Venue: NeurIPS 2022 Conference

Reviews:

final_score: rating: 4: Borderline reject: Technically solid paper where reasons to reject, e.g., limited evaluation, outweigh reasons to accept, e.g., good evaluation. Please use sparingly.
review_content: summary: In this paper, the authors propose a framework that can find sufficient explanations for any model of the form $x,f(x)$ and don't explicitly require access to the black box model $f$. One of their key claims to is to propose the first method to provide local rule-based explanations for the regression problem. They leverage prior art on Same Decision Probability (SDP) and in order to obtain a consistent SDP estimator to obtain MSE's they build upon ideas from Quantile Regression Forests and Projected Forests. Certain heuristics are used to alleviate the computational burden which are also inspired from more recent prior art. Empirical results include comparison against rule-based methods such as Anchors, etc to indicate better performance.
strengths_and_weaknesses: **Strengths**

1) Authors try to address a relatively unaddressed problem on local rule-based explanations for regression problems.
2) Empirical results and overall writeup are coherent with the theme the authors wanted to convey.

**Weakness**

1) Choice on certain heuristics like choosing 10 (line 290) seem to be directly used from prior art with no justification.
2) Limited scope of applicability to tabular datsets only
questions: 1) How would you justify choices of certain parameters/heuristics as mentioned above ?

2) What notion of stability are you presenting here (line 387). There are several notions of stability within the XAI literature hence mathematical definition or citation should  be provided ? For example is it the stability defined from here (Alvarez-Melis David, Jaakkola Tommi S. On the robustness of interpretability methods -  ICML Workshop on Human Interpretability in Machine Learning. 2018.)

3) I do not see any citation or comparison w.r.t Contrastive Explanations techniques (https://arxiv.org/pdf/1802.07623.pdf) ? These have been applied successfully to tabular data also and seem very relevant work to compare against? https://arxiv.org/abs/1906.00117



limitations: Yes
review_title: null

final_score: rating: 7: Accept: Technically solid paper, with high impact on at least one sub-area, or moderate-to-high impact on more than one areas, with good-to-excellent evaluation, resources, reproducibility, and no unaddressed ethical considerations.
review_content: summary: This paper focuses on the problem of explaining the model output by extending the notion of probabilistic sufficient explanations (P-SE) to regression problems and non-binary settings. To that end, the authors extend the notion of same decision probability (SDP) to regression tasks and propose an estimator for it based on ideas from projected forest and quantile regression forest. Finally, they also introduce a local-rule based explanation, namely minimal sufficient rules, by generalizing sufficient explanations.
strengths_and_weaknesses: (+) The paper proposes several local explanation methods to address an interesting problem of explaining regression models.

(+) A fast estimator for the SDP is also a novel and significant contribution. A theoretical analysis of its convergence is provided as well.

(+) The paper is overall well written, and related works are discussed clearly.

(-) For empirical evaluation on regression tasks, only a toy example is considered. 

(-) Local explanatory importance was introduced but not discussed or evaluated further.
questions: How does the local explanatory importance compare, for example to SHAP values, on the tasks discussed in the experiments section? I am also unsure about its value as local feature attribution in practical settings, as it requires computing the A-SE or M-SE first which is expensive. (Unless there’s an efficient algorithm to compute/estimate it, which I could not find in the paper).

I would encourage the authors to also evaluate the proposed explanations on real-world benchmark datasets for regression tasks. In the synthetic model, most features are noise variables which is not what most real-world data or models would look like.

Table 1: Is correctness the same as consistency described in the previous paragraph (end of page 8)?

Lines 359-360: typo with comma and decimal points
limitations: Yes
review_title: null

final_score: rating: 5: Borderline accept: Technically solid paper where reasons to accept outweigh reasons to reject, e.g., limited evaluation. Please use sparingly.
review_content: summary: The paper proposes LXI, a feature importance metric, and Minimal Sufficient Rule, a generalization of Minimal  Sufficient Explanation. 
 - A Minimal Sufficient Explanation (M-SE) of an instance in a model is the instance's smallest subset of features such that, w/ high probability, the model's prediction using the subset is close to the prediction when using all features.
 - LXI defines the important features of an instance in a model to be the subset of features that frequently appears in the instance's M-SE. 
 - A Minimal Sufficient Rule of an instance in a model is the maximal bounding box around a subset of the instance's feature values such that every M-SE to the instance is also a SE to every point inside the box.

