2.2.2. Ensembles of Trees

Ensembles of Trees (ET) is one of the most popular techniques for building regression models [37,38]. Ensemble models combine results from many weak learners into one high-quality ensemble model. This approach has been applied frequently in fields such as remote sensing and statistics [39,40]. The function used to predict values is as follows:

$$\mathcal{G}\_i = \sum\_{j=1}^{K} f\_j(\mathbf{x}\_i), \ f\_j \in F \tag{1}$$

where *y*ˆ*<sup>i</sup>* is the predicted value of the *i*-th sample, *K* is the number of trees, *xi* is the *i*-th sample vector, *fj* denote the structure of the *j*-th independent tree and *F* is the ensemble space of trees.

In this paper, a bagging tree is applied to build the ET. It draws its training set from the original sample set. In each round, n training samples are drawn from the original sample set using Bootstraping (some samples may be drawn multiple times in the training set, while some samples may not be drawn at all) [41]. A total of k rounds of extraction are performed to obtain k training sets, which means that k models will be built. The k training sets are independent of each other [42]. In this paper, k = 30 and the minimum leaf size is 8. Therefore, if several similar datasets are created by resampling with replacement and regression trees are grown without pruning, the variance component of the output error is reduced [41].
