Regional Explanations: Bridging Local and Global Variable Importance

We sincerely thank the reviewer for their thorough evaluation and insightful comments. This feedback is invaluable for improving the quality and clarity of our work. Below, we address each point in detail.

Q: On the Definition of Local Importance: how our definition of local importance: “the product of feature values and their corresponding coefficients”, applies to non-piecewise linear models (e.g., second-order models with or without interactions), and what measure of importance is used as ground truth for these models.

A: The correct definition for our experiments is indeed the “product of feature values and their corresponding coefficients.” We will revise the text following Definition 2.1 to ensure this definition is applied consistently throughout the paper.

For the non-piecewise linear models in Section 5.2, we define the ground-truth feature contribution using a standard functional decomposition, similar to a functional ANOVA.

For a model $f(X)$ that can be decomposed into main effects and interactions:

$f(X) = \sum_{i} f_i(X_i) + \sum_{i < j} f_{i,j}(X_i, X_j) + \dots,$

the total contribution of a feature $X_k$ at a point $X$ is the sum of all components that include $X_k$. We will clarify this in the final version.

For example, in our interaction model, the contributions are:

$\text{Contribution of } X_1 = \text{Contribution of } X_2 = 3 \sqrt{3} \, X_1 X_2.$

However, as we are not interested in directionality, we take the absolute value of the contributions for computing TP and FP.

Q: On the LOCO Model Fit within a Specific Cluster

A: As noted in Figure 6 (where we provide details), once the regions are identified, a practitioner can apply any global importance method of choice to characterise them. In our experiments, the different approaches perform similarly. We plan to move Figure 6 into the main text and highlight this part more clearly.

Regarding the proof of the theorem, while we presented it using regional estimators, we also noted that the version using global minimisers can be easily derived. In fact, using the global minimiser $f_{-j}(X) = \mathbb{E}[f(X) \mid X_{-j}]$ still satisfies the proof’s conditions, which requires that the estimator $f_{-j}(X)$ does not depend on variables outside the corresponding linear model used for the observation $X$. This condition is met whenever $X_j$ is locally important: removing this variable in the condition does not alter the switching variable, so both $f(x)$ and $f_{-j}(X)$ evaluate to the same region-specific affine function. We'll revise the explanation for clarity.

Q: On the Counter-Example

A: We thank the reviewer for this excellent and insightful counter-example. The original counter-example uses the model:

$f(X_1, X_2) = X_2 \cdot \text{sgn}(X_1)$

with a squared-loss conformity score. This leads to an importance vector of: $(X_2^2, X_2^2)$ for all points, making the two regions $X_1 < 0$ and $X_1 \ge 0$ impossible to separate. This example underscores a key point we discuss in the paper (L389-391): the feature importance representation used for clustering is crucial, and motivates a promising direction for future work on enriching these representations to capture different facets of model behaviour.

Before addressing this issue, we would like to emphasise that even in this example, if R-LOCO were to find an incorrect cluster or return just one cluster, the model would still avoid attributing importance to unused and independent variables, in contrast to SHAP, which is the main point of our paper.

Now, regarding the importance of $X_2$. The clustering algorithm does not “see” $X_1$ at all; it only sees a single value $X_2^2$ that determines the point’s position in the importance space. Consequently, the algorithm partitions data based on $X_2^2$, and may forms clusters like:

• Cluster 1 (Low Importance): Points where $X_2^2$ is small (i.e., $X_2$ is close to 0).
• Cluster 2 (High Importance): Points where $X_2^2$ is large (i.e., $X_2$ is close to -1 or 1).

This is still a valid description of the model’s behaviour with respect to $X_2$, as it reveals regions where the magnitude of importance is homogeneous.

Adressing the Core Issue: Enhanced Importance Vectors for Clustering

The issue arises because squared loss is sign-agnostic: squaring discards the direction of the effect, which is crucial in distinguishing the two regions in the counter-example.

