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arxiv: 2606.28498 · v1 · pith:OZT5X4SZnew · submitted 2026-06-26 · ✦ hep-ph · hep-ex

Defining a Minimum Resolution for Unbinned Analyses

Manuel Szewc This is my paper

Pith reviewed 2026-06-30 00:43 UTC · model grok-4.3

classification ✦ hep-ph hep-ex
keywords Minimum Resolution LikelihoodFiducial Signal Regionmachine learning background estimationsignal strengthunbinned analysessystematic uncertaintiesdi-Higgs searches
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The pith

The Minimum Resolution Likelihood method defines a Fiducial Signal Region that converts systematic effects from machine learning background estimation into statistical uncertainties.

A machine-rendered reading of the paper's core claim, the machinery that carries it, and where it could break.

Collider analyses use machine learning models to estimate background likelihoods, but these can introduce hard-to-quantify systematic biases when estimating signal parameters. The paper presents the Minimum Resolution Likelihood method to define a Fiducial Signal Region that turns those systematic effects into statistical uncertainties. Demonstrations in toy examples and a realistic di-Higgs search with the HI-SIGMA technique show that signal strength estimates end up unbiased or consistent with zero. A reader would care because the approach addresses a practical obstacle to using advanced machine learning in unbinned collider data analysis without leaving hidden biases.

Core claim

We present the Minimum Resolution Likelihood (MRL) method, which defines a Fiducial Signal Region that effectively turns the systematic effects into statistical uncertainties. We show with examples that the resulting signal strength estimation is either unbiased or consistent with zero. We consider both toy examples and a realistic application based on the HI-SIGMA technique applied to di-Higgs searches.

What carries the argument

The Minimum Resolution Likelihood (MRL) method, which defines a Fiducial Signal Region to convert ML-induced systematic effects from background estimation into statistical uncertainties.

If this is right

  • Signal strength estimation remains unbiased when the MRL-defined region is applied.
  • When no signal is present, the estimated strength is consistent with zero.
  • Systematic effects from machine learning background models become statistical uncertainties.
  • The method works for both simplified toy cases and full di-Higgs searches using HI-SIGMA.

Where Pith is reading between the lines

These are editorial extensions of the paper, not claims the author makes directly.

  • The approach could extend to other machine-learning-driven searches in high-energy physics beyond the di-Higgs channel.
  • It might reduce reliance on separate systematic uncertainty modeling in future unbinned analyses.
  • Further validation in additional final states would test whether the conversion from systematics to statistics holds more broadly.

Load-bearing premise

Defining a Fiducial Signal Region via the Minimum Resolution Likelihood method can systematically convert all relevant systematic effects arising from ML background estimation into statistical uncertainties without introducing new unaccounted biases or selection effects.

What would settle it

A simulation or data analysis after MRL application in which the extracted signal strength exhibits a bias exceeding the size of the converted statistical uncertainties.

Figures

Figures reproduced from arXiv: 2606.28498 by Manuel Szewc.

Figure 1
Figure 1. Figure 1: The three fits done on a single pseudo-experiment for the 1D Gaussian [PITH_FULL_IMAGE:figures/full_fig_p009_1.png] view at source ↗
Figure 2
Figure 2. Figure 2: Lmin determination obtained by comparing a Calibration Region and a set of toys for the 1D Gaussian example. Left: The probability distribution of the model likelihood under the background model and the true background. Right: The fraction difference distribution as a function of the critical likelihood Lc obtained from comparing the toy and Calibration datasets. We observe how Lmin captures the crossing b… view at source ↗
Figure 3
Figure 3. Figure 3: 100 pseudo-experiment runs for different signal injection for the 1D [PITH_FULL_IMAGE:figures/full_fig_p011_3.png] view at source ↗
Figure 4
Figure 4. Figure 4: The three fits done on a single pseudo-experiment for the 2D example [PITH_FULL_IMAGE:figures/full_fig_p012_4.png] view at source ↗
Figure 5
Figure 5. Figure 5: Lmin determination obtained by comparing a Calibration Region and a set of toys for the 2D Gaussian example. Left: The probability distribution of the model likelihood under the background model and the true background. Right: The fraction difference distribution as a function of the critical likelihood Lc obtained from comparing the toy and Calibration datasets. We observe how Lmin captures the crossing b… view at source ↗
Figure 6
Figure 6. Figure 6: 100 pseudo-experiment runs for different signal injection for the 2D [PITH_FULL_IMAGE:figures/full_fig_p014_6.png] view at source ↗
Figure 7
Figure 7. Figure 7: A single run of HI-SIGMA+MRL , where p(⃗x|m ∈ SB) has not been masked. The figures show, in clockwise order: the mγγ distribution for the Signal Region and when applying the Fiducial Signal Region cuts, the signal strength test statistic landscape using four diffferent strategies, the fraction difference dis￾tribution as a function of the critical likelihood Lc obtained from comparing the toy and Calibrati… view at source ↗
Figure 8
Figure 8. Figure 8: A single run of HI-SIGMA+MRL , where p(⃗x|m ∈ SB) has been masked. The figures show, in clockwise order: the mγγ distribution for the Signal Region and when applying the Fiducial Signal Region cuts, the signal strength test statis￾tic landscape using four diffferent strategies, the fraction difference distribution as a function of the critical likelihood Lc obtained from comparing the toy and Cal￾ibration … view at source ↗
Figure 9
Figure 9. Figure 9: 5 pseudo-experiment runs for the di-Higgs dataset, with sideband mask [PITH_FULL_IMAGE:figures/full_fig_p018_9.png] view at source ↗
read the original abstract

Collider analyses combine rigorous statistical techniques with state-of-the-art Machine Learning models. However, when the latter are used directly to estimate the likelihood function of the background, hard to quantify systematic effects may bias the estimation of the relevant signal parameters. To address this problem, we present the Minimum Resolution Likelihood (MRL) method, which defines a Fiducial Signal Region that effectively turns the systematic effects into statistical uncertainties. We show with examples that the resulting signal strength estimation is either unbiased or consistent with zero. We consider both toy examples and a realistic application based on the HI-SIGMA technique applied to di-Higgs searches.

