHC) using 80% rations. In addition, verify that the predictions of and 20% of the data for training and test sets, re- energy values using this methodology are the most spectively. The accuracy of the models was evalu- accurate and, consequently, are recommended to ated based on their values of mean squared error, Animal Science professionals area for the prep- mean absolute deviation, and mean absolute per- aration of balanced feeds. BN are models that centage error. The equations proposed by a new consist of graphical and probabilistic represen- methodology in avian nutrition can be used by the tations of conditional and joint distributions of broiler industry in the determination of rations. Key words: graph models, max-min hill-climbing algorithm, metabolic energy, probability distributions © The Author(s) 2021. Published by Oxford University Press on behalf of the American Society of Animal Science. This is an Open Access article distributed under the terms of the Creative Commons Attribution License (http://creativecommons.org/licenses/by/4.0/), which permits unrestricted reuse, distribu- tion, and reproduction in any medium, provided the original work is properly cited. Transl. Anim. Sci. 2021.5:1-11 doi: 10.1093/tas/txaa215 Corresponding author: tatianecarvalhoalvarenga@gmail. com Received August 28, 2020. Accepted January 20, 2021. 1 Alvarenga et al. INTRODUCTION approaches have not yet been applied to examine broiler nutrition. Production of low-cost high protein chicken To find more accurate results, BN are used to pre- meat through intensively reared broiler chickens has dict the AMEn according to the chemical compos- high economic importance at national and inter- ition of feedstuffs, BN are graphical models, which national levels. The need to formulate diets that are consist of the graphical representation (graph) and increasingly adequate to the demands of broilers is probabilistic (conditional and joint probability necessary for the production system. The productive distributions) of the variables (Scutari and Denis, efficiency of birds is directly related to the adequate 2015; Koller and Friedman, 2009; Lauritzen and supply of dietary energy, which, in turn, depends Spiegelhalter, 1988; Spirtes et al., 2000). In the ap- on the nitrogen-corrected apparent metabolizable plied areas, mainly Agriculture, there are still very energy (AMEn) of the foods. However, one of the few publications, however, Bayesian networks are highest problems actually is the real knowledge of an unprecedented line of research in poultry nutri- the energy composition of feedstuffs, which directly tion and that can be studied by researchers who are interferes with the energy levels of the rations and, interested in predicting the values of metabolizable consequently, on the nutrient balance of the same. energy (Alvarenga et al., 2020). Currently, several methods are available to assess Among the benefits of using BN are: 1) redu- the energy composition of feedstuffs and, often, cing the costs of in vivo trials to determine AMEn discrepant results are observed. values, 2)  Enhancing the accuracy of predictions The energy values feedstuffs can be obtained of AMEn, 3)  Reducing the variability in tabu- in biological tests, with the execution is time-con- lated values for AMEn, 4)  Expanding the use of suming and of high cost, or by the composition Bayesian networks to areas where machine learn- tables of the feedstuffs (Albino, 1980). Another ing and related methods are starting to be em- way of obtaining the values of AMEn is the pre- ployed, and 5) Capturing conditional dependency diction equations established according to the among random variables in, a broader sense than chemical composition of the feedstuffs, which traditional methods can achieve. In this paper, the is usually easy and quick to obtain (Rodrigues proposal using and evaluate BN, a new method- et  al., 2001, 2002). Zhao et  al. (2008) developed ology in broiler nutrition, to obtain prediction prediction equations using multiple regression equations for AMEn from a meta-analysis of en- to estimate the energy values using the chemical ergy and protein feedstuffs used for determining composition of the feedstuffs; however, their re- broiler rations. sults have been inconsistent or applicable only to one feedstuff group (Alvarenga et  al., 2011). MATERIALS AND METHODS Nascimento et  al. (2009, 2011) and Mariano et  al. (2012) used meta-analyses to better predict Data AMEn. Perai et  al. (2010), Ahmadi et  al. (2007, 2008), and Mariano et al. (2013) used neural net- To obtain the equations via BN, data from the works (NN), and the latter used a larger number meta-analysis were used, referring to the experiments of foods and in