Iterative HOMER with uncertainties

Abstract

We present iHOMER, an iterative version of the HOMER method to extract Lund fragmentation functions from experimental data. Through iterations, we address the information gap between latent and observable phase spaces and systematically remove bias. To quantify uncertainties on the inferred weights, we use a combination of Bayesian neural networks and uncertainty-aware regression. We find that the combination of iterations and uncertainty quantification produces well-calibrated weights that accurately reproduce the data distribution. A parametric closure test shows that the iteratively learned fragmentation function is compatible with the true fragmentation function.

Figures (15)

• Figure 1: Illustrative diagram of the HOMER method and its iHOMER extension: HOMER learns a data-driven fragmentation function via the reweighting and factorization steps. iHOMER improves upon its performance by iterating these steps.
• Figure 2: Schematic visualization of iHOMER, including uncertainties and iterations. Step 1 and Step 2 networks are defined by their weights $\theta$ and $\phi$ respectively.
• Figure 3: (Left) Step 1 classifier AUCs over iterations. For 10 independent runs, the points show the BNN-averaged value and (negligible) associated uncertainty estimated from 10 BNN samples in the test dataset. The gray histogram shows the iterations selected by the stopping criterion. (Right) Relative effective sample size over iterations, computed for event- and history-level iHOMER weights.
• Figure 4: Step 1 log-weight distributions for iteration 4. The histogram count and uncertainty comes from computing mean and standard deviation of 10 BNN samples, respectively, allowing count values below 1.
• Figure 5: High-level observable reweighting, comparing iHOMER with a naive parametric fit. The bottom subpanel shows the ratio to the exact reweighting of the simulation, but the $\chi^2/N_\text{bins}$ values indicated in the legend evaluate the agreement with "Data".