As said in (L389-391), we could, for example, enrich the feature importance vectors to improve the clustering. In those lines, we suggested incorporating higher-order LOCO (e.g., removing subsets of features to compute LOCO). However, in this specific case, a more informative dimension would be the signed effect:

$\delta_j(X) = f(X) - f_{-j}(X)$

In the counter-example, this yields:

$\delta_1^b(X) = \delta_2^b(X) = f(X)$

So the full feature importance vector becomes $\gamma$:

• For $$ X_1 < 0 $: f(X) = -X_2 → (X_2^2, X_2^2, -X_2, -X_2)$
• For $$ X_1 \ge 0 $: f(X) = X_2 → (X_2^2, X_2^2, X_2, X_2)$

In this signed importance space, the two regions are now distinct and separable. For $X_2 \neq 0$, points in $X_1 < 0$ and $X_1 \ge 0$ are mapped to opposite sides of the origin, allowing a standard clustering algorithm (e.g., K-Means) to easily distinguish the two groups.

Q: On Citation of [1]

A: We thank the reviewer for bringing the Effector package [1] to our attention. This is indeed relevant prior work, and we will add an appropriate citation and discussion in the revised manuscript.

I wish to thank the autors for responding to my concerns, especially to my counter example. I will increase my score to "borderline accept".

I am still wondering how practical it is to augment the feature importance space with $\delta_j$ (and potentially feature interactions). Like, what empirical criteria should be used to decide that the feature importance space should be augmented. For a toy example that is piecewise linear over regions, we can design the space so that the regions are separable in feature importance space. But what about real world data?

Thank you for increasing your score.

As outlined in the paper, the main goal of clustering in this context is to reduce the variance of feature attributions within each cluster. To achieve this, practitioners may choose to augment the feature importance representation, analogous to how feature engineering is used to improve predictive performance, guided by validation criteria. The key difference here is that the objective is not accuracy, but improved clustering quality in the importance space.

Figure 3 highlights this effect: when comparing clustering in input space versus feature importance space, the per-feature variance is significantly lower in the latter. This supports our argument that clustering in the feature importance space leads to more coherent regions.

We also plan to include your counterexample in the final version of the paper as a case study, to demonstrate when and how augmenting the space can be beneficial. Thank you again for this insightful contribution. We will include a note of acknowledgement to the anonymous reviewer in the final version.

We thank the reviewer for their comments and the opportunity to clarify our contributions. Below, we address the specific points raised.

Q: Could you provide some intuition for why clustering in the feature importance space works better than clustering in input space as demonstrated in Section 5? Specifically, what causes the reduced variance of R-LOCO in Section 5.4?

A: Consider the model

$f(X) = (X_1 + X_2)\cdot 1_{X_6 \le 0} + (X_3 + X_4)\cdot 1_{X_6 > 0},$

Clustering in the feature importance space (generated by R-LOCO with squared loss conformity score) yields a more robust and functionally meaningful separation of the model's two operational regions than clustering in the original input space. Below, we demonstrate this by analysing the decision rules associated with clustering in each space.

Part 1: Clustering in Input Space

The model defines two regions based on the value of $X_6$:

• Region A ($R_A$): $X_6 \le 0$
• Region B ($R_B$): $X_6 > 0$

The effectiveness of clustering depends on the geometric separation between the point clouds of $R_A$ and $R_B$. We analyse this by computing their theoretical centroids:

The centroid of Region A is

$C_A = \mathbb{E}[X \mid X \in R_A] = (0, 0, 0, 0, 0, -0.5),$

and the centroid of Region B is
$C_B = \mathbb{E}[X \mid X \in R_B] = (0, 0, 0, 0, 0, 0.5)$.

Proof:
For $i \in \{1, ..., 5\}$, $X_i$ is independent of $X_6$, so
$\mathbb{E}[X_i \mid X_6 \le 0] = \mathbb{E}[X_i] = 0$.
$X_6 \sim \text{Uniform}[-1, 0] \Rightarrow \mathbb{E}[X_6 \mid X_6 \le 0] = -0.5$.

