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arxiv: 2604.11223 · v1 · submitted 2026-04-13 · 📊 stat.ML · cs.AI· cs.LG

Regional Explanations: Bridging Local and Global Variable Importance

Salim I. Amoukou , Nicolas J-B. Brunel This is my paper

Pith reviewed 2026-05-10 15:51 UTC · model grok-4.3

classification 📊 stat.ML cs.AIcs.LG
keywords local attributionglobal attributionfeature importanceR-LOCOShapley valuesLIMEregional explanationsvariable importance
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The pith

R-LOCO segments the input space into regions of similar feature importance to produce faithful local attributions.

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

The paper shows that Local Shapley Values and LIME can assign importance to features that neither affect the model output nor correlate with relevant features, even when features are independent and calculations are exact. It argues that sound local methods must avoid such assignments. R-LOCO corrects this by dividing the input space into regions where feature importances behave alike, then running global attribution inside each region and assigning an instance's contributions according to its region. This yields local explanations that stay stable and specific without losing accuracy on irrelevant features.

Core claim

R-LOCO segments the input space into regions with similar feature importance characteristics. It then applies global attribution methods within these regions, deriving an instance's feature contributions from its regional membership. This approach delivers more faithful local attributions while avoiding local explanation instability and preserving instance-specific detail.

What carries the argument

R-LOCO (Regional Leave Out COvariates), which partitions the input space into regions sharing similar feature importance patterns and derives per-instance contributions from regional membership using global methods.

Load-bearing premise

The input space can be segmented into regions with similar feature importance characteristics in a way that delivers more faithful local attributions while preserving instance-specific detail.

What would settle it

A linear model with independent features where some coefficients are zero; if R-LOCO still assigns non-zero importance to those zero-coefficient features inside any region, the claim fails.

Figures

Figures reproduced from arXiv: 2604.11223 by Nicolas J-B. Brunel, Salim I. Amoukou.

Figure 1
Figure 1. Figure 1: Diabetes dataset [PITH_FULL_IMAGE:figures/full_fig_p007_1.png] view at source ↗
Figure 3
Figure 3. Figure 3: Feature attributions from R-LOCO and R-LOCOIC on the first-order model, highlighting the intra-group variance of feature importance [PITH_FULL_IMAGE:figures/full_fig_p008_3.png] view at source ↗
Figure 5
Figure 5. Figure 5: Variability of LIME coefficients wrt bandwidth selection on the German credit dataset (n = 1000, p = 20) from UCI [Dua and Graff, 2017] A primary concern with LIME stems from its reliance on arbitrary heuristics in its definition. Specif￾ically, choosing the sampling distribution P ′ poses challenges, as the commonly used distribution disregards feature dependencies, and there is no guarantee that the mode… view at source ↗
Figure 6
Figure 6. Figure 6: This diagram presents and contrasts our proposed method ( [PITH_FULL_IMAGE:figures/full_fig_p020_6.png] view at source ↗
read the original abstract

We analyze two widely used local attribution methods, Local Shapley Values and LIME, which aim to quantify the contribution of a feature value $x_i$ to a specific prediction $f(x_1, \dots, x_p)$. Despite their widespread use, we identify fundamental limitations in their ability to reliably detect locally important features, even under ideal conditions with exact computations and independent features. We argue that a sound local attribution method should not assign importance to features that neither influence the model output (e.g., features with zero coefficients in a linear model) nor exhibit statistical dependence with functionality-relevant features. We demonstrate that both Local SV and LIME violate this fundamental principle. To address this, we propose R-LOCO (Regional Leave Out COvariates), which bridges the gap between local and global explanations and provides more accurate attributions. R-LOCO segments the input space into regions with similar feature importance characteristics. It then applies global attribution methods within these regions, deriving an instance's feature contributions from its regional membership. This approach delivers more faithful local attributions while avoiding local explanation instability and preserving instance-specific detail often lost in global methods.

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

3 major / 1 minor

Summary. The paper claims that Local Shapley Values and LIME violate a fundamental principle for local attributions by assigning importance to features that neither influence the model output nor exhibit statistical dependence with relevant features, even under exact computation and feature independence. It proposes R-LOCO, which segments the input space into regions with similar feature importance characteristics and then applies global attribution methods within those regions to derive instance-specific feature contributions, aiming to deliver more faithful local attributions while avoiding instability.

