Deep Regression of Muon Energy with a K-Nearest Neighbor Algorithm

Within the context of studies for novel measurement solutions for future particle physics experiments, we developed a performant kNN-based regressor to infer the energy of highly-relativistic muons from the pattern of their radiation losses in a dense and granular calorimeter. The regressor is based on a pool of weak kNN learners, which learn by adapting weights and biases to each training event through stochastic gradient descent. The effective number of parameters optimized by the procedure is in the 60 millions range, thus comparable to that of large deep learning architectures. We test the performance of the regressor on the considered application by comparing it to that of several machine learning algorithms, showing comparable accuracy to that achieved by boosted decision trees and neural networks.