Inferring correlated distributions: boosted top jets

TL;DR

This paper develops a Bayesian density-estimation framework for collider analyses that explicitly accounts for correlations between observables within each class. Starting from a conditionally independent multinomial model, it introduces a simulation-assisted extension with transfer matrices $C^{k}_{ij;i'j'}$ derived from MC simulations to capture correlations between observables such as $N_{\mathrm{clus}}$ and jet mass $\mathrm{Mass}$. The transfer matrices are estimated via an EM algorithm on MC data, and posterior inference is performed with Hamiltonian Monte Carlo, enabling unbiased estimates of class fractions and marginals even when simulations are biased. Using the Top Quark Tagging Reference Dataset, the authors show that including correlations yields markedly improved reconstructions of top and QCD jet distributions, as quantified by KL divergences and feature posteriors, particularly for boosted top jets; priors influence convergence and the effectiveness of corrections, with looser priors generally allowing data to dominate as sample size grows. The work provides a practical, extensible framework for data-driven density estimation in high-dimensional collider analyses and suggests paths toward learning correlations from data and expanding to additional jet classes.

Abstract

Improving the understanding of signal and background distributions in signal-region is a valuable key to enhance any analysis in collider physics. This is usually a difficult task because -- among others -- signal and backgrounds are hard to discriminate in signal-region, simulations may reach a limit of reliability if they need to model non-perturbative QCD, and distributions are multi-dimensional and many times may be correlated within each class. Bayesian density estimation is a technique that leverages prior knowledge and data correlations to effectively extract information from data in signal-region. In this work we extend previous works on data-driven mixture models for meaningful unsupervised signal extraction in collider physics to incorporate correlations between features. Using a standard dataset of top and QCD jets, we show how simulators, despite having an expected bias, can be used to inject sufficient inductive nuance into an inference model in terms of priors to then be corrected by data and estimate the true correlated distributions between features within each class. We compare the model with and without correlations to show how the signal extraction is sensitive to their inclusion and we quantify the improvement due to the inclusion of correlations using both supervised and unsupervised metrics.

Figures (12)

• Figure 1: Graphical model for the conditionally independent model. Solid white (blue) circles represent latent (observed) variables. Boxes represent the repeated sampling of variables.
• Figure 2: Graphical model for the simulation-assisted model with the addition of the transfer matrices, which are hyperparameters at this level.
• Figure 3: True two-dimensional distributions for QCD and top jets. We observe a non-negligible correlation in the top distribution.
• Figure 4: Inferred probability of top jets $\pi_1$ as a function of the number of events in the test samples for $\Sigma = 100$. The blue(orange) points stand for this probability for the model with(without) correlations.
• Figure 5: Number of clusters, mass and the probability of top jets distributions for the model with (bottom row) and without (upper row) correlations with $\Sigma = 100$. See text for the details.