Significance. If the segmentation procedure can be made explicit and the empirical demonstrations substantiated, R-LOCO would offer a principled way to combine the stability of global methods with instance-level detail, addressing a recognized weakness in local explanation techniques for machine learning models.

major comments (3)
  1. [Abstract] Abstract: the demonstrations that Local SV and LIME violate the stated principle are asserted without any experimental details, baselines, error bars, datasets, or derivation steps, so the central empirical claim cannot be verified from the provided text.
  2. [R-LOCO proposal] R-LOCO description: the segmentation of the input space into regions with similar feature importance is load-bearing for the entire approach, yet no concrete algorithm, clustering criterion (e.g., on partial dependence, gradients, or feature values), or stability guarantee is supplied; without this, it is impossible to determine whether regions are reproducible, non-arbitrary, or actually preserve locality rather than collapse to smoothed global attributions.
  3. [Method and experiments] Method and experiments: the claim that R-LOCO provides more accurate and faithful attributions than Local SV or LIME lacks any reported comparisons, metrics, or ablation on the effect of region granularity, leaving open whether the regional fix resolves the identified violations or merely trades one form of instability for another.
minor comments (1)
  1. Notation for feature importance and regional membership could be clarified with explicit equations to avoid ambiguity when deriving instance contributions from regional membership.

Simulated Author's Rebuttal

3 responses · 0 unresolved

We are grateful to the referee for their constructive feedback on our paper 'Regional Explanations: Bridging Local and Global Variable Importance'. We address each of the major comments below and outline the revisions we will make to strengthen the manuscript.

read point-by-point responses

  1. Referee: [Abstract] Abstract: the demonstrations that Local SV and LIME violate the stated principle are asserted without any experimental details, baselines, error bars, datasets, or derivation steps, so the central empirical claim cannot be verified from the provided text.

    Authors: The abstract summarizes the key findings, but we acknowledge it does not include experimental specifics. The full paper provides theoretical derivations in Section 2 demonstrating the violations for Local Shapley Values and LIME, even with exact computations and independent features, using linear models as examples. Synthetic experiments are presented in Section 4. To improve verifiability, we will revise the abstract to include a high-level description of the experimental validation and key results. revision: yes

  2. Referee: [R-LOCO proposal] R-LOCO description: the segmentation of the input space into regions with similar feature importance is load-bearing for the entire approach, yet no concrete algorithm, clustering criterion (e.g., on partial dependence, gradients, or feature values), or stability guarantee is supplied; without this, it is impossible to determine whether regions are reproducible, non-arbitrary, or actually preserve locality rather than collapse to smoothed global attributions.

    Authors: We recognize that the segmentation procedure is crucial. The manuscript introduces R-LOCO as segmenting the input space into regions with similar feature importance characteristics before applying global methods regionally. However, the specific implementation details were not fully elaborated. In the revision, we will provide an explicit algorithm, including the clustering method (e.g., based on feature importance estimates like gradients), criteria for region formation, and discussion of reproducibility and how it maintains locality without reducing to global attributions. revision: yes

  3. Referee: [Method and experiments] Method and experiments: the claim that R-LOCO provides more accurate and faithful attributions than Local SV or LIME lacks any reported comparisons, metrics, or ablation on the effect of region granularity, leaving open whether the regional fix resolves the identified violations or merely trades one form of instability for another.

    Authors: We agree that empirical validation is necessary to support the claims. The current version focuses on the conceptual advantages of R-LOCO in avoiding the identified violations. We will expand the experiments section to include direct comparisons with Local SV and LIME using appropriate metrics for attribution accuracy and faithfulness, along with ablations on region granularity to assess its impact on stability and performance. revision: yes

Circularity Check

0 steps flagged

No significant circularity in the derivation or proposal of R-LOCO

full rationale

The paper identifies limitations in Local SV and LIME by arguing they violate a stated principle on feature attribution, then proposes R-LOCO as an algorithmic alternative that segments the input space into regions of similar feature importance characteristics before applying global methods within regions. No equations, derivations, or steps are shown that reduce the regional segmentation, the resulting attributions, or the core claims to the paper's own inputs by construction (e.g., no fitted parameters renamed as predictions, no self-definitional loops, and no load-bearing self-citations or ansatzes). The method is presented as an independent bridge between local and global explanations rather than a result forced by its own definitions or prior self-referential work. The derivation chain is therefore self-contained against external benchmarks.