Conclusion for Part 1:

Although the centroids are distinct, the difference lies only in $X_6$, such that any variability in the other five dimensions $X_1,\dots, X_5$ introduces noise, making geometric separation in input space unreliable for clustering, as we can show by considering the decision rule:

$x \in R_A$ if $d(x,C_A)^2-d(x,C_B)^2<0$.

This rule is the one that underlies K-means clustering, where each observation is attributed to the region with the closest centroid. Expanding this gives:

$d(x,C_A)^2-d(x,C_B)^2 = -2 \langle x, (C_A-C_B) \rangle + \Vert C_A \Vert^2 - \Vert C_B \Vert^2$,

So the clustering decision rule reduces to

$x \in R_A \Leftrightarrow -2 <x,(C_A-C_B)> + \Vert C_A \Vert^2 - \Vert C_B \Vert^2 < 0$ or $\langle x, (C_A-C_B) \rangle > 0$

This rule is similar to the classical linear SVM $sign(\langle x,(C_A-C_B) \rangle +b)$ (where +1 means $R_A$, and -1 means $R_B$) with normal vector $(C_A-C_B)=(0,0,0,0,0,-1)$. Thus, only $X_6$ is used for discriminating between the two groups (and roughly speaking $sign(X_6)$). Although the centroids are distinct in the $X_6$ dimension, noise from the other five features (which are irrelevant to the decision boundary) hinders reliable clustering in input space. We show in part 2 that the clustering in R-LOCO Importance Space gives much better separation.

Part 2: Clustering in R-LOCO Importance Space

Each point $X$ is mapped to an importance vector

$\gamma(X) = (\Delta_1, \dots, \Delta_6),$

where $\Delta_j(X) = (f(X) - f_{-j}(X))^2,$ and the LOCO predictor is $f_{-j}(X) = \mathbb{E}[f(X) \mid X_{-j}]$.

For $X \in R_A$, the importance vector is

$\gamma_A(X) = \left(X_1^2, X_2^2, 0, 0, 0, 0.25(X_1 + X_2 - X_3 - X_4)^2 \right).$

Proof:
In Region A, $f(X) = X_1 + X_2$.

• $f_{-1}(X) = \mathbb{E}[X_1 + X_2 \mid X_{2..6}] = \mathbb{E}[X_1] + X_2 = X_2 \Rightarrow \Delta_1 = X_1^2$

• $f_{-2}(X) = \mathbb{E}[X_1 + X_2 \mid X_{1,3..6}] = X_1 + \mathbb{E}[X_2] = X_1 \Rightarrow \Delta_2 = X_2^2$

• For $j \in \{3,4,5\}$, $\Delta_j = 0$

• $f_{-6}(X) = 0.5(X_1 + X_2) + 0.5(X_3 + X_4) \Rightarrow$

  $\Delta_6 = \left(X_1 + X_2 - 0.5(X_1 + X_2 + X_3 + X_4) \right)^2 = 0.25(X_1 + X_2 - X_3 - X_4)^2$

As previously, we compute in the feature space the decision rule for clustering the feature vectors by computing the centroids.

The centroid of Region A’s importance vectors is

$C_{\gamma,A} = \left(\tfrac{1}{3}, \tfrac{1}{3}, 0, 0, 0, \tfrac{1}{3} \right).$

Proof:
Since all $X_i \sim \text{Uniform}[-1,1]$:
$\mathbb{E}[X_i^2] = 1/3$, and all cross terms vanish due to independence and zero mean.