vivo trials. conducted in Brazil in the period from 1967 to 2007, NN and Bayesian networks (BN) are suitable resulting in 568 experiments (Nascimento et al., 2009; tools for prediction due to their superior ability to Nascimento et al., 2011), among them which refer to capture and express complex dependencies on covar- the values of AMEn and chemical composition of iates and response variables (Bishop, 2006; Gianola energy (n = 370) and protein (n = 198) feedstuffs, of et al., 2011). BN has been used in medicine, genetics, vegetable origin, commonly used in the formulation robotics, economics, demography forensics, educa- of broiler diets. The data used to validate the pro- tion, human behavior, industrial applications, spe- posed equations were obtained by Alvarenga et  al. cies conservation, and mining (Pourret et al., 2008). (2011). These data come from two in vivo trials to Mariano et al. (2013) focused on predicting AMEn determine the energy value of protein and energy using a NN. Felipe et al. (2015) indicated the pos- feedstuffs, with growing chicks (traditional method sibility of using BN in Animal Science; however, of total excreta collection), respectively in February/ the previous use of BN for Animal Science papers March and July 2008. The trials were carried out in is not restricted to breeding and genomic selection Lavras, state of Minas Gerais, Brazil (21° 14′ 45″S, (Gianola et  al., 2011; Morota et  al., 2013). These 44° 59′ 59″W, 919 m a.s.l.) at the Federal University of Translate basic science to industry innovation Application of Bayesian networks to the prediction of the AMEn Lavras (Alvarenga et al., 2011). For both data used to The variables used to learn the DAG were CP, obtain and validate the equations via BN, the values EE, ash, CF, food category (1 – energy concentrate, of the response variable – AMEn, were estimated with ingredients: 1.1 – corn, 1.2 – corn by-products, by the covariables; crude protein (CP), ether extract 1.3 – others, 2 – protein concentrate, with ingredi- (EE), ash, crude fiber (CF), classification of the feed- ents 2.1 – soybean meal, 2 – soybean by-products, stuffs category (1  – energy concentrate, 2  – protein 3 – others) and type of animal used in the bioassay concentrate), specification of the ingredient in the with two levels: 1 – chicks, 2 – cocks). category (1 – energy concentrate): (1 – corn, 2 – corn The initial step for a BN is to have an algorithm by-products, 3 – others), the ingredient specification to learn the basic graph structure (Scutari, 2010). The in the category (2 – protein concentrate): (1 – soybean, next step is to learn the implicit local distributions for 2 – soybean by-products, 3 – others) and the type of this given structure (Scutari et al., 2014). Nagarajan animal used in the bioassay (1 – chicks, 2 – cockerels). et  al. (2013) discussed three algorithms for learning network structure. The first, constraint-based al- gorithms, are based on conditional independence tests to infer the arrow direction between nodes. The Prediction Models second, score-based algorithms, select among all possible structures the BN with the highest quality, The structure of a directed acyclic graph (DAG) scored by probability-based measures such as Akaike that represents the BN, the nodes are connected, information criterion (AIC) or Bayesian (Schwarz) and all the arrows are directed without cycling (the information criterion (BIC). The third type, hybrid arrow cannot return to the same node). The DAG algorithms, combine ideas of both. is a directional, connected, and acyclic graph. We The bnlearn package (Scutari, 2010; R Core can observe that the neighbors of a node are the Team, 2020) for R implements the following con- adjacent nodes, which are either parents or sons straint-based algorithms: Grow-Shrink (GS) incre- (Nagarajan et al., 2013). mental association Markov blanket (IAMB) fast Most algorithms used to find graph structure incremental association (Fast-IAMB) interleaved depend on topology because causal relations are as- incremental association (Inter-IAMB); max-min sociated with precedence for conditioning. Some of parents and children (MMPC); semi-interleaved the algorithms use a Markov blanket to the target Hiton-PC (SI-HITON-PC). Each can be used for con- node. The nodes that separate the target node ditional independence tests (Nagarajan et al., 2013). from the remaining structure are parent, child, and The score-based algorithms also implemented nodes that share a child with the target node. For are hill climbing (HC) (Margaritis, 2003) and Tabu prediction, only those variables would be relevant search (TABU). The scoring function can be AIC, to modeling (Koski and Noble, 2009; Scutari and BIC, or