## 5 Conclusions  
To conclude, we provide a brief summary of the results observed using this new technique:  
* For the _Out-of-Sample_ study, the proposed Spln-CFR approach is among the top three methods based on the median _RMSE_ obtained for 100 independent runs (Table 1). * For the statistical test of the _Out-of-Sample_ rankings, Spln-CFR is statistically similar to the second-ranked method, _Random Forest_, in Figure 2b. * In terms of the _Out-of-Domain_ median _RMSE_ obtained for 100 runs, Spln-CFR is ranked first (Table 1). * For the statistical test of the _Out-of-Domain_ rankings in Figure 3b, Spln-CFR is the best method, with a median ranking close to second, and is statistically similar to the second-best regressor, _XGBoost_, which has a median ranking between second and third. * Spln-CFR correctly predicted 108 unique materials with critical temperature values greater than or equal to 89 K in the _Out-of-Domain_ test, nearly twice the number achieved all the other regression methods combined, which was 60 (Table 3). Table 2 reveals interesting characteristics of the different methods that deserve further consideration as an area of research. First, it can be noted that the twenty top materials for the different methods are not necessarily the same, although a few intersections obviously exist. In the _Out-of-Domain_ study, the top twenty predicted critical temperature values by Spln-CFR were all above 98.9 K, with eighteen being above 100 K. The average _RMSE_ critical temperature on this set (103.64 K) is nearly the same as the predicted one (103.08 K). The _RMSE_ of xg-b, however, is nearly three times smaller, while the method's top predictions are materials with relatively smaller values (average of 91.31 K). For the collected information of the materials in the dataset, we observed that the top suggestions of critical temperatures in superconductors are closer to the measured temperatures, at least on the average, when using Spln-CFR. Therefore, the use of Spln-CFR as a surrogate model to explore the possibility of testing the superconductivity of materials may provide better returns. Interestingly, while we observed similarities in the behavior of xg-b and other multivariate regression techniques, there were important differences worth noting. For instance, _Linear Regression_, perhaps the simplest scheme of them all, shows interesting behavior; its top twenty highest predictions are all in the range of 81.83-91.59 K while the actual values are in the interval 98.00-132.60 K. For the multi-layer perceptron method (mlp), the top twenty highest predictions are all in the range of 90.01-100.81 K, yet the true values are in the interval 109.00-131.40 K. By considering the rankings given to several materials, as opposed to the predicted values, valuable information about materials can be obtained with these techniques when trained using the MSE, allowing prioritization of materials for testing. Overall, our results show the limitations of the current dataset. One limitation is the lack of other useful molecular descriptors that can provide important problem domain  
Figure 7: Critical difference (CD) plot showing the statistical significance of rankings achieved by the regression methods for 100 runs on the six datasets form [8]. knowledge about the structure of the materials and their properties. In addition,careful segmentation of the different materials may be necessary. In a sense, the results of our experiments an help the AI community to reflect on how to carry out such analyses and provide motivation for closer collaboration with superconductivity specialists in order to provide other molecular descriptors. The inherent difficulties in prediction using in this dataset can be compared to other areas in which some of us have been working extensively, such as the prediction of survivability in breast cancer using transcriptomic data. In both cases, the obtained models showed poor generalization capability when the training samples were not separated into meaningful subgroups.