Refining Counterfactual Explanations With Joint-Distribution-Informed Shapley Towards Actionable Minimality
Explainable artificial Intelligence;Feature attributions;Counterfactual explanations
# Response to Other "Minor Points 1,3,4,5,6"

**Q7** “1. Line 51: "some CE algorithms assume differentiable models, whereas others are designed specifically for tree-based or ensemble models" -- this is misleading, as many CE algorithms work for black-box ML models, you can find them in the Verma et al. survey paper.”

**A7:**  We would like to **take the reviewer’s suggestion** and revise the sentence to be “To our best knowledge, there has not been an unified way to refine counterfactuals generated by arbitrary CE algorithms without assumptions on models.”

**Q8:** “3. Line 124 $M_{c_{ik}}$ is not defined which makes understanding Eq 1(d) and 1(e) hard. Also how does having $c_{ik} = 0$ allows no change in its value? I don't see that being implied from the equation”

**A8:**  **There is no $M_{c_{ik}}$ defined in our paper**. In the following response, we assume the reviewer was referring to the notation $M$ that is multiplied to the variable $c_{ik}$. This is a technique in writing mathematical formulation, and is stated in line 134: “….if $c_{ik}=1$, remark that $M$ is a sufficiently large constant such that $z_{ik}$ has good freedom to change.” To further explain it, if $c_{ik}=1$, (1d) and (1e) becomes $-M\leq z_{ik}\leq M$. Since $M$ is large enough, $z_{ik}$ has sufficient freedom. On the contrary, if $c_{ik}=0$, (1d) and (1e) become $z_{ik}\leq x_{ik}$ and $z_{ik}\geq x_{ik}$ respectively, and they have to be satisfied simultaneously. Hence $z_{ik}=x_{ik}$, which means that for any $i$ and $k$, $z_{ik}$ is not allowed to change to any value other than $x_{ik}$.

**Q9:** “4. B-SHAP and RB-SHAP have different background distributions and it is clear to the community about the advantages and disadvantages of each. You define CF-SHAP, but never state what trade-off does one expect when using background distribution from CF distribution instead of the training distribution. Please explain what should one expect from such a FA method.”

**A9:**  **This is simply not true**. It is not us who defined CF-SHAP. The researchers propose the CF-SHAP method in [3] and we just cited their work as shown in lines 186-187. As indicated by the authors in [3], CF-SHAP outperforms the Shapley methods that do not use CF distribution when one wants to do contrastive feature attribution. This conclusion aligns exactly with our results in the paper. However, remark that the distribution of counterfactuals is not always available, imposing limitations on this method. Our results further demonstrate that even if such a counterfactual distribution is known, it may not be the best option, as the proposed p-SHAP can outperform it.

**Q10:** “5. Line 197, correct the typo from RB-SHAP to B-SHAP.”

**A10:**  **Thank you for this**. We will correct the typo in our revised version.

**Q11:** “6. The first paragraph of section 4 is obvious, it is just a generalization of the notations from Equations 4-6, I don't think there is a need to give so much attention and explanation for it.”

**A11:**  **Disagree.** Ours in (7a) and (7b) differ fundamentally with (4)-(6), explained as follows. The CF-SHAP proposed in [3] replies on a concrete counterfactual algorithm to define the counterfactual distribution $\mathcal{D}$ in (6). Hence, CF-SHAP is dependent on a CE algorithm. Our proposed p-SHAP, however, is completely independent of CE algorithms. As for (4) and (5), they do not use counterfactual distribution and differ from ours. This is why this paragraph is mandatory. And we would like to extend this part further in the revised version.

# References
[1] Guidotti, Riccardo. "Counterfactual explanations and how to find them: literature review and benchmarking." Data Mining and Knowledge Discovery 38.5 (2024): 2770-2824.

[2] Scott M Lundberg and Su-In Lee. A unified approach to interpreting model predictions. Advances in neural information processing systems, 30, 2017.

[3] Albini, Emanuele, et al. "Counterfactual shapley additive explanations." Proceedings of the 2022 ACM Conference on Fairness, Accountability, and Transparency. 2022.

[4] Ramaravind K. Mothilal, Amit Sharma, and Chenhao Tan (2020). Explaining machine learning classifiers through diverse counterfactual explanations. Proceedings of the 2020 Conference on Fairness, Accountability, and Transparency.

