# Machine Learning Approach in Heterogeneous Group of Algorithms for Transport Safety-Critical System
## 4 Results
\begin{table}
\begin{tabular}{c c c c c c} \hline
**Record** & **X** & **sX** & **Pr (X \textless{} 8.0)** & **Pr (X \textgreater{} 40.0)** & **90 Percent Interval** & **XREAL** \\ \hline
1 & 7.5901 & 1.1125 & 0.638447 & 0.0 & 5.6189 & 6.04 \\ \hline
2 & 8.9423 & 4.5804 & 0.421507 & 1.241341 \(\times\) 10\({}^{-6}\) & 0.8266 & 8.50 \\ \hline
3 & 10.4178 & 1.2074 & 0.032779 & 5.551115 \(\times\) 10\({}^{-16}\) & 8.2784 & 10.64 \\ \hline
4 & 22.3606 & 1.3488 & 1.415263 \(\times\) 10\({}^{-9}\) & 4.545264 \(\times\) 10\({}^{-11}\) & 19.9708 & 23.75 \\ \hline
5 & 22.3789 & 4.6541 & 0.003560 & 7.687263 \(\times\) 10\({}^{-4}\) & 14.1326 & 24.77 \\ \hline
6 & 36.9891 & 1.5087 & 5.122037 \(\times\) 10\({}^{-14}\) & 0.033197 & 34.3159 & 36.45 \\ \hline
7 & 39.7402 & 0.9383 & 1.519116 \(\times\) 10\({}^{-18}\) & 0.394970 & 38.0776 & 39.04 \\ \hline
8 & 39.7640 & 1.0177 & 6.820442 \(\times\) 10\({}^{-18}\) & 0.411707 & 37.9608 & 39.83 \\ \hline
9 & 43.1567 & 0.9128 & 1.334947 \(\times\) 10\({}^{-19}\) & 0.998410 & 41.5394 & 41.73 \\ \hline \end{tabular}
\end{table} 
Table 2: Sample predictions of X along with their corresponding threshold-crossing probabilities \(\Pr\left(X<8.0\right)\) and \(\Pr\left(X>40.0\right)\) and \(90\) percent tolerance intervals. The real value of X is given in the last column. column). Each row in the table shows the values averaged over 15 independent experiment runs with different random seeds. The seeds governed the inclusion of the records in the training set as well as the random initialization of neural networks generating the models. The average precision of our trained machine learning model is expressed through Correlation Coefficients (CorrCoef column) and Root Mean Squared Error (RMSE column). The Time column shows the average time in seconds needed for one modeling cycle, i.e., for training the model on NumRec randomly selected records in the training set and then predicting the target value for the remaining records in the dataset. The Intervals column shows the total number of interval estimates performed and column Correct the number of those that did encompass the real value XREAL. The Ratio column then shows their success rate, which is defined as the ratio of intervals. Since these estimates were meant to represent 0.9 tolerance intervals, the values in the Ratio column should be no less than 0.90. We can see that it is indeed so for all the rows except the last two, where the small size of the training set (<100 records) negatively impacted the success rate as well as precision (lowering the Correlation Coefficients and increasing the Root Mean Squared Errors). Nevertheless, \begin{table}
\begin{tabular}{c c c c c} \hline \hline
**Method** & **R\({}^{2}\)** & **RMSE** & **Training Time (MPa)** & **Testing Speed (obs/s)** \\ \hline Decision Tree & 0.912 & 0.133 & 1.092 & 140,000 \\ \hline Gaussian Process & 0.921 & 0.125 & 156.89 & 18,200 \\ \hline Random Forest & 0.903 & 0.104 & 3.79 & 31,300 \\ \hline Quadratic SVM & 0.867 & 0.188 & 141.93 & 26,000 \\ \hline \hline \end{tabular}
\end{table} 
Table 4: Comparison of any model performance. \begin{table}
\begin{tabular}{c c c c c c} \hline \hline
**Correl. Coef** & **RMSE** & **Time** & **Correct** & **Intervals** & **Ratio** \\ \hline  
\hline \end{tabular}
\end{table} 
Table 3: Dependence of model precision (CorrelCoef, RMSE), calculation time (Time) and the success rate of 0.9 tolerance interval estimates (Ratio) on the number of records in the training set. we consider the experimental evaluation a success, because, for sufficiently representative training sets (>100 records), the success rate of interval estimates reached or crossed 0.9, as expected. In fact, for training sets with 120 records or more, the success rate consistently exceeded 0.9. We thus feel entitled to conclude that the proposed algorithm can be practically deployed in various experimental scenarios. In the future, we plan to test our approach on other datasets and conduct an in-depth analysis of experimental results.