Axiom & Free-Parameter Ledger

1 free parameters · 1 axioms · 0 invented entities

Abstract-only review prevents exhaustive audit. R-LOCO rests on the domain assumption that feature importance is regionally consistent and that global methods applied regionally yield faithful instance attributions; segmentation likely requires free parameters (e.g., number of regions or clustering thresholds) not specified here.

free parameters (1)
  • region segmentation parameters
    Number of regions, clustering thresholds, or similarity metrics for dividing input space; required for the method but unspecified in abstract.
axioms (1)
  • domain assumption Feature importance characteristics are consistent within defined regions of the input space.
    Central premise of R-LOCO as stated in the abstract.

pith-pipeline@v0.9.0 · 5501 in / 1481 out tokens · 45385 ms · 2026-05-10T15:51:51.353073+00:00 · methodology

discussion (0)

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Reference graph

Works this paper leans on

7 extracted references · 7 canonical work pages

  1. [1]

    By definition, the global piecewise model f(x) = Pm k=1 fk(x)1x∈Ak simplifies to the active local model for any point within its region

    Analysis of the full model, f(x l):For any observation (xl, yl)∈C k⋆, our core assumption implies xl ∈A k⋆. By definition, the global piecewise model f(x) = Pm k=1 fk(x)1x∈Ak simplifies to the active local model for any point within its region. Therefore, for all xl ∈C k⋆: f(x l) =f k⋆(xl) =a T k⋆ xl +b k⋆ This shows that the first term, V(f(x l), yl), de...

    work page

  2. [2]

    contaminated

    Analysis of the reduced model, f−j(xl):The proof is particularly concerned with features j that are not globally important, meaning they are not used to define the region boundaries. Let G={i∈[p]| ∃ks.t.A i,k ̸=R} be the set of globally important features. If j /∈G, the conditionx∈A k⋆ does not depend on the value ofx j. Consequently, for any xl ∈C k⋆ ⊆A ...

    work page 2017

  3. [3]

    The importance-space centroid for RA is Cγ,A = 1 3 , 1 3 ,0,0,0, 1 3

    = 1/3. The importance-space centroid for RA is Cγ,A = 1 3 , 1 3 ,0,0,0, 1 3 . By symmetry, for X∈R B (wheref(X) =X 3 +X 4), the centroid isC γ,B = 0,0, 1 3 , 1 3 ,0, 1 3 . Decision Rule and InterpretationThe K-Means separating direction in this space is: Cγ,A −C γ,B = 1 3 , 1 3 ,− 1 3 ,− 1 3 ,0,0 . This decision ruleonlydepends on the components (∆1,∆ 2,∆...

    work page

  4. [4]

    For each inputx, compute the feature importance scores usingA(x)

    work page

  5. [5]

    • The bottom-kleast important features (Bottom-kIndices)

    Identify the indices of: • The top-kmost important features (Top-kIndices). • The bottom-kleast important features (Bottom-kIndices)

    work page

  6. [6]

    ground truth explanation

    Create two modified versions ofx: xmasked,top-k :Replace values at Top-kindices with zero, xmasked,bottom-k :Replace values at Bottom-kindices with zero. H.3 Error Calculation We compute the average model error over the dataset under three conditions: Original Average Error (Baseline): AvgErrorOriginal = 1 n X (x,y)∈D E(x, y) Top-kMasked Average Error: Av...

    work page 2021

  7. [7]

    Guidelines: • The answer NA means that the paper does not involve crowdsourcing nor research with human subjects

    Institutional review board (IRB) approvals or equivalent for research with human subjects Question: Does the paper describe potential risks incurred by study participants, whether such risks were disclosed to the subjects, and whether Institutional Review Board (IRB) approvals (or an equivalent approval/review based on the requirements of your country or ...

    work page 2025