Multivariate methods and the search for single top-quark production in association with a $W$ boson in ATLAS

This thesis describes three machine learning algorithms that can be used for physics analyses. The first is a density estimator that was derived from the Green’s function identity of the Laplace operator and is capable of tagging data samples according to the signal purity. This latter task can also be performed with regression methods, and such an algorithm was implemented based on fast multi-dimensional polynomial regression. The accuracy was improved with a decision tree using smooth boundaries. Both methods apply rigorous checks against overtraining to make sure the results are drawn from statistically significant features. These two methods were applied in the search for the single top-quark production with a $W$ boson. Their separation power differ highly in favour for the regression method, mainly because it can exploit the extra information available during training. The third method is an unsupervised learning algorithm that offers finding an optimal coordinate system for a sample in the sense of maximal information entropy, which may aid future methods to model data.