[5] Kaivalya Rawal and Himabindu Lakkaraju. Beyond individualized recourse: Interpretable and interactive summaries of actionable recourses. Advances in Neural Information Processing Systems, 33:12187–12198, 2020.

[6] Dan Ley, Saumitra Mishra, and Daniele Magazzeni. Globe-ce: a translation based approach for global counterfactual explanations. In International Conference on Machine Learning, pp. 19315–19342. PMLR, 2023.

[7] Verma, Sahil, Keegan Hines, and John P. Dickerson. "Amortized generation of sequential algorithmic recourses for black-box models." Proceedings of the AAAI Conference on Artificial Intelligence. Vol. 36. No. 8. 2022.
**Q5:** “d.) An underlying and unstated key assumption in the formulation of the paper is that sparsity is the most important metric to consider when generating CFEs. This is atleast not agreed upon by the community, see the list of metrics proposed in Verma et al. survey paper.”

**A5**:  **We never had such assumption at all**. 

Our goal of seeking more sparse explanations is **NOT** equivalent to “we assuming that sparsity is the most important metric to consider when generating CE explanations”. It is out of the scope of this paper to discuss which metric is the most important to be considered when generating CE explanations.  

In our opinion, which metric is the most important would-be task-specific. We refer to [Fact 2], that one should select a proper CE method, and, if sparsity is desired, then apply our proposed method to refine the explanations.

**Q6:** “The paper needs to really strengthen its experimental results section. I would expect something like a table, where the columns are the various metrics along with a CFE is evaluated, like validity, proximity, sparsity, distance of training data manifold, adherence to causal constraints, and the time to generate the CFEs (including dependence on any other technique) and the rows to be a large set of baselines.Only when the numerical results demonstrate the superiority of COLA, can the supporting theory, theorems, and the claims of near-optimal performance be useful.”

**A6**:  **We have already reported validity, proximity, and sparsity** in Table 3. Namely, 
- Validity is referred to as “counterfactual effect” and is shown in columns 3 and 4 in Table 3, and we are showing how the refined explanations remain the desired counterfactual with significantly better sparsity. 
- Proximity is $\|\mathbf{z}-\mathbf{x}\|$, and we already reported in the subcolumns of columns 3 and 4 in Table 3 (normalized by $\|\mathbf{r}-\mathbf{x}\|$). 
- Sparsity is reported as the “# of Modified Features” in columns 3 and 4. Our proposed Shapley method is benchmarked towards other four Shapley methods proposed in [2] and [3] combined with different joint probability distributions setups.

Our experiments are designed to demonstrate the versatility of the proposed COLA and the effectiveness of the proposed p-SHAP. (See A3 above). 

At last, as explicitly mentioned by the other **Reviewers iyvf, hbcQ, WJ7H**, our experiments are **exhaustive and robust**. Thus, we argue that **this judgment of “extremely weak experiments” is not fair**.

# Response to “2. [Major]”

The problem being addressed in this paper is challenging because:

- (For the first challenge mentioned) To our best knowledge, existing sparse CE algorithms are task-specific. No refinement mechanism can be used for arbitrary model and CE tasks (see [Fact 2]). Expecting a single (sparse) CE, as proposed by others, to meet all the needs universally is unrealistic. Hence, **whether a versatile sparsification mechanism is possible remains open and challenging**. 
- (For the second challenge mentioned) First, we are unaware of any existing sparse CE algorithm that made no assumptions (e.g., model differentiability, model architecture, available causal graph, specific tasks, focused CE metrics, etc.). If the reviewer could point out a concrete work, we’d happily refer to the work in our paper (see [Fact 2]). Second, this paper proposes a sparsification mechanism named COLA that can be used to refine the explanations generated from any existing CE algorithm. So even if there is already any “universally applicable sparse CE method”, our proposed COLA can be applied to that method to sparsify its generated explanations further, (see [Fact 1]). Hence, **whether such a mechanism exists or not, remained open before our paper. And proposing such a mechanism is challenging**.
- (For the third challenge mentioned). First, feature attributions (FA) mechanisms such as Shapley are not specifically designed for CE. Hence, it is obviously challenging to integrate feature attribution (like Shapley) to improve CE (because FA is not designed for CE, essentially). Second, some researchers have tried to use FA in finding CEs, and we demonstrated in our paper that our proposed method outperforms theirs in obtaining sparser CEs. As the reviewer stated, “A feature that is marked as important by some FA method does not necessarily mean that it is an effective way to change the prediction.” This is true, so **finding an effective way to conduct FA specifically for CE is challenging**. This is addressed in our paper.
**Q2**: “2. The experimental results are very weak for the following reasons: a.) Result 1 in Section 6 (lines 415 - 421) are not useful when a datapoint does not achieve the desired classification. In other words, if a datapoint does not achieve y* classification (which makes it a valid CFE), there is no point in mentioning the sparsity of that, because it is an invalid and not useful CFE. Therefore the third column in Table 3 is not useful at all. ”