Editorial analysis

A structured set of objections, weighed in public.

Desk editor's note, referee report, simulated authors' rebuttal, and a circularity audit. Tearing a paper down is the easy half of reading it; the pith above is the substance, this is the friction.

Referee Report

2 major / 1 minor

Summary. The manuscript introduces the Minimum Resolution Likelihood (MRL) method, which defines a Fiducial Signal Region to convert systematic effects arising from machine-learning estimates of background likelihoods into statistical uncertainties in unbinned collider analyses. The central claim is that the resulting signal-strength estimation is either unbiased or consistent with zero, supported by toy-model examples and one realistic application to di-Higgs searches via the HI-SIGMA technique.

Significance. If the MRL construction can be shown to avoid new selection biases in general, the approach would offer a practical way to mitigate hard-to-quantify ML systematics in unbinned fits, strengthening the reliability of signal-parameter extraction. The provided examples supply initial evidence, but the absence of a general derivation or exhaustive validation against correlated error modes reduces the assessed impact.

major comments (2)
  1. [Abstract] Abstract: the assertion that signal-strength estimation is unbiased or consistent with zero is presented without derivation, validation details, or quantitative checks, leaving open whether the toy models and single application actually support the claim against ML systematics.
  2. [Toy examples and HI-SIGMA application] Toy examples and HI-SIGMA application: the demonstrations are confined to specific cases; no exhaustive scan over ML error modes (e.g., shape distortions correlated with signal-like kinematics) is reported, so the assumption that the fiducial-region definition introduces no new selection biases remains untested and load-bearing for the unbiased claim.
minor comments (1)
  1. The term 'Fiducial Signal Region' is introduced as a new construct; a brief comparison to existing fiducial definitions in the literature would improve clarity.

Simulated Author's Rebuttal

2 responses · 0 unresolved

We thank the referee for their constructive review and for identifying areas where the presentation of our results can be strengthened. We respond to each major comment below and indicate the revisions we will make.

read point-by-point responses

  1. Referee: [Abstract] Abstract: the assertion that signal-strength estimation is unbiased or consistent with zero is presented without derivation, validation details, or quantitative checks, leaving open whether the toy models and single application actually support the claim against ML systematics.

    Authors: The abstract summarizes the empirical findings reported in Sections 3 and 4. While no general analytic derivation is provided, the toy-model studies and HI-SIGMA application contain explicit quantitative checks (bias measurements, pull distributions, and coverage tests) demonstrating that the extracted signal strength is unbiased or consistent with zero under the tested ML-induced systematics. We will revise the abstract to state explicitly that the property is shown empirically in the presented examples and to reference the relevant validation sections. revision: yes

  2. Referee: [Toy examples and HI-SIGMA application] Toy examples and HI-SIGMA application: the demonstrations are confined to specific cases; no exhaustive scan over ML error modes (e.g., shape distortions correlated with signal-like kinematics) is reported, so the assumption that the fiducial-region definition introduces no new selection biases remains untested and load-bearing for the unbiased claim.

    Authors: We agree that the validation is limited to the specific toy configurations and the single realistic di-Higgs application described. An exhaustive scan over all conceivable ML error modes, including arbitrary correlated shape distortions, lies outside the scope of this work. The MRL construction is intended to convert ML systematics into statistical uncertainties by construction of the fiducial region; the examples illustrate this mechanism but do not constitute a proof against every possible bias. We will add a dedicated limitations paragraph discussing the representativeness of the tested cases and the possibility of residual selection effects, while retaining the claim that no new biases were observed in the reported studies. revision: partial

Circularity Check

0 steps flagged

No circularity: MRL method and unbiasedness shown via examples, not by construction

full rationale

The paper introduces the Minimum Resolution Likelihood (MRL) method as a definition for a fiducial signal region that converts ML background systematics into statistical uncertainties. It then validates the resulting signal strength estimation (unbiased or consistent with zero) through explicit toy examples and one HI-SIGMA di-Higgs application. No load-bearing step reduces by the paper's own equations to a fitted input renamed as prediction, a self-referential definition, or a self-citation chain; the central claim rests on empirical demonstration rather than algebraic identity or imported uniqueness theorems. This is the most common honest outcome for a methods paper whose result is externally falsifiable via the provided examples.

Axiom & Free-Parameter Ledger

0 free parameters · 0 axioms · 1 invented entities

Abstract-only review; no explicit free parameters, axioms, or invented entities beyond the named method itself can be identified.

invented entities (1)
  • Fiducial Signal Region no independent evidence
    purpose: Region in which ML systematic effects are redefined as statistical uncertainties
    Central construct of the MRL method introduced to achieve the claimed bias reduction

pith-pipeline@v0.9.1-grok · 5615 in / 1102 out tokens · 27275 ms · 2026-06-30T00:43:19.644943+00:00 · methodology

discussion (0)

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