## 2 Background
### Machine Learning Classifier  
Recently, machine learning algorithms have been widely used in areas including business and finance, health care, and production due to their superior performance in sophisticated tasks [36; 37; 38; 39; 40]. We employed four widely used machine learning classifiers to predict the stature. The brief descriptions of these classifiers are as follows. Logistic regression is a basic classifier that assumes the logarithm of the ratio between the probability of positive class to that of negative class as a linear combination of independent variables as in Equation (1):  
\[\log\left(\frac{p_{1}}{p_{0}}\right)=b_{0}+b_{1}x_{1}+b_{2}x_{2}+b_{3}x_{3}+ \cdots b_{p}x_{p}. \tag{1}\]  
Because Equation (1) cannot be solved analytically for general cases, it is usually solved by iteratively reweighted least squares. It can be extended to multiclass classification by setting the log odds, the logarithm values of the ratios between the probability of a certain class and that of the reference class, as linear combinations of independent variables as in Equation (2):  
\[\log\left(\frac{p_{i}}{p_{K}}\right)=b_{i,0}+b_{i,1}x_{1}+b_{i,2}x_{2}+b_{i,3 }x_{3}+\cdots b_{ip}x_{p},\ i=1,\ \ldots,\ K-1. \tag{2}\]  
where \(K\) denotes the number of classes. Naive Bayes classifier (NB) is a probabilistic classifier based on Bayes theorem [41]. It usually assumes that all features are conditionally independent of one another given the class of an instance; thus, the classifier becomes as follows:  
\[P(y=k|x_{1},x_{2},\ldots,x_{p})=\frac{1}{Z}P(y=k)P(x_{1},x_{2},\ldots,x_{p}|y= k)=\frac{1}{Z}P(y=k)\prod_{i=1}^{p}P(x_{i}|y=k). \tag{3}\]  
where \(x_{i}\) is the \(i\)-th feature of an instance, \(P(y=k)\) is a prior probability that the instance belongs to class \(k\), and \(Z=\sum_{k=1}^{K}P(y=k)\prod_{i=1}^{p}P(x_{i}|y=k)\) is a normalization factor, usually called evidence. In general, prior probabilities are defined proportional to the number of instances belonging to the class before training. Thus, in a training phase, a model finds the parameters in the likelihood distribution, \(P(x_{i}|y=k)\), that best fits the training instances. Artificial neural networks (ANNs) are one of the most famous machine learning models today because they encompass deep learning, the most powerful algorithms in many applications. Neural networks were originally inspired by the human brain, which consists of several interconnected neurons [42]. In a neural network algorithm, as in a central nervous system, each neuron receives signals from other neurons, processes them into a new signal, and transmits it to others. The output of each neuron is calculated as follows:  
\[\text{output}=g\left(\sum_{i=1}^{M}w_{i}x_{i}\right) \tag{4}\]where \(x_{i}\)'s are inputs from other neurons, \(w_{i}\)'s are weight parameters, and \(g(\cdot)\) is an activation function that gives a neural network model nonlinearity; rectified linear unit, sigmoid, and hyperbolic tangent functions are typical choices for the activation function. In multilayer perceptron, a neural network model for regression and classification, the layers containing a number of neurons are located sequentially, and the neurons in one layer receive inputs from the neurons in the previous layer and transmit outputs to those in the next layer. After calculating the final output values in the output layer, the weight parameters between layers are trained to minimize the cost function by backpropagation [43]. Support vector machine (SVM), proposed by [44], is one of the most famous kernel-based classifiers and has advantages in both sparsity and robustness. It finds a hyperplane, a decision boundary, which maximizes the margin, the distance between a decision boundary and the closest data point, in the feature space, a high-dimensional space mapped from the original space. By mapping from the original space to the high-dimensional feature space, the separating hyperplane can be found even when it does not exist in the original space.