The paper proposed to construct a Minimal Sufficient Rule using projected forest and quantile regression forest. 
strengths_and_weaknesses: Given my understanding of the definition of Minimal Sufficient Rule, I don't think I can make assertive judgment about the paper: As noted in the paper and the Anchor paper, a "rule" is a set of if-then predicates. How can a set of bounding boxes be interpreted as such?

The main contribution of the paper, the construction of a Minimal Sufficient Rule, is explained in only 10 lines (line 294-304). Perhaps a longer explanation together with some examples can help me better understand the the paper.

What is the purpose of LXI? It seems disconnected to the rest of the paper. As a feature importance metric, it is not compared to other feature importance metric in the literature, nor is it used in the proposed method. 

The paper claims to "introduce" Minimal Sufficient Explanations, but this is not true. It has been extensively studied in some of the references, e.g. Wang et al 2021. Perhaps this paper is the first to extend the definition to regression?
questions: I'd appreciate if the authors can confirm or reject my understanding of the various definitions in my summary. 
limitations: Yes
review_title: null

final_score: rating: 6: Weak Accept: Technically solid, moderate-to-high impact paper, with no major concerns with respect to evaluation, resources, reproducibility, ethical considerations.
review_content: summary: This paper proposes a method for finding important features as Consistent Sufficient Explanation.
The essential building block of the method is the conditional probability estimation with conditioning on arbitrary subset of the features.
The authors proposed using Quantile Regression Forest and Projected Forest to estimate such conditional probability.
The authors also proved that the estimated conditional probability converges to the true probability as the number of samples goes to infinite.
The experimental results show that the proposed estimator provides more accurate estimate of important features than the existing methods such as LIME, SHAP, INVASE, and Anchors.
strengths_and_weaknesses: ## Strength
### Originality
The notion of Consistent Sufficient Explanation was proposed in a previous study.
The major novelty of the paper is therefore on constructing an estimator of the conditional probability with conditioning on arbitrary subset of the features.
This will be a topic that is less explored in the literature.
The proposed estimator based on Quantile Regression Forest and Projected Forest seems reasonable, particularly for tabular data.

### Clarity, Quality
Both the notion of Consistent Sufficient Explanation and its extensions as well as the proposed estimator are described clearly.

### Significance
The results on the experiments with synthetic data and a few real world datasets looks promising.

## Weakness
*(My comment here is rather suggestion than Weakness.)*
In the paper, the authors focused on the conditional probability estimation based on random forest.
I wonder if there is any other type of approaches we can think of.
Discussing possible alternative approaches would be beneficial to the readers.
One naive approach would be to train a generative model $p(X_{-S} | X_S)$, e.g., by using neural networks [Ref1,2,3,].
We can then estimate the conditional probability $p(Y | X_S) = \int p(Y | X_S, X_{-S}) p(X_{-S} | X_S) d X_{-S}$, e.g., by sampling $X_{-S}$ from the generative model.
Although this is apparently computationally expensive, this can be an alternative approach when the tree-based models are not appropriate such as images.

[Ref1] Variational Autoencoder with Arbitrary Conditioning
[Ref2] ACFlow: Flow Models for Arbitrary Conditional Likelihoods
[Ref3] Arbitrary Conditional Distributions with Energy

questions: Are there any other possible approaches for estimating the conditional probability estimation with conditioning on arbitrary subset of the features?
limitations: The authors mentioned that the proposed method is suitable for tabular data.
review_title: null

Meta-review: metareview: I have read all comments and responses carefully.

Reviewers praise the novelty of the solution and recognized the under-explored nature of the problem. The proposed estimator seems reasonable, particularly for tabular data. Reviewers complained about the lack of explanation on some heuristics used and the limited scope of applicability of the method.

Overall, reviewers agree that this is an important and yet underexplored problem and the authors have provided useful contributions. I, therefore, have decided to recommend the acceptance of the paper.
confidence: Less certain
Decision: Accept