Likelihood free inference with advanced machine learning techniques

Abstract

Although many theories locate hypothetical phenomena beyond the Standard Model at energy scales far above the current experimental reach, tiny deviations from the Standard Model prediction are expected to show in the tails of data collected with the Compact Muon Solenoid experiment at the Large Hadron Collider at CERN. These deviations can be described through the insertion of effective operators of mass dimension higher than four, treating the Standard Model as a low-energy approximation of the hypothetical high energy theory. In this thesis, we adopt novel machine learning techniques based on simulation (simulation-based inference) to teach the machine the optimal test statistic according to the Neyman-Pearson lemma for four-fermion operator insertions in four-top production and production of two top and two bottom quarks. The centerpiece of this approach consists in exploiting the polynomial structure of the effective field theory prediction as a function of the coefficients of the operators, i.e., the Wilson coefficients. Hence, learning only a small number of coefficient functions allows to parametrize an optimal classifier in the full parameter space. With the learned coefficient functions at hand, we then set nuisance-free limits in an unbinned likelihood ratio test up to quadratic order in the polynomial expansion. In this way, we investigate the neural network's performance in learning the yield- and shape-related modifications, thus probing new forces between four heavy quarks. On the machine learning side, we combine Deep Neural Networks with Long Short Time Memory layers to extract information not only from scalar observables, but also from the variable length jet system in analogy to speech recognition. By also probing this Multivariate Analysis setup in the simpler, more robust setting of multi-classification, we test, optimize and cross-validate the configuration of the network. In instantiating a complete workflow of sample generation, training with simulation-based inference, and the limit setting procedure, we obtain projected limits on the Wilson coefficients of four-fermion operators in tttt and ttbb with and without tt background. Thus, we demonstrate the potential of these novel neural network architectures and machine learning techniques for future analyses.