Profiling systematic uncertainties in Simulation-Based Inference with Factorizable Normalizing Flows

TL;DR

This paper introduces a novel simulation-based inference framework using Factorizable Normalizing Flows to efficiently profile systematic uncertainties and measure multivariate distributions, significantly reducing computational costs in complex analyses.

Contribution

It proposes a new method combining Factorizable Normalizing Flows with an amortized training strategy for simultaneous distribution extraction and nuisance profiling in SBI.

Findings

Successfully models systematic variations as parametric deformations.

Achieves efficient profiling without repetitive training during likelihood scans.

Validated on a synthetic high-energy physics dataset with multiple systematic sources.

Abstract

Unbinned likelihood fits aim at maximizing the information one can extract from experimental data, yet their application in realistic statistical analyses is often hindered by the computational cost of profiling systematic uncertainties. Additionally, current machine learning-based inference methods are typically limited to estimating scalar parameters in a multidimensional space rather than full differential distributions. We propose a general framework for Simulation-Based Inference (SBI) that efficiently profiles nuisance parameters while measuring multivariate Distributions of Interest (DoI), defined as learnable invertible transformations of the feature space. We introduce Factorizable Normalizing Flows to model systematic variations as parametric deformations of a nominal density, preserving tractability without combinatorial explosion. Crucially, we develop an amortized training strategy that learns the conditional dependence of the DoI on nuisance parameters in a single optimization process, bypassing the need for repetitive training during the likelihood scan. This allows for the simultaneous extraction of the underlying distribution and the robust profiling of nuisances. The method is validated on a synthetic dataset emulating a high-energy physics measurement with multiple systematic sources, demonstrating its potential for unbinned, functional measurements in complex analyses.