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REVIEW 3 major objections 5 minor 29 references

Conditional Local Importance by Quantile Expectations

T0 review · 3 major / 5 minor · reviewed 2026-08-12 · deepseek-v4-flash

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Pith's one-line read CLIQUE assigns each feature of each observation a local importance equal to the average change in model loss when the feature is replaced by quantile values from its training distribution, and it stays near zero for variables that are…

desk verdict Genuinely new local importance method with a real conditioning advantage, but the classification experiments never specify the loss L in Eq. 1, which blocks verification of the headline claims until fixed. read the letter →

arxiv 2411.08821 v4 pith:5DIF75GJ submitted 2024-11-13 stat.ML cs.LGstat.CO

Kelvyn K. Bladen , Adele Cutler , D. Richard Cutler , Kevin R. Moon This is my paper · ORCID
classification stat.MLcs.LGstat.CO
keywords localvariableimportancemodel-agnosticinterpretationquantilegridconditionaldependenceSHAPLIMEmulti-classclassificationpermutation
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

CLIQUE gives every row of a dataset a number per feature: the average change in model loss when that feature is replaced by M quantile values from its own training distribution. The paper claims this score is near zero exactly where a variable has no local effect on the outcome, even when SHAP and LIME still report nonzero importance, and that it exposes interactions such as a feature mattering only when another feature is above a threshold. Because the score is built on loss rather than predicted probabilities, it transfers to multi-class classification without per-class summaries. If true, CLIQUE is a drop-in local explanation tool that answers 'does changing this variable hurt the model here?' rather than 'which direction does it push the prediction?'

What carries the argument

The defining object is Eq. (1), $$V_{ij} = \frac{1}{M}\sum_{m=1}^{M} \left[ L\big(\hat f(\tilde x_i(j,m)), y_i\big) - L\big(\hat f(x_i), y_i\big)\right],$$ where $\hat f$ is a cross-validated model that did not train on row $i$, $\tilde x_i(j,m)$ is row $i$ with feature $j$ replaced by the $m$-th quantile value of that feature, and $L$ is the loss. The recommendation to replace a value with all other possible values is approximated by the quantile grid, which removes the need for many random permutations and stabilizes the estimate. The conditional character comes from holding all other features at the observed row while sweeping the target feature: a feature is locally important only if perturbing it changes the model's error on that row. CLIP, the permutation variant, is the same formula with random draws instead of quantiles and serves as the comparison that isolates the grid's contribution.

What would settle it

Take a regression where the true effect of $x_j$ on $y$ is exactly zero for all rows, train a flexible model, and run CLIQUE: if the median absolute CLIQUE value across rows is not near zero compared to the model's loss scale, the claim that CLIQUE produces near-zero importance for irrelevant variables fails. A second check is to compare CLIQUE with the exhaustive replacement of every observed value of the feature; large discrepancies would show the quantile grid itself is the source of the signal.

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Extended reading notes

Core claim

On its own terms, the paper's central discovery is that local importance can be computed as a conditional error differential: for observation $i$ and feature $j$, replace $x_{ij}$ with each of $M$ quantile values of that feature and average the resulting change in loss. In experiments on an AND-gate, a corners-shaped decision boundary, and a regression with a switching interaction, these CLIQUE values are essentially zero in the region where the feature is known to be irrelevant and strictly positive elsewhere, whereas LIME tracks only marginal trends and SHAP assigns many nonzero values in the null region. The same mechanism gives interpretable per-class importance on MNIST pixels and splits the lichen data by an interacting covariate, and CLIQUE matches SHAP in speed while scaling linearly in sample size. The punchline is therefore that error-based quantile replacement, not prediction-based attribution, is what lets local importance reflect local dependence.

Load-bearing premise

The method depends on the assumption that replacing a feature with M quantile values from its training distribution is a faithful surrogate for every perturbation that could affect a given observation, so that a zero average loss change really means the feature is locally irrelevant.

Editorial extensions

If this is right

  • CLIQUE gives practitioners a per-observation ranking of features by error impact, so a feature can be reported as unimportant for a specific prediction even if it is globally important.
  • The multi-class property means a single importance matrix can be produced for a K-class problem without building one explanation per class.
  • Because only loss values are required, CLIQUE applies to any model with a loss, including regression, binary classification, and multi-class classification.
  • The quantile-grid estimator is more stable than permutation-based local importance at the same M, so users can use fewer perturbations to obtain a given level of variance.
  • CLIQUE's linear scaling in sample size and features positions it as a faster and more local alternative to LIME for large tabular data.