By symmetry, for $X \in R_B$:

$\gamma_B(X) = \left(0, 0, X_3^2, X_4^2, 0, 0.25(X_1 + X_2 - X_3 - X_4)^2 \right)$

and the centroid is

$C_{\gamma,B} = \left( 0, 0, \tfrac{1}{3}, \tfrac{1}{3}, 0, \tfrac{1}{3} \right).$

Conclusion for Part 2:

As before, the decision rule is

$sign(<\gamma(x), (C_{\gamma,A}-C_{\gamma,B})> +b)$,

where +1 means $R_A$, and -1 means $R_B$ and $C_{\gamma,A}-C_{\gamma,B}= \left(\tfrac{1}{3}, \tfrac{1}{3}, -\tfrac{1}{3}, -\tfrac{1}{3}, 0 \right)$. Thus,

$x \in R_A$ if $sign(<\gamma(x), C_{\gamma,A}-C_{\gamma,B})>0$.

The features used for each cluster $R_A, R_B$ are only based on the local important features, unlike input space clustering, the importance space reveals separation across multiple dimensions $\Delta_1, \Delta_2, \Delta_3, \Delta_4$. More precisely,

• Region A
  If a point is in Region A, $f(\mathbf{X})$ depends on $X_{1}$ and $X_{2}$.
  Thus, $\Delta_{1}$ and $\Delta_{2}$ will be large, while $\Delta_{3}$ and $\Delta_{4}$ will be zero.
  The expression will be positive.

• Region B
  If a point is in Region B, $f(\mathbf{X})$ depends on $X_{3}$ and $X_{4}$.
  Thus, $\Delta_{3}$ and $\Delta_{4}$ will be large, while $\Delta_{1}$ and $\Delta_{2}$ will be zero.
  The expression will be negative.

This captures fundamentally different patterns of feature usage, exactly what R-LOCO is designed to uncover.

Final Conclusion:
While clustering in input space gives only information on the globally important variable, R-LOCO reveals a multi-dimensional separation aligned with the model's logic. It transforms the problem from finding a geometric partition to identifying consistent feature relevance patterns.

Q: The paper didn’t clearly state how the model determines which features are non-important. If the means are all non-zero as shown in Section 5.1, it’s confusing how negatives are identified. A clearer description of the decision rule would improve readability.

A: Lines 276–278 explain that we focus solely on variables directly involved in the computation of the final prediction after the condition. We use the absolute product of feature values and their corresponding coefficients as a measure of importance.

We are not concerned with directionality here. Our primary test is whether a method assigns importance to independent and unused variables, not whether it captures sign.

For example, for a model

$f(X) = \sum_i f_i(X_i) + \sum_{i < j} f_{i,j}(X_i, X_j) + \dots,$

the total contribution of a feature $X_k$ at point $X$ is the sum of all components involving $X_k$. In our interaction model:

$\text{Contribution of } X_1 = \text{Contribution of } X_2 = 3 \sqrt{3} X_1 X_2.$

As we are not interested in directionality, we take the absolute value of the contributions for computing TP and FP.

We will clarify this in the revision.

Q: The authors only considered cases where the population can be clustered. What happens when the population is homogeneous? Could a sensitivity analysis help validate R-LOCO’s robustness?

A: Our main goal is to demonstrate a clear failure case for traditional baselines. Piecewise models are the most natural example where locality breaks down, hence our focus on them.

However, our real-world example, where the population is likely not clusterable, shows that R-LOCO remains robust and effective compared to existing methods.

Q: Why use the 10th and 95th percentiles for non-important feature attributions in Section 5.1? Why not 5th and 95th?

A: No particular reason, we verified that the conclusions hold using the 5th and 95th percentiles. We will update the manuscript accordingly.

Q: In the German Credit dataset (20 features), why are only 19 shown in Figure 5 (Supplementary Material E)?

A: This was a mistake. The last feature was accidentally omitted while improving figure visibility in Inkscape.

Q: The “Mean Performance Drop” in Figures 1 and 2 is negative. Shouldn’t it be positive when important features are perturbed?

A: Apologies for the confusion. We used the error, not accuracy. The base error is used as the baseline.

Q: For clarity, the dimension of the 2nd-order interaction model in Section 5.1 should be mentioned.

