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REVIEW 5 major objections 5 minor 51 references

Multi-criteria Rank-based Aggregation for Explainable AI

T0 review · 5 major / 5 minor · reviewed 2026-08-07 · deepseek-v4-flash

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Pith's one-line read This paper claims that weighting LIME, SHAP, and ANCHOR explanations by multi-criteria performance scores into a single rank aggregation produces more robust explanations, consistently best or second-best on complexity and faithfulness…

desk verdict The MCDM aggregation framework is a reasonable idea, but the NRC metric defined in Eq. (1) is constant for any tie-free ranking, so the headline robustness results cannot follow from the stated formulas. read the letter →

arxiv 2505.24612 v1 pith:YXDOMOVI submitted 2025-05-30 cs.LG

Sujoy Chatterjee , Everton Romanzini Colombo , Marcos Medeiros Raimundo This is my paper
classification cs.LG
keywords explainableAImulti-criteriadecisionmakingrankaggregationTOPSISWSUMLIMESHAPexplanationrobustness
verification ladder T0 review T1 audit T2 compute T3 formal

The pith

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

The reading

Different explainers give conflicting feature rankings for the same prediction, and no single explainer wins on all quality axes: complexity, faithfulness, and stability trade off against each other. This paper tries to make explanations more robust by treating explanation choice as a multi-criteria decision problem: score each component explainer with new rank-based versions of the three metrics, use a multi-criteria method (TOPSIS or EDAS) to turn those scores into weights, then fuse the explainers' feature rankings with a weighted rank aggregation (WSUM). The central claim is that the resulting aggregate explanation is more robust than any individual explainer, consistently achieving the best or second-best normalized rank-based complexity and faithfulness while avoiding the worst stability score across five public datasets. If true, this gives practitioners a way to combine off-the-shelf explainers into a single, more dependable local explanation without retraining the black-box model.

What carries the argument

The carrying mechanism is a two-stage weighting procedure: rank-based metrics defined directly on feature-importance rankings, followed by MCDM-to-rank-aggregation fusion. The rank-based metrics—NRC $\mu_{\text{NRC}}(f,g;x)=\left(\sum_{i=1}^{d}1/R_i\right)\log(d+1)(1+\alpha\,\operatorname{std}(R))$, rank-based faithfulness using the correlation between inverse ranks and prediction change, and Spearman stability on autoencoder-noised data—let explainers be scored in ranking space. TOPSIS then assigns each explainer a closeness-to-ideal weight, and WSUM combines the rankings with those weights using squared inverse ranks; this is what produces a single aggregate ranking that inherits the best aspects of its components.

What would settle it

Take a dataset with known ground-truth feature importance (for example, a synthetic linear model where the true weights are known), run the full TOPSIS-WSUM aggregation, and check whether the aggregate ranking recovers the true features at least as well as the best single explainer; separately re-run the experiment with $\alpha=0$ and $\alpha=1$ and check whether the aggregate still avoids worst-case stability—if either check fails, the robustness result depends on the tuned metric rather than the aggregation.

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Extended reading notes

Core claim

On the paper's own terms, the discovery is that an ensemble of explanations constructed from rank-based quality metrics is better than any of its parts. For each instance to be explained, LIME, SHAP, and ANCHOR each produce a feature-importance ranking; the paper scores those rankings with three new rank-based metrics—NRC for complexity, a rank-based faithfulness measure, and a Spearman-based stability measure computed with autoencoder-generated in-distribution noise—arranged in a 3x3 matrix. TOPSIS (or EDAS) converts that matrix into a scalar weight per explainer, and a weighted rank aggregation (WSUM, using squared inverse ranks) merges the three rankings into one. In experiments across German credit, Taiwan credit, PAKDD2010, breast cancer, and student depression data, the aggregate explanation lands at the top or second place on NRC and faithfulness and never takes the worst stability value, whereas each component explainer is best on some axis and worst on another. The paper further argues that TOPSIS and WSUM are the best algorithm choices among the eight MCDM methods and three rank aggregation methods tested.