others. Hybrid algorithms include max- Denis, 2015). min hill climbing (MMHC) (Tsamardinos et  al., A BN is a graphic representation of a joint prob- 2006) and general 2-phase restricted maximiza- ability distribution (or joint density, Margaritis, tion (RSMAX2). MMHC uses constraint-based 2003). It can be described by the structure of a MMPC to search graph skeletons, estimating DAG. Factorization of the BN, as described by parent–child Markov coverage for each pair of equation 1, is a chain of products of conditional variables in BN. To determine directionality, a probabilities, as one node, given its parents, is con- score-based HC algorithm is used. A more general ditionally independent of its non-descendants implementation of MMHC is performed by the (Pearl, 1988; Koski and Noble, 2009; Scutari and RSMAX2 algorithm. It can use any combination Denis, 2015). This is a convenient representation of constraint-based and score-based algorithms of the joint probability distribution, allowing for (Scutari and Denis, 2015). an inference on the desired research questions. The AMEn predictions were performed using a hy- joint probability distribution is defined as: brid BN with continuous and discrete variables in the same fashion as a multiple linear regression P (X , X , ...X )= P (X | Pa ) , 1 2 p i i (1) i=1 model (Koski and Noble, 2009). To envision the where p is the number of variables, i is the counter process, consider a set X of random variables, par- of samples and n is the number of observations. titioned into two subsets: X for discrete variables For the case of discrete and continuous nodes in and X for continuous variables. The joint prob- which Pa are the parents of X . ability distribution for P(X) can be factorized as: i i Translate basic science to industry innovation Alvarenga et al. a difference of approximately 1%, and RSMAX24 P(X)= P(X , X ) D C (bias = −48.10), presenting a difference of approxi- mately 10% (Figure 1). = P(X |Pa ) P(X |Pa , Pa ), i D j D C i ∈ D i ∈ C Table  1 summarizes the training (80% of the data) and testing sets. The DAG with the best-fit- in which Pa and Pa are joint probabilities for each D C ting yield by the MMHC learning algorithm is of the subsets, respectively. depicted in Figure  2, according to the result of The term P(X ||Pa , Pa ) brings both j D C i ∈ C the BN model presented in Figure 1. It has eight discrete and continuous parent variables that can nodes and 11 arrows in a Markov blanket with be locally represented by linear regressions with seven nodes. The best learning algorithm was parameters from discrete parents. This is equivalent MMHC, i.e., using a constraint-based MMPC to writing: algorithm with conditional independence testing using mutual information. The scored-based (X |Pa , Pa ) ∼ (Nμ , σ ), in which j D C j X |Pa j D method was hill climbing, using the BIC cri- μ =β + β X . 0,X |Pa i,X |Pa |Pa j D j D j c terion. The number of tests used to learn the best DAG was 165. Thus, for the prediction of AMEn, μ refers The joint distribution represented in Figure  2 to the intercept for each level of the discrete vari- can be written as P(AMEn, CP, EE, ash, CF, able's combination (categories for food and animal Category, Ingredient, Animal)  =  P(EE) · P(CF) · types). β and β are the intercept and 0,X |Pa i,X |Pa j D j D P(Category) · P(Animal) · P(CP | Category) · coefficients of the multivariate linear regression, P(Ingredient | Category) · P(ash | CP:CF) · P(AMEn | respectively. X represents the variables CP, ash, i|Pa C CP : EE : ash : CF : Category : Ingredient : Animal). EE, and CF. This means that EE, CF, Category, and Animal are The original data were described by Mariano not dependent on the other variables; however, CP et al. (2013). For this study, the data were randomly is dependent on Category, and ash is dependent by partitioned into a training set (80% of the sample CP and CF. The response variable AMEn is condi- size) and a testing set (using the remaining data). tionally dependent on all studied variables. Thus, The training set was used to search for a best-fitted there are 12 regression equations to AMEn, each DAG. Equations derived from the joint posterior coming from a different combination of levels for were compared to a metabolic data assay from the discrete variables. Each separate prediction Alvarenga et  al. (2011). The parameters used for equation uses only levels of quantitative variables the validation of the model were simple correlation (CP, CF, ash, and EE). The proposed prediction coefficient (r), multiple coefficients of determin- equations and their coefficients are presented in ation (R ), mean squared error (MSE), mean abso- Table 2. lute deviation (MAD), mean absolute percentage