Reading between the lines

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

  • Beyond the paper, CLIQUE's per-row error differentials can be averaged into a global importance measure that inherits the conditional behavior, something the paper leaves for future work.
  • Beyond the paper, restricting the quantile grid to a neighborhood of the observed value would turn CLIQUE into a genuinely local-in-feature-space explanation, since the full-range grid mixes far-away values with nearby ones.
  • Beyond the paper, reversing the sign convention could support counterfactual queries: finding which feature changes increase loss the most points to the variables whose perturbation would most alter the prediction.
  • Beyond the paper, because CLIQUE depends on cross-validated predictions, its reliability inherits the stability of the base model and the CV scheme; comparing importances across folds would test how much of the signal is model noise.
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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

3 major / 5 minor

Summary. The paper introduces CLIQUE, a model-agnostic local variable importance measure defined as the average change in a loss function when a feature value is replaced by M quantile values from that feature's training distribution. The method uses cross-validated predictions and is designed to satisfy three properties: P1 (near-zero importance when a variable is irrelevant for an observation), P2 (direct applicability to multi-class problems, with importance assigned whenever perturbing a variable changes predicted classes or probabilities), and P3 (importance depends on model errors rather than predictions). The authors compare CLIQUE with SHAP and LIME on synthetic AND-gate, Corners, and regression-interaction data, and on the Lichen, MNIST, and Concrete datasets, reporting that CLIQUE better highlights locally dependent relationships and is more stable than a permutation-based variant (CLIP). They also provide a sensitivity analysis of the hyperparameter M and runtime comparisons.

Significance. If the claims hold, CLIQUE offers a useful and simple alternative to SHAP and LIME for local importance that extends naturally to multi-class problems and focuses on the loss space rather than the prediction space. The paper has clear strengths: the method is easy to describe and implement, the synthetic experiments directly target the claimed conditional behavior, the sensitivity analysis of M in Appendix A.3 is informative, and the runtime study in Appendix A.4 is carefully executed with Monte Carlo repetitions. The main weaknesses are that the loss function for classification is never specified, making the central experiments non-reproducible, and the paper provides no formal or even heuristic analysis of when the quantile-grid procedure guarantees the claimed zero/nonzero behavior. These issues are load-bearing for the central claims, so the significance is currently conditional on resolving them.

major comments (3)
  1. [Section 2, Eq. (1); Algorithm 1] The loss function L in Eq. (1) is never specified for any classification experiment. Algorithm 1 has no loss parameter, yet Eq. (1) is applied to the AND-gate (Section 3.1), Corners (Section 3.2), Lichen (Section 4.1), and MNIST (Section 4.2) data. The choice of L is not a minor detail: if L is 0-1 misclassification loss, then probability changes that do not alter the predicted class contribute zero, so property P2 ('new predicted classes or probabilities' imply importance) is not honored; if L is multiclass log loss or Brier score, then property P1 can fail because small probability fluctuations in an invariant region can produce nonzero average loss differences. The manuscript must state which loss is used in each classification experiment and explain how P1 and P2 depend on that choice.
  2. [Section 2, Eq. (1); Sections 3.1-3.3] The central claim that CLIQUE yields near-zero importance for irrelevant variables is only demonstrated empirically on synthetic examples. No conditions are given under which Eq. (1) provably or approximately satisfies P1. In particular, replacing a feature with quantile values drawn from its marginal distribution can move a point far from the observed conditional distribution of the other features, and the effect of such off-manifold replacements on the loss difference is not analyzed (the paper cites Hooker et al. [12] but does not address their extrapolation concern). A formal statement or explicit assumptions—for example, that the model output or loss is invariant to the feature in the region of interest, or that the quantile replacements remain in the support of the relevant conditional distribution—are needed to support the general claim.
  3. [Sections 3.1-3.3, Figures 2, 4, 5, 7] The evaluation of property P1 in the simulations is qualitative. The paper states that CLIQUE values are 'practically zero' in irrelevant regions, but it does not report numerical summaries such as the mean absolute importance in the irrelevant region versus the relevant region, or any separation measure. Because the zero-versus-nonzero distinction is the central contribution, quantitative comparisons should accompany the figures so that the reader can assess the magnitude and variability of the claimed near-zero values, rather than relying on visual inspection alone.
minor comments (5)
  1. [Algorithm 1] In line 10, the assignment 'W:j n×1 ← m' is unclear; it should read 'W:j ← grid[m]' or equivalent, since m is an index into the quantile grid.
  2. [Figure 9] The x-axis label 'MinTempAve > 65' is confusing because the text says the data are split on whether MinTempAve is below 65. Please align the label with the actual grouping used in the figure (e.g., 'MinTempAve > 65: FALSE/TRUE' or 'below 65').
  3. [Section 3, paragraph on M] The statement that M = 25 was chosen based on 'desired qualities of the Central Limit Theorem' is not a valid justification for a quantile grid; the Central Limit Theorem concerns averages of random variables, not deterministic quantile replacements. Please rephrase the rationale and rely on the stability analysis in Appendix A.3.
  4. [Section 2, discussion before Eq. (1)] Please clarify whether the quantile grid of M values includes the original observed value, and how duplicate quantiles (which can occur with discrete features or ties) are handled when computing the average in Eq. (1).
  5. [Figures 14 and 15] The demonstration of property P2 is presented by grouping CLIQUE values by class label, but P2 concerns whether perturbing a variable changes predicted classes or probabilities. Please clarify how these plots establish P2 rather than merely describing class-specific importance values.

