# Application of Machine Learning Ensemble Methods to ASTRI Mini-Array Cherenkov Event Reconstruction
## 10 Discussion  
In this work, we have investigated novel Machine Learning techniques distinct from the existing methods implemented in A-SciSoft, the official data reduction and analysis software of the ASTRI project, and showed the effectiveness of their application on simulated ASTRI Mini-Array data. Figure 17: On-axis energy bias achieved with the best Machine Learning methods (orange points) against the benchmark (A-SciSoft, blue points), before (**Up**) and after (**Bottom**) the correction of the energy bias. We have restricted our studies to the case of on-axis gamma-ray analysis. Generalization to off-axis gamma-ray samples may be carried out in future works. However, given the rather flat acceptance of the ASTRI Mini-Array performance as a function of off-axis [7], we expect that the methods investigated in this work can also be effective in the off-axis case and give similar results, in terms of gamma/hadron separation and energy reconstruction, to those found in the on-axis analysis case. We have assessed and compared several supervised Machine Learning methods for gamma/hadron segregation and energy estimation, including the Random Forest method, Extra Trees method, and Extreme Gradient Boosting (XGB). Through extensive testing and optimization, we identified two Stacking Ensemble methods as the most effective for our purposes. For gamma/hadron segregation, the optimal Stacking Ensemble method was composed of 42% Extra Trees, 28% Random Forest, and 30% XGB. This composition was determined based on the performance of each individual method in the ensemble, and the specific values were derived through a process of hyperparameter tuning and cross-validation. For energy estimation, the optimal Stacking Ensemble method was composed of 45% XGB, 27.5% Extra Trees, and 27.5% Random Forest. Once again, these weights were determined through extensive testing and optimization to provide the best performance for our specific dataset and analysis. By carefully selecting and fine-tuning the composition of the Stacking Ensemble methods, we were able to achieve high accuracy and sensitivity in both gamma/hadron segregation and energy estimation. We observe from the results shown in the previous sections that the proposed Stacking Ensemble methods demonstrate superior performance compared to the more classical Random Forest method for the ASTRI Mini-Array event reconstruction both for the energy resolution and bias and for the gamma/hadron discrimination. The most significant results we obtained from our study can be summarized as follows:  
* The investigated new Machine Learning methods can provide a performance, in terms of sensitivity, angular resolution, and energy, that is in line if not better than the standard methods implemented in A-SciSoft (based on Random Forest);
* In particular, the new energy reconstruction methods provide a significant reduction in the energy bias with respect to that obtained by the standard methods; this is particularly important in view of the reconstruction of real data (soon to be taken with the ASTRI Mini-Array);
* The results obtained with the new reconstruction methods, which are completely independent of the standard ones, provide an important verification of the robustness of the current standard reconstruction chain implemented in A-SciSoft, which have already been used to obtain detection of the Crab Nebula source with the ASTRI-Horn prototype [26] and to evaluate the performance of the Mini-Array [7]. In future investigations, to ensure the reliability and robustness of our findings, we plan to include a sample of diffuse gamma ray events in our analysis. These events are characterized by having directions uniformly distributed throughout the field of view, which helps us eliminate any potential bias stemming from a preferential source direction present in the data used thus far. Nevertheless, we anticipate that the performance of our method will remain consistent.