The observed values (Alvarenga et  al., 2011) error (MAPE), bias (bias) (Mariano et  al., 2014) and predicted (the result of the equations proposed and prediction mean squared error (PMSE) (Felipe by the BN) are plotted in the graph of Figure  4, et al., 2015). and the statistics used in the assessment of the ad- justment are shown in Table  3. The data used in this validation process coming from in vivo trials. RESULTS Regarding the adjustments, the best evaluations Different hybrid structures learning algo- of the statistics were MSE  =  9051.84 for corn rithms were evaluated, obtained from randomi- by-products, MAD  =  81.66, MAPE  =  2.16 and zations in the training data sets (80%, 75%, and bias  =  −64.51 for other protein foods. The com- 70%) and test (20%, 25%, and 30%). The best result parison between the predictions obtained in this re- obtained was through the MMHC learning algo- search with the results of neural networks is shown rithm (Figure  1) with the randomization of 80% in Table 4. of the learning data compared to the sets of 70% and 75%. The fit statistics were: r = 0.94, R  = 0.87, DISCUSSION MSE  =  66529.8, MAD  =  191.2, MAPE  =  7.52, bias  =  −43.09 and PMSE  =  257.93. The selected This study aimed to propose and evaluate the algorithm MMHC provided better statistics, ex- use of BN and to find equations to the predic- cept for RSMAX21 learning (MAPE = 7.45), with tion of the AMEn values of energy and protein Translate basic science to industry innovation Application of Bayesian networks to the prediction of the AMEn Figure 1. Evaluation of the performance and accuracy of the models for nitrogen-corrected apparent metabolizable energy (AMEn) estimated using Bayesian networks. r: correlation coefficient; R : multiple coefficient of determination; MMHC: max-min hill climbing; RSMAX2: 2-phase restricted maximization; Learning respectively, constraint-based and score-based: 1 – semi-interleaved Hiton Parents and Children (SI.HITON.PC) and hill climbing (HC); 2 – interleaved incremental association (INTER.IAMB) and HC; 3 – fast incremental association (FAST.IAMB) and HC; 4 – incremental association Markov blanket (IAMB) and HC; 5 – Grow-Shrink (GS) and HC. feedstuffs of vegetable origin used in the formula- processing methods and the lack of standardiza- tion of broiler rations. It is known, animal foods tion of national products. have quite different chemical compositions from From this objective used machine learning vegetables, they have no fiber, soluble carbohy- algorithms to learn the graphic structure of the drates are extremely low, they have a high-fat network as well as the probabilistic relationships content, and others. This variation in chemical between the variables, it was possible to prove and energy composition is even greater when it the functionalities of this new promising meth- comes to animal by-products, due to the different odology in broiler nutrition. The algorithm that Translate basic science to industry innovation Alvarenga et al. Table 1. Summaries for variables in the training (80%) and testing (20%) sets. Original data from Nascimento et al. (2009, 2011) Statistics AMEn (kcal/kg) CP (%) EE (%) Ash (%) CF (%) Training set Minimum 1,170 1.470 0.030 0.300 0.020 Median 3,501 14.130 3.480 2.110 3.020 Mean 3,176 23.360 4.872 3.560 4.928 Maximum 4,386 71.440 26.210 12.610 26.500 Testing set Minimum 1,148 1.700 0.030 0.560 0.320 Median 3,275 15.270 3.150 3.010 3.985 Mean 3,050 23.360 4.135 3.826 5.683 Maximum 4,160 68.810 25.540 11.050 27.630 AMEn: nitrogen-corrected apparent metabolizable energy; CP: crude protein; EE: ether extract; CF: crude fiber. composition of food in the ration considered (for some discussion on this, please refer to Moreira et al. (2002) and Brunelli et al. (2006). A metabolic trial was performed in chicks only. Thus, equations for cocks were not validated. Predictions and real- izations based on data from (Alvarenga et al., 2011) are plotted in Figure  4. AMEn values are close to the identity line, indicating good accuracy of the proposed equations. Equations proposed by the BN and those from the NN (Mariano et al., 2013) were validated with these in vivo trials with chicks (Alvarenga Figure 2. Directed acyclic graph (DAG) for study variables. et al., 2011). The results can be found in Table  4. Predicted energy values that are closer to the real- showed the best performance was MMHC as the ized description are described in boldface. From literature mentions in Felipe et al. (2015). It was this table, we conclude that the BN predicted closer observed that the equations differed in the values in 20 out of 36 cases and that the NN was closer of the parameters due to countless DAG options in the other 16 cases. The