Load-bearing premise

The load-bearing premise is that the three new rank-based scores (complexity, faithfulness, stability) genuinely measure explanation quality: the paper supports them only by correlation with older metrics, and the complexity penalty $\alpha=0.5$ was tuned in preliminary experiments, so if the scores do not track real quality, both the weighting of the explainers and the evaluation of the aggregate are wrong.

Editorial extensions

If this is right

  • Practitioners can obtain one local explanation per prediction that is designed to avoid the worst quality failures of any single explainer, at the cost of running the explainers roughly as many times as SHAP.
  • The rank-based metrics let non-scoring explainers like ANCHOR be compared directly with scoring explainers like LIME and SHAP on the same ordinal scale.
  • Autoencoder-based in-distribution noise gives a way to measure stability of explanations on tabular data with categorical features, replacing ad hoc Gaussian noise.
  • TOPSIS with WSUM can be used as a default aggregation recipe, with EDAS as a close alternative.
  • Because the aggregate avoids worst-case stability, the resulting explanation is less likely to flip dramatically under small data perturbations, which matters for audits and stakeholder trust.

Reading between the lines

Editorial extensions of the paper, not claims the author makes directly.

  • The equal criterion weights are an assumption, not a result; a natural next experiment is to weight complexity, faithfulness, and stability by task-specific stakes and see whether the aggregate remains robust.
  • Since $\alpha=0.5$ in NRC was tuned, a sensitivity sweep over $\alpha$ would reveal whether the complexity advantage of the aggregate survives outside the chosen operating point.
  • The robustness claim is an average over 5 or 10 random samples per dataset; one could test whether the aggregate ranking itself is stable across repeated runs, which would strengthen the stability argument.
  • The method's cost scales with SHAP, so a practical variant could approximate SHAP or use cheaper explainers while preserving the rank-aggregation benefit.
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Editorial analysis

A structured set of objections, weighed in public.

Desk editor's note, referee report, and a circularity audit.

Referee Report

5 major / 5 minor

Summary. The paper proposes a multi-criteria rank-based aggregation framework for local explanations. It converts three existing XAI metrics (complexity, faithfulness, stability) into rank-based forms, uses MCDM methods (TOPSIS, EDAS, and others) to assign weights to component explainers (SHAP, LIME, ANCHOR), and then applies weighted rank aggregation (WSUM, Condorcet, Borda) to form an aggregate explanation. The authors evaluate the aggregate on five datasets and report that it often achieves best or second-best scores on the proposed metrics, concluding that the method improves robustness. The paper also compares eight MCDM methods and three rank aggregation methods and identifies TOPSIS and WSUM as the best candidates.

Significance. If the proposed metrics and aggregation were valid, the paper would make a useful practical contribution to explainable AI by turning a multi-criteria decision problem into a rank aggregation problem. Strengths include the model-agnostic formulation, the public code repository, and the use of multiple public datasets. However, the paper's central quantitative claim rests on a metric that is mathematically constant for the standard no-tie ranking case, and on an evaluation that is circular because the aggregate is scored with the same metrics used to construct its weights. Both issues are load-bearing; they cannot be repaired by local editing of the presentation, and the current evidence does not support the conclusion that the proposed method produces more robust explanations.