A: We will include this detail. However, note that only the variables actually used in the model's definition are considered.

Q: In most of the literature, local importance typically refers to the importance assigned to a single prediction. In that sense, can R-LOCO be understood as calculating global importance for clusters?

Yes.

We thank the reviewer for their comments and the opportunity to clarify our contributions. Below, we address the specific points raised.

Q: Could you provide examples of the regions identified by R-LOCO using AffinityPropagation and include a discussion on the interpretability vs "clustering quality" trade-off? Such a discussion should be included in subsection 5.4.

A: Thank you for the suggestion. We agree that illustrating the identified regions will improve our analysis. However, most clustering algorithms only assign group labels without offering interpretability. In response, we fit a decision tree to predict the cluster labels, providing an interpretable proxy for the regions identified.

Interestingly, we observed that R-LOCO correctly identifies the important regions by first splitting on the sign of X6, in contrast to clustering in the input space. This insight will be incorporated into Subsection 5.4 to better illustrate the interpretability vs clustering quality trade-off as suggested. See the regions found below:

The region for R-LOCO in feature importance space is:

|--- X6 <= 0.00
|   |--- X5 <= -0.86
|   |   |--- class: 0
|   |--- X5 >  -0.86
|   |   |--- class: 0
|--- X6 >  0.00
|   |--- X4 <= -0.56
|   |   |--- class: 1
|   |--- X4 >  -0.56
|   |   |--- class: 0

and the region for R-LOCO in input space is:

|--- X5 <= -0.01
|   |--- X2 <= -0.00
|   |   |--- class: 0
|   |--- X2 >  -0.00
|   |   |--- class: 1
|--- X5 >  -0.01
|   |--- X6 <= 0.05
|   |   |--- class: 2
|   |--- X6 >  0.05
|   |   |--- class: 3

Q: In Section 6, how were the multiple feature importance views combined into a single ranking for Figure 1 and 2? Why not include LOCO in the comparison?

A: In this experiment, we were interested in comparing the “local” methods by perturbing each instance based on its absolute instance-wise importance. Since real-world data lacks ground-truth explanations, we rely on perturbation-based proxies that operate at the instance level. Using LOCO would result in the same perturbation across all instances, which does not align with the local evaluation setup.

However, we agree it is a valid point, and we will include LOCO as a baseline in the revised version. In our experiments, it performed less well than R-LOCO.

Q: As a follow up question, what would be the importance ranking provided by R-LOCO with true clusters for the first order model used in the paper? Since $X_6$ has no importance on both regions would it be ranked after $X_1, \cdots, X_4$? If so, it seems that by chosing carefully the paramaters, the performance of can be made arbitrarily low, which seems to me like an undesirable property.

A: Comparing the importance of the splitting variable to other features is not straightforward. We excluded it from our evaluation to avoid introducing bias as the splitting variable can be viewed as globally important. Instead, we focus on variables that are either locally important (as per our definition) or not important at all (i.e., functionally and statistically independent).

To clarify further, we conducted a more fine-grained analysis (See proof in rebuttal of reviewer GsiJ). For the first-order model, assuming $R_A = {X_6 \leq 0}$ and $R_B = {X_6 > 0}$ we explicitly computed the feature importance variable

• For $X \in R_A$: $$\gamma_A(X) = \left(X_1^2, X_2^2, 0, 0, 0, 0.25(X_1 + X_2 - X_3 - X_4)^2 \right)$$
• For $X \in R_B$: $$\gamma_B(X) = \left(0, 0, X_3^2, X_4^2, 0, 0.25(X_1 + X_2 - X_3 - X_4)^2 \right)$$

Averaging these expressions over their respective regions yields equal importance for the relevant features in each region:

• For $X \in R_A$: $$E_{R_A}[\gamma_A(X)] = \left(1/12,1/12, 0, 0, 0, 1/12 \right)$$
• For $X \in R_B$: $$E_{R_B}[\gamma_B(X)] = \left(0, 0, 1/12, 1/12, 0, 1/12 \right)$$

We will include this analysis in the appendix.