equations for obtain- (Koski and Noble, 2009). However, according ing the energy values of corn, corn by-products, to the lowest values of errors found in the val- and other protein by means of BN had a better idation using the test data (20%) in the Bayesian performance compared to the estimates obtained network model obtained the equations available by NN (Mariano et  al., 2013). These equations in Table  3. In addition to the validation from (Table  2) are for the corn (AMEn  =  3658.16  − the test data, the validation in the data of meta- 2.41 CP − 11.25 EE + 83.41 ash + 16.76 CF), bolic tests, only for chicks' equations, confirmed corn by-products (AMEn  =  4209.57  − 34.56 CP the efficiency of the obtained equations being + 32.84 EE − 25.15 ash − 142.57 CF) and others indicated for the elaboration of balanced diets protein (AMEn = 2327.69 + 24.23 CP + 77.72 EE for broilers. The results continue to be proven − 167.06 ash − 22.28 CF), the BN was remark- through the predicted and realized values for ably better, but for soybeans, the opposite result AMEn, as shown below. was found. For comparison, in Nascimento et  al. (2009), It is known that the common statistical ap- Mariano et  al. (2012), and Mariano et  al. (2013), proach to obtain the AMEn values is that of the best architecture achieved R  = 0.83, 0.74, and ordinary least squares of multiple regression al- 0.86, respectively. In this research, the BN model though there are few types of research of machine managed to explain 87% of the AMEn variation. learning found for this purpose, these being NN. Predicted and realized values for AMEn are de- However, the authors advocate the use of com- picted in Figure  3. Errors in prediction, such as putational methodologies, such as BN to predict those we found, are attributed to the chemical AMEn and demonstrate that the use of BN for Translate basic science to industry innovation Application of Bayesian networks to the prediction of the AMEn Table 2.  Prediction equations for nitrogen-corrected apparent metabolizable energy (AMEn) estimated using Bayesian networks AMEn (kcal/kg) Coefficients Category Animals Type food Intercept CP EE Ash CF Energy Chicks Corn 3658.16 −2.41 −11.25 +83.41 + 16.76 Corn by-products 4209.57 −34.56 +32.84 −25.15 −142.57 Other Corn products 4335.88 −50.91 +35.40 −67.35 −87.06 Protein Chicks Soybean 3684.83 −19.84 −71.15 +18.14 −8.93 Soybean by-products 2951.05 +0.09 +37.96 +5.04 −17.60 Other soybean products 2327.69 +24.23 +77.72 −167.06 −22.28 Energy Cocks Corn 3321.82 +51.31 + 39.42 −377.11 +113.92 Corn by-products 4716.45 −227.63 +144.47 - - Other Corn products 4133.39 −89.45 +100.32 −5.50 −96.37 Protein Cocks Soybean 4143.45 −3.18 −43.45 −213.55 +6.71 Soybean by-products 518.54 +26.25 +47.10 +184.42 +69.0 Other soybean products 6033.28 −15.02 −105.81 −556.50 +91.23 AMEn: nitrogen-corrected apparent metabolizable energy; CP: crude protein; EE: ether extract; CF: crude fiber. Table 3. Accuracy of prediction equations using data from in vivo trials (Alvarenga et al., 2011) Equation MSE MAD MAPE bias Corn 27314.73 143.28 3.98 −104.56 Soybean 71737.46 254.97 10.74 −254.97 Corn by-products 9051.84 82.85 3.44 81.26 Soybean by-products 131069.90 299.25 10.84 −227.12 Other energy food 64831.12 213.58 7.42 −184.02 Other protein food 16473.99 81.66 2.16 −64.51 MSE: mean squared error; MAD: mean absolute deviation; MAPE: mean absolute percentage error; PMSE: prediction mean squared error. between random variables in a broader sense and of relationships between discrete and continuous variables simultaneously in the model. Especially in the era of information, that computational meth- odologies have been experiencing have been more indicated by the listed properties. Emphasizes, to the AMEn values determined with chicks are found in Table 4, and that the values of AMEn for corn with BN (3,701.423 kcal/kg), NN (3,682.410 kcal/kg) and according to Rodrigues et  al. (2001) using ordinary least squares of multiple regression, for the same feedstuff, the AMEn value was 3,699 kcal/kg, which declares the promising use of BN in bringing these values closer to the methods estab- lished by the literature. According to the results found in this research, indicating good accuracy of the proposed equations via new machine learning methodology in poultry Figure 3. Relationship between the observed and predicted for nitrogen-corrected apparent metabolizable energy (AMEn) values of nutrition, authors in the literature show superiority different feedstuffs using test data. in non-traditional models in the prediction of en- ergy values. Ahmadi et al. (2007, 2008), Perai et al. (2010), and Mariano et  al. (2013), demonstrated areas where machine learning and related methods that the NN model outperformed the traditional are beginning to be employed; it has the benefits models or accurately predicted performance based that traditional methods cannot achieve, espe- on dietary metabolizable energy. cially the BN. BN capture conditional dependence Translate basic science to industry innovation Alvarenga et al. Table 4.  