major comments (5)
  1. [V-A, Eq. (1)] The NRC metric is constant for any explanation whose importance ranking has no ties. Under Eq. (1), R_i is the rank of feature i; for continuous-valued explainers such as SHAP and LIME, R is a permutation of {1,...,d} in the generic case, so sum_i 1/R_i equals the harmonic number H_d and std(R) equals sqrt((d^2 - 1)/12). Both factors are independent of the explanation, so NRC is constant for all such explanations. The distinct average NRC ranks reported in Tables III-XII can therefore only arise if ties or an unstated modification to the rank construction are present, and neither is specified. The headline NRC results are unsupported by the stated formula, and the alpha=0.5 hyperparameter selected in preliminary experiments (Section VII) cannot rescue a constant metric. The metric must be redefined (for example, using normalized importance scores or a tie-aware rank statistic) and all NRC-based comparisons recomputed.
  2. [V, 'Validating the Aggregate Explanation'] The evaluation is circular. The MCDM weights in Section V are computed from exactly the three proposed metrics (NRC, faithfulness, stability), and the same three metrics are then used in Tables III-XII to score the aggregate explanation against the component explainers. Because the aggregation procedure is explicitly designed to favor high scores on these criteria, the observation that the aggregate often achieves a best or second-best score is at least partly by construction. To support the claim of enhanced robustness, the aggregate should be evaluated with independent metrics, with ground-truth feature importance, or on criteria not used in the weighting step.
  3. [VI-B] The experimental basis is very small. Only 10 random instances per dataset are used for RQ2 and RQ3, and only 5 for RQ4, with no error bars, confidence intervals, or effect sizes. The parenthetical Friedman/Finner counts in the tables are based on these tiny samples, so the 'best or second-best' claims are statistically fragile. The concluding statement about a 'comprehensive experimental analysis across five datasets' overstates what 10 (or 5) points per dataset can establish.
  4. [VI-D] The comparison of MCDM methods is incomplete and not reproducible. The text states that preliminary experiments showed TOPSIS and EDAS consistently outperformed the other six methods, but those preliminary experiments are not described, no results are shown, and no code or protocol is provided. Similarly, Section VI-E omits Borda count results 'due to space constraints'. The abstract's claim that TOPSIS and WSUM are the best candidates is therefore not verifiable from the paper; at minimum, the omitted comparisons should be provided as supplementary material or the claims should be restricted to the reported methods.
  5. [V-A.c, VI-B] The autoencoder-based stability metric depends on free parameters that are never specified: the number K of nearest neighbors in the latent space and the number of features changed to construct the noisy training set. Section VI.B only reports the 500 training epochs. Since stability is one of the three criteria used both for weighting and evaluation, the stability results cannot be reproduced or interpreted without these parameter values and a sensitivity analysis.
minor comments (5)
  1. [III] The heading 'AUTOENCODERMODELDESCRIPTION' appears immediately after the ANCHOR subsection with no spacing or separate heading; the formatting should be corrected.
  2. [V] The phrase 'we chose the squared inverse of the features’ ranks as this value' introduces an unexplained transformation; please justify this choice or cite a source, and specify whether this applies to the rank aggregation only or also to the metrics.
  3. [V-A, Eq. (2)] The notation r(g(f,x))_i in Eq. (2) is ambiguous: it should clearly denote the rank of feature i under the explanation ranking, rather than the i-th element of an undefined vector.
  4. [VI] The text uses inconsistent capitalization for SHAP ('Shap' appears in the discussion of Tables III-V), and the table footnotes describe the Friedman/Finner procedure with inconsistent footnote numbers (for example, footnote 2 vs. footnote 3) that should be harmonized.
  5. [VI-C, Table II] The negative correlations for sensitivity/stability are explained as expected, but the actual magnitudes are not interpreted; it would be helpful to report whether the sign flip yields equivalent rankings, since a Spearman correlation of -0.60 on PAKDD2010 is only moderate.

Circularity Check

1 steps flagged · score 6.0 of 10

Equation (1)'s NRC metric is a constant for any tie-free ranking, so the reported NRC rankings are generated by the formula rather than by the explanations; the aggregate-robustness claim retains independent content only through faithfulness and stability.

  1. other [Section V.A(a), Eq. (1); evaluated in Section VI.D (Tables IIIa-VIIb)]
    "µN RC(f, g;x) = ( Σd i=1 1 Ri ) · log(d + 1) · (1 + α · std(R)), where R = r(g(f, x)). (1)"

    For any explanation whose d feature-importance scores have no ties, R is a permutation of {1,...,d}; hence Σ 1/R_i is the harmonic number H_d and std(R) = sqrt((d^2−1)/12). Both factors are constants independent of the explanation, so Eq. (1) assigns exactly the same NRC value to every tie-free explanation. The tables (e.g., IIIa: Aggregate 1.6 vs ANCHOR 1.7 vs SHAP 3.4) report distinct NRC average ranks, which cannot follow from the stated formula unless an unstated tie-breaking or modified metric is used. Therefore the conclusion that the aggregate explainer is 'best or second-best' in NRC is an artifact of the formula, not an empirical result derived from the explanations.