Q: In Definition 2.1, is the function required to be continuous? Also, the term "-CPWL" is introduced but not used again.

A: The definition was adapted from the cited papers. However, in our specific setting, we focus on each m function being affine. The definition was meant to introduce the class of piecewise linear functions used in the following theorem. We will revise the text to make it clearer and use the affine function instead of continuity. Thank you for pointing this out.

Q: In the proof of Theorem 4.1, it is assumed that $\hat{f}{0},\hat{f}{j}$ are estimated for each region, which seems to contradict lines 191-192 that present them as estimators of population minimizers. Could you clarify this point? In your implementation, is the clustering done using local or global minimizers?

A: Thank you for pointing this out. Clustering is performed using global minimisers.

As we mentioned in Figure 6 (which we will move into the main paper), once regions are identified, in principle, any global method can be applied within each region.

The proof uses regional estimators for $f_{-j}(X)$. However, as we said in L567, the other case can be easily deduced. In fact, using the global minimiser $f_{-j}(X) = \mathbb{E}[f(X) \mid X_{-j}]$ still satisfies the proof’s conditions, which requires that it does not depend on variables outside the corresponding model used for the observation $X$. This condition is met whenever $X_j$ is locally important: removing this variable in the condition does not alter the switching variable, so both $f(x)$ and $f_{-j}(X)$ evaluate to the same region-specific affine function. We'll revise the explanation for clarity.

Q: Line 215 – Is the boundary set used in practice? What local attribution is computed there?

A: As mentioned, the boundary set can be treated as a separate group. However, such cases are very rare in practice. Typically, ties can be broken by randomly assigning the sample to one of the valid regions. We will clarify this in the final version.

Q: Line 247 – What criterion is used for clustering in input space?

A: We use the same clustering algorithm and criterion as for the feature importance. We just swap the input matrix with the feature importance matrix.

Q: Line 281 – The claim seems questionable (LOCO values being between (0, 1). Could you elaborate or provide a reference?

A: Thank you for pointing this out. LOCO is often linked to the variance explained (e.g., Sobol indices); its values are positive, and when properly normalised, typically fall within a defined range. We will clarify this and cite sources such as: "Feature Importance: A Closer Look at Shapley Values and LOCO."

Q: Lines 277–278 – Could you provide the formula for ground-truth attributions, especially for the interaction model?

A: Yes, we use the absolute product of feature values and their corresponding coefficients as the ground-truth measure of importance. We do not account for directionality in this evaluation.

For example, for a model

$f(X) = \sum_i f_i(X_i) + \sum_{i < j} f_{i,j}(X_i, X_j) + \dots,$

the total contribution of feature $X_k$ at point $X$ is the sum of all components involving $X_k$. In our interaction model:

$ \text{Contribution of } X_1 = \text{Contribution of } X_2 = 3 \sqrt{3} X_1 X_2

We compute true/false positives using the absolute value of the contributions.

We thank the reviewer for their comments and the opportunity to clarify our contributions. Below, we address the specific points raised.

Q: Request: Please report wall clock training and inference time (and memory usage) for R-LOCO vs. L-SV/LIME on the Diabetes and California datasets and discuss scaling behavior as p grows.

A: Thank you for this helpful suggestion. We have now conducted a detailed runtime and memory usage analysis for R-LOCO, LIME, and SHAP on both the California and Diabetes datasets.

We find that R-LOCO is significantly faster at inference time than the baselines. While our method incurs additional cost during training, due to clustering and model fitting, it performs inference with minimal overhead, as only the cluster assignment is required per sample. We observe a similar pattern for memory usage.