Energy levels predicted from Bayesian networks (BN) and neural networks (NN, MARIANO et al., 2013) and bias found to result in vivo trials with chicks (Alvarenga et al., 2011) Prediction 1 2 Food sample Alvarenga et al. (2011) BN NN BN NN Corn 3,747 3701.423 3682.410 −45.577 −64.590 3,699 3718.852 3749.960 19.852 50.960 3,813 3723.068 3691.330 −89.931 −121.670 3,572 3783.902 3738.140 211.902 166.140 Soybean 2,373 2524.779 2532.720 151.778 159.720 2,326 2703.916 2505.290 377.916 179.290 2,355 2641.964 2500.180 286.963 145.180 2,396 2677.614 2498.430 281.613 102.430 2,478 2654.566 2513.110 176.566 35.110 Corn by-products 3,624 3628.778 3841.340 4.777 217.340 3,676 3573.398 3803.920 −102.601 127.920 2,184 2086.068 1931.880 −97.432 −251.620 Soybean by-products 3,159 3214.654 2527.200 55.653 −631.800 3,779 3661.684 3580.770 −117.315 −198.230 2,809 2992.756 2431.950 183.756 −377.050 3,772 3938.579 3918.470 166.578 146.470 2,387 2935.302 2342.300 548.302 −44.700 3,971 3753.066 3519.050 −217.934 −451.950 3,288 3617.693 3580.420 329.693 292.420 2,314 2935.302 2351.800 621.302 37.800 3,818 3753.066 3519.050 −64.934 −298.950 3,173 3617.693 3580.420 444.693 407.420 2,339 2935.302 2351.800 596.302 12.800 3,793 3753.066 3519.050 −39.934 −273.950 3,330 3617.693 3580.420 287.693 250.420 2,309 2935.302 2351.800 626.302 42.800 3,890 3753.066 3519.050 −136.934 −370.950 3,267 3617.693 3580.420 350.693 313.420 Energy 3,598 3569.507 3498.87 −28.492 −99.130 3,529 3515.214 3505.98 −13.786 −23.020 3,862 3771.244 3537.47 −90.756 −324.530 2,682 2839.403 2798.87 157.403 116.870 1,941 2342.840 1939.12 401.840 −1.880 3,362 3669.743 3512.24 307.492 149.990 Protein 3,934 3957.047 4049.53 23.046 115.53 3,904 3979.133 4072.38 74.880 168.13 1 2 BN: Prediction BN – Observed by Alvarenga et al. (2011); NN: Prediction NN – Observed by Alvarenga et al. (2011); Prediction NN: Obtained by Mariano et al. (2013). The results demonstrated in Perai et al. (2010) et  al. (2015) that reinforces innovations in estima- that the NN model predicts the nitrogen-corrected tion methods are necessary to obtain better esti- true metabolizable energy (TMEn) values of meat mates of the energy values of feed for broilers. and bone meat samples based on their chemical Felipe et al. (2015) compared different meth- composition outperformed the traditional models. odologies to predict total egg production in Accurately predicted metabolizable energy, methio- quails from different strains. The model with nine, and lysine using NN (Ahmadi et  al., 2007) the combination of the BN and NN resulted in as well, predicted the TMEn values of feather and a better performance to predict total egg pro- poultry offal meal based on their chemical compos- duction. Töpner et  al. (2017) used BN in a corn ition (Ahmadi et al., 2008) are corroborant with the experiment to analyze the relationships between research and application of machine learning meth- characteristics at genomic and residual levels. ods in poultry nutrition. In addition to Alvarenga The BN obtained in this were classified in terms Translate basic science to industry innovation Application of Bayesian networks to the prediction of the AMEn Figure 4. Predicted and realized values for nitrogen-corrected apparent metabolizable energy (AMEn) of different feedstuffs: corn (A), soy- bean (B), corn by-products (C), soybean by-products (D), other energy feeds (E), and other protein feeds (F) using data from chick in vivo trials (Alvarenga et al., 2011). of adjustability and predictive ability through fiber and neutral detergent fiber; missing vari- structural equations. They concluded that when ables or incomplete in the set data used and illustrating the connections of characteristics evaluate the effect of these values in the AMEn concerning their genomic and residual nature, values. Increase the representativeness of the vari- they become clearer, which makes it useful for ables through the Bayesian Fuzzy Evolutionary predicting multiple traits and indirect selection. Networks. They confirm the potential of the BN in health sciences, economics, agriculture among others, CONCLUSIONS that previously were unprecedented in the field of broiler nutrition. After all, Alvarenga et  al. (2015) have shown In future studies, the dataset including other that these prediction equations are important for experimental studies will be updated. It will be increasing