Machine Learning techniques to search for New Physics

The purpose of this project consisted in formulating the classic hypothesis-statistical construction as the training of a neural network with a customized loss function. Doing so, one could generalize searches for physics beyond the standard model (e.g., those at the LHC), replacing model-dependendent signal hypotheses with the broad class of signal shapes that a given network could learn. Starting from the univariate case, the aim has been finding out a possible way to extend it to multivariate cases. Two different approaches were considered: as a first approach, multivariate problems were treated as a ”sum” of univariate ones, which in terms of algorithms means applying the 1D algorithm to each distinct 1D variable and then combining the results. This method was guaranteed to be efficient only if all the variables were uncorrelated, otherwise could provide a loss of performance. Thus, alternative ways to combine the univariate variables taking care of the correlations were also discussed. To speed up the computation an optimization of the 1D algorithm was implemented. Further analysis of the 1D algorithm allowed to define a heuristic method for tuning both 1D and 2D algorithms only based on background samples. Using this algorithm, the divergence of the algorithm and instability were prevented allowing the search for extensions to multivariate hypothesis tests to be carried on.