Applying Self-organizing Maps to the Inverse Problem

Abstract

In the inverse problem in particle physics, given an unexpected observation, one aims to identify a unique choice from amongst several competing hypotheses. We explore a novel approach of applying self-organizing maps to the inverse problem in a search for vector-like leptons in a trilepton final state. We define an approach combining the inherent clustering of these maps and elements of supervised learning. We compare the performance of this approach with a multiclassfying neural network. We find that the method using self-organizing maps competes well (despite not using any standard model processes in the training), and provides additional tools that would help characterize any observed excesses in searches.

Figures (14)

• Figure 1: The distributions of the kinematic variables are shown for the selected three-lepton events, for three different VLL mass hypotheses. The top row (from left to right) shows , , mos$^{\mathrm{high}}$ and $m_{\ell\ell\ell}$, and the bottom row (from left to right) shows $m_{\mathrm{T}}^{\mathrm{high}}$, $\pt^{\ell j}$, mos$^{\mathrm{low}}$ and $m_{\mathrm{T}}^{\mathrm{all lep}}$.
• Figure 2: The one-versus-others ROC curves for the multiclassifying DNN for the three signal hypotheses that the DNN is trained to identify.
• Figure 3: The distribution of the scores of the observed events for case 1 (left) and case 2 (right) on the four output neurons of the DNN. The median value for each distribution is shown in the legend. For case 1, the highest median is for the $n1000$ score, while for case 2, it is for the $n1500$ score.
• Figure 4: The distribution of the output neuron scores of the observed events for case 3. The left plot shows the distributions for all events, while the right plot shows the distribution after requiring that $nSM$ score $<0.8$. The median value for each distribution is shown in the legend.
• Figure 5: The distribution of the output neuron scores of the observed events for case 4. The left plot shows the distributions for all events, while the right plot shows the distribution after requiring that $nSM$ score $<0.8$. The median value for each distribution is shown in the legend.