## 4 Discussion
#### Extrapolation Capability of the Regressors in General  
As all of the results presented in this work are for a special case of finding models for the extrapolation of the critical temperature of superconductors, we included more robust experimental outcomes with a set of six datasets used in [8]. This additional test can help to evaluate the extrapolation capabilities of the regressors in other problem domains.  
[PERSON] proposed a Multivariate Adaptive Regression Splines (MARS) algorithm in [24] which aggregates multiple linear regression models throughout the range of target values. We used the implementation of the MARS algorithm from the pyearth Python library ([[https://contrib.scikit-learn.org/py-earth/content.html#multivariate-adaptive-regression-splines](https://contrib.scikit-learn.org/py-earth/content.html#multivariate-adaptive-regression-splines)]([https://contrib.scikit-learn.org/py-earth/content.html#multivariate-adaptive-regression-splines](https://contrib.scikit-learn.org/py-earth/content.html#multivariate-adaptive-regression-splines)) accessed on 8 October 2021). We included a comparison of MARS with Spln-CFR and other regressors to assess their extrapolation capability.  
Here, the samples from each of the datasets were sorted based on the target value, which was then split into the out-of-domain setting by taking samples with the lower 90% target values for training and the higher 10% target values for testing. We took half of the samples uniformly and at random from the out-of-domain training set to build the model and used the same ratio from the out-of-domain test set for prediction for each of the 100 independent runs. We applied min-max normalization on the training set and used the same distribution to normalize the test set.  
We analyze the regressors' performance statistically in Figure 7; it can be seen that MARS has a median ranking of fifth and is statistically significantly different from only krnl-r, sgd-r, and lasso-l. On the other hand, the proposed Spln-CFR achieves the first rank among all the methods, with a median ranking between two to three. To calculate how many predictions surpass the threshold (which matches the highest target score in the training data) in out-of-domain scenarios, we can convert the predictions of each model back to their original scale, i.e., denormalize them. Table 5 shows the full denormalization results. These counts show that Spln-CFR has the highest number of predictions (13,560), followed by MARS (3716) and l-regr (2594). These results demonstrate the strength of the regressors in terms of their extrapolation capability.  
\begin{table}
\begin{tabular}{c c c c} \hline
**Reter 1** & **Rater 2** & **Value of Kappa (x)** & **Level of Agreement** \\ \hline mlp & l-svr & 0.208516 & Fair \\ mlp & krnl-r & \(-\)0.000899 & No Agreement \\ l-regr & l-svr & 0.053874 & None to Slight \\ l-regr & krnl-r & 0.666457 & Substantial \\ l-svr & krnl-r & \(-\)0.000915 & No Agreement \\ \hline \end{tabular}
\end{table}
Table 4: _Cont._  
\begin{table}
\begin{tabular}{c c c c c} \hline
**Regressor** & **in Range** & **Regressor** & **in Range** & **Regressor** & **in Range** \\ \hline Spln-CFR & 13,560 & grad-b & 1227 & ada-b & 0 \\ MARS & 3716 & mlp & 1158 & lasso-l & 0 \\ l-regr & 2594 & xg-b & 826 & rf & 0 \\ l-svr & 2045 & krnl-r & 735 & sgd-r & 0 \\ \hline \end{tabular}
\end{table}
Table 5: Number of predictions by the different regressor methods which fall within the out-of-domain threshold range for the test set during 100 repeated runs on six datasets from [8].