## 5 Comparison of Popular MI Techniques beyond BDTs with Adaboost
When looking at the global picture, we see that PyTorch performs better with the high-level features, while for Keras, the results tend to be better when choosing all features. The situation is slightly more balanced for Skalearn, although all features tend to provide a worse performance. Additionally, the use of low-level features does not provide the best performance in every library, but this still does not dramatically affect the power of discrimination, which indicates that the algorithms we use are robust. For reference, all the features used in this study can be found in Appendix A. Note that, as an additional element to judge the best choice, fewer features and smaller datasets can help to train the models faster and is more manageable in terms of, e.g., grid searches. \begin{table}
\begin{tabular}{c c c} \hline \(B\to\mu^{+}\mu^{-}\) & high-level features–high stats & PyTorch \\ \(B\to\pi^{+}\pi^{-}\) & high-level features–high stats & PyTorch \\ \(B\to 3\pi\) & high-level features–high stats & PyTorch \\ \(B\to 4\pi\) & high-level features–high stats & PyTorch \\ \hline \end{tabular}
\end{table} 
Table 10: Best training option for the data and library for each analysis. \begin{table}
\begin{tabular}{c c c c} \hline \(B\to 4\pi\) & PyTorch & Keras & Skalearn \\ \hline low-level features–low stats & 0.958 & 0.956 & 0.955 \\ low-level features–high stats & 0.961 & 0.961 & 0.953 \\ high-level features–low stats & 0.960 & 0.958 & 0.958 \\ high-level features–high stats & 0.967 & 0.961 & 0.964 \\ all features–low stats & 0.960 & 0.961 & 0.954 \\ all features–high stats & 0.967 & 0.964 & 0.964 \\ \hline \end{tabular}
\end{table} 
Table 8: \(B\to 4\pi\) channel: AUC scores for the different classifiers with all the libraries. \begin{table}
\begin{tabular}{c c c c c} \hline \hline  & \(B\to\mu^{+}\mu^{-}\) & \(B\to\pi^{+}\pi^{-}\) & \(B\to 3\pi\) & \(B\to 4\pi\) \\ \hline low-level features–low stats & PyTorch & PyTorch & PyTorch & PyTorch \\ low-level features–high stats & PyTorch & PyTorch & PyTorch & Keras \\ high-level features–low stats & PyTorch & PyTorch & PyTorch & PyTorch \\ high-level features–high stats & PyTorch & PyTorch & PyTorch & PyTorch \\ all features–low stats & PyTorch & PyTorch & PyTorch & PyTorch \\ all features–high stats & PyTorch & PyTorch & PyTorch & PyTorch \\ \hline \hline \end{tabular}
\end{table} 
Table 9: Best library for each analysis and each training option for the data. The convenience of using BDTs or NNs has long been a subject of discussion in the particle physics literature. For instance, Reference [52] discusses how BDTs can improve the performance of NNs for PID in neutrino detectors. Note that these results do not include some of the latest progress concerning the training of NNs, which provided essential improvements in the last decade [53]. It is is remarkable how these improvements recover NNs as the best solution in the same dataset [54]. Other examples, which are more related to the type of analysis we present here, look into different algorithms in datasets that are often used by the ATLAS and CMS experiments, finding consistently better or similar results when comparing NNs to BDTs with different types of boosting, such as XGBoost [55; 56]. One of the first attempts to apply QML in a data sample comparable to ours, composed of \(B\) meson decays [57], is also notable. The AUC achieved in this study manages to improve on those of other classical methods, although no NNs are included. Reference [58] compares QML algorithms to NNs in a different HEP dataset, achieving better or similar AUC scores, although this depends on the size of the training sample. Another interesting example concerns the use of these algorithms for the simulation of HEP data [59], where, again, NNs beat BDTs in terms of regression. Regarding the libraries used, the advantages of using PyTorch to deal with NNs are becoming well known, and several toolkits based on it have recently been developed for different HEP applications. Examples include Lumin [60; 61] and Ariadne [7].