## 2 Materials and Methods
### The Modeling of the Key Risk Factors Using Machine Learning Algorithms
In this case, \(\theta_{\mathrm{k}}\) is an independent equally distributed l-dimensional random vector, the coordinates of which are independent discrete random variables that take values from the subset \(\{1,2,3,\ldots\}\) with equal probabilities. The implementation of a random vector \(\theta_{\mathrm{k}}\) determines the precedent numbers of the training sample, which form the bootstrap (i.e., the return sample, more details in the following sections) of the sample used in constructing the k-th decision tree. The averaging of observational results can give a more stable and reliable estimate, as the effect of random fluctuations in a single dimension is weakened. The development of algorithms for combining models was based on a similar idea. The construction of their ensembles turned out to be one of the most powerful machine learning methods, which often surpasses other methods in the quality of forecasts. One solution that provides the necessary variety of models is their re-learning on samples randomly selected from the general population or other subsets of data constructed from existing ones. To obtain a stable forecast, the predictions of these models are combined in one way or another, for example, by simple averaging or voting (possibly weighted). Statistical bootstrap (bootstrapping) is a practical computer method for determining statistics of probability distributions based on multiple generations of samples by the Monte Carlo method based on the available sample. Allows you to easily and quickly evaluate various statistics (confidence intervals, variance, correlation, and so on) [25]. Just as the averaging of several observations reduces the estimate of data variance, a reasonable way to reduce the forecast variance is to obtain a large number of data from the general population, build a predictive model for each training sample and average the forecasts obtained. If instead of separate training samples (which we, as a rule, always do not have enough) to execute a bootstrap and based on the generated pseudo-samples to construct \(n\) trees of regression, the average collective forecast \(\hat{f}_{bag}\) will have a lower variance. This procedure is called bootstrap. Bagging can be performed with respect to regression trees and other models: reference vectors, linear discriminants, Bayesian probabilities, and others. Another method of improving forecasts is boosting, which is an iterative process of sequential construction of private models [26]. Each new model is learned using the information about the mistakes made in the previous step. The resulting function is a linear combination of the whole ensemble of models while minimizing the penalty function. Like bagging, boosting is a general approach that can be applied to many statistical methods of regression and classification. Here we will limit ourselves to discussing gradient boosting in the context of regression trees. The AdaBoost is model where for any subsequent model the check and elimination of observations-emissions, erroneous conclusions of the previous model are carried out [27]. Stacking (Stacked Generalization) is a combination of heterogeneous classifiers [26]. To do this, models of any type are combined to create a composite model. It is similar to bagging, but is not limited to the decision tree. The initial data for basic training create features that can recombine with the data. A majority vote or weighing can combine basic training inputs. Additional data for retention is required if meta-learning parameters are used. It also increases the complexity of the model.