full rationale

The paper is self-contained on the aggregation pipeline: TOPSIS/EDAS weights are computed from the three rank-based metrics and then WSUM/Condorcet combine the component rankings, with no load-bearing self-citation and no imported uniqueness theorem. The faithfulness and stability metrics are meaningfully rank-based, and the aggregate's avoidance of worst-case stability is an empirical finding. However, the NRC metric as written is degenerate: for tie-free rankings it depends only on d and α, so the NRC columns in Tables III-XII cannot be produced by Eq. (1). This makes one of the three evaluation criteria on which the 'more robust explanations' claim rests vacuous as stated, and the paper acknowledges α=0.5 was chosen from preliminary experiments. The central robustness conclusion still has independent content through faithfulness and stability, so the circularity is partial, not total.

Assumptions & free parameters 3 free parameters · 4 assumptions · 0 invented entities

The method rests on several unvalidated assumptions: the new metrics lack theoretical grounding, the autoencoder noise method is not benchmarked, and the evaluation uses the same metrics that determine the weights. These assumptions are load-bearing because the central claim of improved robustness is measured with metrics that are themselves part of the method.

free parameters (3)
  • alpha (NRC rank dispersion penalty) = 0.5
    Selected via preliminary experiments to balance lower-ranked feature importance and rank dispersion, as stated in the Limitations section.
  • Rank transformation exponent (squared inverse of ranks) = 2
    Chosen as the value for converting ranks to scores in rank aggregation; no justification provided, arbitrary design choice.
  • Autoencoder noise parameters (number of neighbors K and number of features changed)
    Not reported in the paper; these parameters control the noisy dataset used in the stability metric and are likely set by the implementer, affecting results.
assumptions (4)
  • ad hoc to paper The rank-based metrics NRC, faithfulness, and stability correctly measure explanation complexity, fidelity, and stability.
    These metrics are newly proposed and validated only through correlation with traditional metrics on a limited sample (Table II); no theoretical justification.
  • domain assumption The autoencoder-based noise generation produces a meaningful dataset perturbation for stability testing.
    The paper assumes this method handles categorical features and controls noise level intuitively, but no comparison with Gaussian noise or other baselines is provided.
  • domain assumption The same metrics can be used to assign MCDM weights to explainers and to evaluate the aggregated explanation without bias.
    The aggregate is weighted by performance on these metrics and then evaluated on the same metrics, creating a potential circular dependency.
  • domain assumption Equal weights for the three criteria are an appropriate default.
    Acknowledged in Limitations; no sensitivity analysis.

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Cite this review

Pith. "Pith review of Multi-criteria Rank-based Aggregation for Explainable AI." pith.science (2026). https://pith.science/paper/YXDOMOVI

@misc{pith2026250524612,
  author       = {Pith},
  title        = {Pith review of: Multi-criteria Rank-based Aggregation for Explainable AI},
  year         = {2026},
  howpublished = {\url{https://pith.science/paper/YXDOMOVI}},
  note         = {Machine review of arXiv:2505.24612}
}
read the original abstract

Explainability is crucial for improving the transparency of black-box machine learning models. With the advancement of explanation methods such as LIME and SHAP, various XAI performance metrics have been developed to evaluate the quality of explanations. However, different explainers can provide contrasting explanations for the same prediction, introducing trade-offs across conflicting quality metrics. Although available aggregation approaches improve robustness, reducing explanations' variability, very limited research employed a multi-criteria decision-making approach. To address this gap, this paper introduces a multi-criteria rank-based weighted aggregation method that balances multiple quality metrics simultaneously to produce an ensemble of explanation models. Furthermore, we propose rank-based versions of existing XAI metrics (complexity, faithfulness and stability) to better evaluate ranked feature importance explanations. Extensive experiments on publicly available datasets demonstrate the robustness of the proposed model across these metrics. Comparative analyses of various multi-criteria decision-making and rank aggregation algorithms showed that TOPSIS and WSUM are the best candidates for this use case.

Figures

Figures reproduced from arXiv: 2505.24612 by the authors.

Figure 1
Figure 1. Representation of the workflow in the proposed method. [PITH_FULL_IMAGE:figures/full_fig_p005_1.png] view at source ↗

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Pith tools

Reviewed August 7, 2026 · model on record in the stance chip above.