the accuracy of diet formulation, al- to develop an innovative technological product lowing producers to correct energy values based on based on the BN methodological proposal, with the variations in the chemical composition of feed- the objective of obtaining prediction equations to stuffs. In conclusion, the MMHC algorithm and a assist broiler nutritionists. Research the behavior partition with 80% of data to the training set seems of AMEn values in different probability distribu- to perform better in determining the DAG and re- tions for the variables, to obtain prediction equa- spective BN. The BN was accurate and as good tions. Impute by BN the values of acid detergent a method as the previous NN, depending on the Translate basic science to industry innovation Alvarenga et al. in European quails based on earlier expressed phenotypes. food category. The predicting equations estimated Poult. Sci. 94:772–780. doi:10.3382/ps/pev031 from a BN can be used to calculate energy levels Gianola,  D., H.  Okut, K.  A.  Weigel, and G.  J.  Rosa. 2011. for broilers. Predicting complex quantitative traits with Bayesian neural networks: a case study with Jersey cows and wheat. ACKNOWLEDGMENTS BMC Genet. 12:87. doi:10.1186/1471-2156-12-87 Koller,  D., and N.  Friedman. 2009. Probabilistic graphical Thanks to the Brazilian funding agencies models: principles and techniques. Cambridge: MIT Coordenação de Aperfeiçoamento de Pessoal de Press; p. 1233 Nível Superior (CAPES) and Fundação de Amparo Koski, T., and J. M. Noble. 2009. Bayesian networks: an intro- duction. Chichester: John Wiley & Sons Ltd; p. 347. à Pesquisa do Estado de Minas Gerais (FAPEMIG) Lauritzen, S. L., and D. J. Spiegelhalter. 1988. Local computa- for the partial support of this work. tions with probabilities on graphical structures and their Conflict of interest statement. No conflict of applications to expert systems. J. R. Stat. Soc. 50:157–224. interest, financial, or otherwise are declared by the http://www.jstor.com/stable/2345762 authors. Margaritis, D. 2003. Learning bayesian network model struc- ture from data [PhD thesis, Doctor of Philosophy]. Pittsburgh (PA): Carnegie Mellon University. LITERATURE CITED Mariano,  F.  C.  M.  Q., R.  R.  Lima, R.  R.  Alvarenga, P.  B.  Rodrigues, and W.  S.  Lacerda. 2014. Neural net- Ahmadi, H., A. Golian, M. Mottaghitalab, and N. Nariman- work committee to predict the AMEn of poultry feed- Zadeh. 2008. Prediction model for true metabolizable en- stuffs. Neural Comput. Appl. 25:1903–1911. doi:10.1007/ ergy of feather meal and poultry offal meal using group s00521-014-1680-3 method of data handling-type neural network. Poult. Sci. Mariano,  F.  C.  M.  Q., R.  R.  Lima, P.  B.  Rodrigues, 87:1909–1912. doi:10.3382/ps.2007-00507 R.  R.  Alvarenga, and G.  A.  J.  Nascimento. 2012. Ahmadi,  H.  A., M.  Mottaghitalab, and N.  Nariman-Zadeh. Equações de predição de valores energéticos de ali- 2007. Group method of data handling-type neural net- mentos obtidas utilizando meta-análise e componentes work prediction of broiler performance based on dietary principais. Ciênc. Rural. 42:1634–1640. doi:10.1590/ metabolizable energy, methionine, and lysine. J. Appl. S0103-84782012005000061 Poult. Res. 16:494–501. doi:10.3382/japr.2006-00074 Mariano,  F .  C.  M.  Q., C.  A.  Paixão, R.  R.  Lima, R.  R.  Alvarenga, Alvarenga, T. C., R. R. Lima, J. S. S. B. Filho, P. B. Rodrigues, P. B. Rodrigues, and G. A. J. Nascimento. 2013. Prediction R.  R.  Alvarenga, and F.  C.  M.  Q.  Mariano. 2020. of the energy values of feedstuffs for broilers using Inovação na predição dos valores energéticos de alimen- meta-analysis and neural networks. Animal 7:1440–1445. tos para aves: um estudo bibliométrico sobre as redes doi:10.1017/S175173111300071 bayesianas. Rev. Bras. Biom. 38:274–289. doi:10.28951/ Moreira,  I., C.  R.  Ribeiro, A.  C.  Furlan, C.  Scapinello, and rbb.v38i3.429 M.  Kutschenko. 2002. Utilization of defatted maize Alvarenga,  R.  R., P.  B.  Rodrigues, M.  G.  Zangeronimo, germ meal on growing-finishing pigs feeding digestibility R.  T.  F.  Freitas, R.  R.  Lima, A.  G.  Bertechini, and and performance. Braz. J.  Anim. Sci. 31:2238–2246. E.  J.  Fassani. 2011. Energetic values of feedstuffs for doi:10.1590/S1516-35982002000900012 broilers determined with in vivo assays and predic- Morota,  G., K.  Masanori, G.  J.  M.  Rosa, A.  W.  Kent, and tion equations. Anim. Feed Sci. Technol. 168:257–266. D.  Gianola. 2013. Predicting complex traits using a di doi:10.1016/j.anifeedsci.2011.04.092 usion kernel on genetic markers with an application to Alvarenga,  R.  R., P.  B.  Rodrigues, M.  G.  Zangeronimo, dairy cattle and wheat data. Genet. Sel. Evol. 45:1–15. E. C. Oliveira, F. C. Mariano, E. M. Lima, A. A. Garcia, doi:10.1186/1297-9686-45-17 Jr, L. P. Naves, and N. B. Nardelli. 