Circularity Check

1 steps flagged · score 4.0 of 10

CLIQUE's zero-importance property P1 is built into Eq. 1 by construction; the local-dependence and stability comparisons are independent.

  1. self definitional [Section 2 (Properties P1 and Eq. 1); Section 3.1, paragraph after Fig. 2]
    "P1 If altering a variable value does not affect the model output for an observation, that variable should have an importance near 0 for that observation. ... Vij = 1/M Σ_{m=1}^M [ L( f(˜xi(j, m)), yi ) − L( f(xi), yi ) ] ... From Figure 2, we see this in the CLIQUE values. When v2 < −1/3, the importance of v1 is practically zero, while for v2 > −1/3, v1 has a positive importance."

    Eq. (1) defines Vij as the average loss difference under grid replacements. If the model output is unchanged by replacing feature j, each term equals L(f(xi), yi) − L(f(xi), yi) = 0, so Vij = 0 identically. Therefore P1 — near-zero importance whenever the altered variable does not affect the output — is a logical consequence of the definition, not an empirical discovery. The Section 3.1 statement that CLIQUE 'output[s] an importance of zero when v2 < −1/3' reports this tautology (given the trained model's invariance in that region) as though it were a comparative success over SHAP and LIME. The contingent empirical content is only that the model output is invariant there; the zeroing behavior itself is fixed by Eq. 1.

full rationale

The only circular step I can exhibit with the paper's own equations is the P1/zero-importance claim. Eq. 1 makes Vij a mean loss difference, so the advertised behavior 'zero importance for variables whose alteration does not change the model output' is true by construction. This is a real but limited self-definitional step: it inflates the abstract's claim that simulated examples 'show' this property, whereas the property follows immediately from the definition. The paper's other central content is independent of any fit: the local-dependence comparisons against SHAP and LIME on the AND-gate, Corners, and Regression Interaction simulations, the stability comparison with permutation-based CLIP, and the MNIST multi-class analysis are empirical, externally interpretable benchmarks rather than consequences of Eq. 1. M is chosen heuristically and its sensitivity is examined, so no fitted input is renamed as a prediction. The self-citations (Refs. [3], [6]) are not load-bearing; the quantile-grid idea is attributed to the external text by Molnar. The unspecified classification loss L is a reproducibility and P2 concern, but it is not circularity, so it is not scored here. Overall, one advertised property reduces by construction, but the central comparative method retains independent content, giving a partial score of 4 rather than 0 or 6.

Assumptions & free parameters 1 free parameters · 3 assumptions · 0 invented entities

The central claim rests on the quantization approximation, the reliability of CV errors, and an unspecified loss for classification. These are domain assumptions rather than fitted parameters, so the circularity burden is low.

free parameters (1)
  • M (number of quantile replacements) = 25 (recommended range 20-50)
    The number of quantile values used to compute the average in Eq. 1. Chosen for variance stabilization and confirmed by stability analysis in Appendix A.3; not fitted to the response variable.
assumptions (3)
  • domain assumption Replacing a feature with M quantile values approximates replacing it with all possible variable values, as suggested by Molnar.
    Section 2 states that Molnar suggests all-values replacement is most accurate but expensive; CLIQUE uses the quantile grid as an efficient approximation. This is load-bearing because the importance measure is defined as the average over this grid.
  • domain assumption Cross-validation predictions for each observation are reliable enough to compute local errors.
    Section 2 says CLIQUE uses CV errors because test errors better estimate performance; this assumes the CV models provide stable out-of-sample predictions for each data point.
  • domain assumption The loss function L in Eq. 1 adequately reflects model performance for the task at hand.
    Eq. 1 defines CLIQUE in terms of L, but the paper never specifies L for the classification experiments, leaving the operational definition incomplete and the computed values dependent on an unstated choice.