In terms of scalability, R-LOCO’s training computational cost grows approximately linearly with the number of features. This behavior is on par with widely-used approaches such as SHAPLoss and variants (Explaining by Removing: A Unified Framework for Model Explanation). Note that it needs to be done only once. Furthermore, R-LOCO can be optimised for tree-based models using approaches such as Projected Forests (SHAFF: Fast and consistent SHApley eFfect estimates via random Forests), where a single model can be reused to efficiently compute multiple conditional expectations.

We believe these additions substantially strengthen the contribution of our paper.

California Dataset

Diabetes Dataset

Q: Please integrate a purity metric (e.g., variance threshold on LOCO vectors) to automatically detect and refine impure clusters. The goal is to answer: under what quantitative purity threshold does performance sharply degrade?

A: Thank you for the suggestion. While we report results with several clustering parameters to give a detailed analysis, in our current implementation, we include a knee-point strategy to choose the number of clusters. We also support any clustering class with fit and predict methods, enabling integration with methods that include automatic cluster validation.

Q: Have you tested R-LOCO on synthetic correlated feature settings (e.g., Gaussian multivariate with block covariance) to gauge robustness? How do correlations affect clustering fidelity and TP/FP rates?

A: We have deliberately avoided introducing correlation in the synthetic experiments because our goal is to evaluate feature importance under the assumption of independence, where ground truth importance can be unambiguously defined.

In correlated settings, disentangling the effects of statistical dependence from true functional importance becomes challenging, making it difficult to compute TP/FP rates in a principled way.

That said, our experiments on real-world datasets inherently include correlations, and we evaluate performance there using perturbation-based evaluation as there is no ground truth available in the real-world setting.

Q: Have you compared Mahalanobis or cosine distances for clustering? Could adaptive metric learning improve region coherence?

A: As noted in lines 210–212 of the main paper, R-LOCO supports any similarity function during inference, including those used by the clustering algorithm. We have experimented with cosine distances in place of the Mahalanobis, and found minimal impact on overall conclusions.

Nonetheless, we agree that in some settings, particularly in domain-specific structures, careful metric selection could yield improvements. Our implementation supports passing a custom distance function and clustering algorithm, giving users full control over this aspect.

Q: Are there specific use cases/applications that benefit from the computational overhead of the proposed method?

A: A significant majority of real-world machine learning applications, particularly in critical sectors like finance, healthcare, retail, and insurance, are in majority built on structured, tabular data. Many applications on tabular data can afford moderate computational overhead in exchange for more faithful and locally accurate explanations.

Moreover, methods with similar computational profiles, such as SHAPLoss and variants (see Explaining by Removing paper) are already used in practice. R-LOCO offers additional interpretability benefits by structuring explanations into coherent regions, which is often desirable in real-world workflows where more localised decisions are important.

Q: However, there is an answer regarding limitations in the checklist. I recommend adding one in the main paper that discusses: • Clustering assumptions: Requirement that clusters align with true functional regions; sensitivity to hyperparameters. • Computational overhead: Multiple model fits for LOCO and clustering steps. • Model/domain scope: Currently validated on tabular, piecewise-linear or tree-based models; adaptation to deep networks or non-tabular data is future work.

A: Thank you for this important suggestion. We agree that these limitations should be more explicitly stated in the main paper and will revise accordingly.

As noted in lines 227–229, we provide a theoretical analysis of the impact of imperfect or contaminated clusters on the fidelity of R-LOCO explanations. Additionally, Section 5.4 and Table 2 present an empirical analysis of how clustering affects performance.

While R-LOCO requires model refitting per feature, similar to methods like SHAPLoss, this overhead is incurred only during training. Inference is highly efficient. Moreover, for tree-based models (commonly used in tabular data), the training cost can be significantly reduced using techniques such as Projected Forests (SHAFF: Fast and consistent SHApley eFfect estimates via random Forests).

Indeed, our method is currently validated on tabular data, as are most feature removal-based explanations. Extending R-LOCO to deep learning models or non-tabular modalities is a promising direction for future work.

We will make these limitations more explicit in the final version of the paper to ensure clarity and transparency.