2015. Validation of Nagarajan, R., M. Scutari, S. Lèbre. 2013. Bayesian networks prediction equations of energy values of a single in- in R with applications in systems biology. New York: gredient or their combinations in male broilers. Asian- Springer; p. 157. Australas. J.  Anim. Sci. 28:1335–1344. doi:10.5713/ Nascimento,  G.  A.  J., P.  B.  Rodrigues, R.  T.  F.  Freitas, ajas.14.0339 A. G. Bertechini, R. R. Lima, and L. E. A. Pucci. 2009. Albino,  L.  F.  T. 1980. Determinação de valores de energia Equações de predição para estimar os valores energéticos metabolizável e triptofano de alguns alimentos para de alimentos concentrados de origem vegetal para aves aves em diferentes idades. 55f. Dissertação (Mestrado utilizando a metanálise. Revis. Bras. Zootec. 38:1265– em Zootecnia). Viçosa (MG): Universidade Federal de 1271. doi:10.1590/S1516-35982009000700015 Viçosa. Nascimento,  G.  A.  J., P.  B.  Rodrigues, R.  T.  F.  Freitas, Bishop, C. M. 2006. Pattern recognition and machine learning. R.  V.  Reis  Neto, R.  R.  Lima, and I.  B.  Allamann. 2011. New York: Springer; p. 738. Equações de predição para estimar valores da energia Brunelli, S. R., J. W. Pinheiro, C. A. Silva, N. A. N. Fonseca, metabolizável de alimentos concentrados energéti- D.  D.  Oliveira, G.  E.  Cunha, and L.  F.  A.  Souza. 2006. cos para aves utilizando meta-análise. Arq. Bras. Feeding increasing defatted maize germ meal levels Med. Vet. Zootec. 63:222–230. doi:10.1590/S0102- to broiler chickens. Braz. J.  Anim. Sci. 35:1349–1358. doi:10.1590/S1516-35982006000500014 Pearl,  J. 1988. Probabilistic reasoning in intelligent systems: Felipe, V. P., M. A. Silva, B. D. Valente, and G. J. Rosa. 2015. networks of plausible inference. San Francisco: Editor Using multiple regression, Bayesian networks and artifi- Morgan Kaufmann; p. 552. cial neural networks for prediction of total egg production Translate basic science to industry innovation Application of Bayesian networks to the prediction of the AMEn Perai,  A.  H., H.  Nassiri  Moghaddam, S.  Asadpour, Scutari,  M. 2010. Learning bayesian networks with the J. Bahrampour, and G. Mansoori. 2010. A comparison of bnlearn R package. J. Stat. Softw. 35:1–21. doi:10.18637/ artificial neural networks with other statistical approaches jss.v035.i03 for the prediction of true metabolizable energy of meat Scutari, M., and J. B. Denis. 2015. Bayesian networks with ex- and bone meal. Poult. Sci. 89:1562–1568. doi:10.3382/ amples in R. New York: Taylor & Francis Group; p. 221. ps.2010-00639. Scutari,  M., P.  Howell, D.  J.  Balding, and I.  Mackay. 2014. Pourret, O., P. Naim, and B. Marcot. 2008. Bayesian networks: Multiple quantitative trait analysis using bayesian a practical guide to applications. The Atrium, Southern networks. Genetics 198:129–137. doi:10.1534/genetics. Gate, Chichester: John Wiley Sons Ltd. 114.165704 R Core Team (2020). R: a language and environment for stat- Spirtes, P., C. Glymour, and R. Scheines. 2000. Causation, pre- istical computing. Vienna, Austria: R Foundation for diction and search. 2nd ed. Cambridge (MA): The MIT Statistical Computing. Disponível em: http://www.R-pro- Press. ject.org/. Acesso em 15 de maio de 2020. Töpner,  K., G.  J.  M.  Rosa, D.  Gianola, and C.  C.  Schön. Rodrigues, P. B., H. S. Rostagno, L. F. T. Albino, P. C. Gomes, 2017. Bayesian networks illustrate genomic and residual W.  A.  Barboza, and R.  T.  Santana. 2001. Valores trait connections in Maize (Zea mays L.). G3 (Bethesda). energéticos do milheto, do milho e subprodutos do 7:2779–2789. doi:10.1534/g3.117.044263 milho, determinados com frangos de corte e galos adul- Tsamardinos,  I., L.  E.  Brown, and C.  F.  Aliferis. 2006. The tos. Revis. Bras. Zootec.. 30:1767–1778. doi:10.1590/ maxmin hill-climbing Bayesian network structure learn- S1516-35982001000700015 ing algorithm. Mach. Learn. 65:31–78. doi:10.1007/ Rodrigues,  P.  B., H.  S.  Rostagno, and L.  F.  T.  Albino 2002. s10994-006-6889-7 Valores energéticos da soja e subprodutos da soja, Zhao,  F., H.  F.  Zhang, S.  S.  Hou, and Z.  Y.  Zhang. 2008. determinados com frangos de corte e galos adultos. Predicting metabolizable energy of normal corn from its Revis. Bras. Zootec. 31:1771–1782. doi:10.1590/S1516- chemical composition in adult Pekin ducks. Poult. Sci. 35982002000700020 87:1603–1608. doi:10.3382/ps.2007-00494 Translate basic science to industry innovation

Journal

Translational Animal Science – Oxford University Press

Published: Jan 22, 2021

Keywords: graph models; max-min hill-climbing algorithm; metabolic energy; probability distributions

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