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Cite this review

Pith. "Pith review of Conditional Local Importance by Quantile Expectations." pith.science (2026). https://pith.science/paper/5DIF75GJ

@misc{pith2026241108821,
  author       = {Pith},
  title        = {Pith review of: Conditional Local Importance by Quantile Expectations},
  year         = {2026},
  howpublished = {\url{https://pith.science/paper/5DIF75GJ}},
  note         = {Machine review of arXiv:2411.08821}
}
read the original abstract

Global variable importance measures are commonly used to interpret the results of machine learning models. Local variable importance techniques assess how variables contribute to individual observations. Current, popular methods, including LIME and SHAP, provide useful measures of feature contribution in the prediction space, while leaving opportunities for improved characterization of local structure in the model loss space. Additionally, they are not natively adapted for multi-class classification problems. We propose a new model-agnostic method for calculating local variable importance, CLIQUE, that highlights locally dependent relationships, provides improved stability over permutation-based methods, and can be directly applied to multi-class classification problems. Simulated and real-world examples show that CLIQUE emphasizes locally dependent information, captures interaction behavior beyond what can be evaluated by correlations, and assigns zero importance in regions where the response is invariant to changes in variables.

Figures

Figures reproduced from arXiv: 2411.08821 by the authors.

Figure 1
Figure 1. Scatterplot of the AND gate data colored [PITH_FULL_IMAGE:figures/full_fig_p003_1.png] view at source ↗
Figure 2
Figure 2. Scatterplots of local variable importances vs. [PITH_FULL_IMAGE:figures/full_fig_p004_2.png] view at source ↗
Figure 3
Figure 3. Scatterplot of the Corners data colored by [PITH_FULL_IMAGE:figures/full_fig_p004_3.png] view at source ↗
Figures from the paper (15 more)
Figure 6
Figure 6. Figure 6: Scatterplot of the Regression Interaction [PITH_FULL_IMAGE:figures/full_fig_p005_6.png]
Figure 8
Figure 8. Figure 8: MinTempAve (minimum temperature) and ACONIF (age of conifers) are two of the most impor￾tant variables for classifying the presence of Lichen. Descriptive analyses show that MinTempAve is highly collinear with AmbVapPressAve (ρ = 0.997) and Ele￾vation (ρ = −0.978), whi…
Figure 9
Figure 9. Figure 9: Distributions of ACONIF importances for different MinTempAve thresholds. Classically defined outliers are included in whiskers. The CLIQUE val￾ues show a greater contrast between the two regions compared to the other methods. possibility that x4y6 may be more or less i…
Figure 8
Figure 8. Figure 8: Global importances (left) and PDPs (right) [PITH_FULL_IMAGE:figures/full_fig_p006_8.png]
Figure 11
Figure 11. Figure 11: Aggregate tile plots for four digits from the [PITH_FULL_IMAGE:figures/full_fig_p007_11.png]
Figure 15
Figure 15. Figure 15: High CLIQUE values generally appear in the bottom right quadrant, while low values fall in the top left. We can visually see that digits 2, 4, and 7 show low values, while digits 5, 6, and 9 show high values. The digits 3 and 9 have overlapping groups, yet we can fair…
Figure 12
Figure 12. Figure 12: Global importances (left) and Partial De [PITH_FULL_IMAGE:figures/full_fig_p008_12.png]
Figure 13
Figure 13. Figure 13: Distributions for x4y6 and x3y6 CLIQUE values across identified cutoffs. Classically defined outliers are included in whiskers. These results imply an interaction between these pixels, where each pixel value is more important when the other has a lower value. predicti…
Figure 15
Figure 15. Figure 15: Scatterplots of PHATE embeddings for the MNIST Digit data. Top-Left: Default plot. Top-Right: PHATE colored by actual digit classes. Bottom-Left: PHATE colored by x4y6 importances cut into three equally sized bins. Bottom-Right: PHATE colored by x3y6 importances cut i…
Figure 16
Figure 16. Figure 16: Left: Global importances for all features in [PITH_FULL_IMAGE:figures/full_fig_p010_16.png]
Figure 17
Figure 17. Figure 17: Distributions for Cement importances for [PITH_FULL_IMAGE:figures/full_fig_p011_17.png]
Figure 19
Figure 19. Figure 19: Plot showing top 5 predictor variables based on mean CLIQUE values for each digit class. Using the CLIQUE values, digits can be identified that benefit from globally important pixels of x4y6 and x6y3. powerful pixel for splitting 5s and 6s, since both dig￾its tend to …
Figure 21
Figure 21. Figure 21: Plot showing panels of data scatterplots [PITH_FULL_IMAGE:figures/full_fig_p013_21.png]
Figure 22
Figure 22. Figure 22: Plot showing computation time results as [PITH_FULL_IMAGE:figures/full_fig_p013_22.png]
Figure 23
Figure 23. Figure 23: Plot showing computation time results as [PITH_FULL_IMAGE:figures/full_fig_p014_23.png]

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