**A2**:  The reviewer **misunderstood** the mechanism of COLA. 

As COLA is to refine/sparsify the explanations generated by other CE methods (see [Fact 1]), that is to say, the to-be-refined explanations already achieve the desired classification (referred to as “the target outcome $\mathbf{y}^*$” in line 269, which is formally defined as $\mathbf{y}^*=f(\mathbf{r})$ in line 260). Otherwise, one would seek an alternative CE method rather than the selected one to obtain the desired classification first. Therefore, The third and fourth columns in Table 3 suggest exactly how good sparsity our method COLA could achieve compared to not using it. 

Besides, to our best knowledge, none of the hundreds of CE methods surveyed in [1] could guarantee an arbitrary desired counterfactual effect. We’d appreciate it if the reviewer would clarify the question further in case it bothers you. 

**Q3**: “b.) Several baselines are mentioned in lines 368-372, but none of them are used in the experimental results section? Why? Aren't these the baselines that you need to compare against to show that your technique is better than them atleast in the one metric you are targeting (which is sparsity)? Instead what you do in Table 3 is compare against 5 variations of your own proposed method. Sure one of your own method is better than the other 4 you mention, that does not tell me anything about how does COLA compare to previous techniques. Please let me know if you disagree. Therefore Result 2 is not useful. ”

**A3**:  **These stay entirely away from the truth**. 

We clarify in [Fact 3] that: 1) lines 368-372 indicate the CE algorithms (not baselines) that we used in the proposed COLA, to evaluate its versatility, and the empirical results are provided in Figures 3 and 4 and Appendix H; 2) the baselines to evaluate the proposed p-SHAP are set in Table 2 and empirical results are provided in Table 3, Figures 3 and 4, and appendix H; 3) other rows in Table 3 except CF_$p_\text{OT}$ are not 5 variations of our own proposed methods. 

In fact, RB-$p_{\text{Uni}}$ is exactly the random Shapley proposed in [2]. RB-$p_{\text{Uni}}$ follows the random Shapley in [2] but changes the joint distribution to the same as CF-$p_{\text{ot}}$ for the ablation study. CF-$p_{\text{Uni}}$ and CF-$p_{\text{Rnd}}$ are the Counterfactual Shapley proposed in [3]. Since it assumes a known counterfactual distribution conditional on each factual data point, whereas it is unknown in our experiment, we used $p_{\text{Uni}}$ and $ p_{\text{Rnd}}$ instead. CF-$p_{\text{Ect}}$ is exactly the Counterfactual Shapley proposed in [3]. When there is a one-to-one alignment between factual and counterfactual data points, Counterfactual Shapley degrades to the Baseline Shapley proposed in [2]. 

Hence, **it is NOT true that we compare our proposed one with its variations**.

 **Q4:** “c.) The baselines considered in the paper (the results for which are not reported atleast in the main paper), are outdated and several new techniques have been proposed that are better at all metrics than DiCE and KNN, for e.g. see Amortized Generation of Sequential Algorithmic Recourses for Black-box Models.”

**A4**:  **This is simply not true**.

As we mention before, CE algorithms are not baselines, and all their results have been reported in Table 3, Figures 3 and 4, as well as Appendix H. Besides, **these CE methods that we use are not outdated, either**. In fact, DiCE [4] was proposed in 2020 and is still the most commonly used CE method in the industry and academia nowadays; KNN (as a CE method) [3] was proposed in 2022; AReS [5] was proposed in 2020; GLOBE [6] was proposed in 2023. By contrast, the specific literature [7] mentioned by the reviewer emerged in 2021 on arXiv and published in early 2022. Moreover, **we do not see why the performance of CE methods matters here**, because the proposed COLA can refine explanations generated by any CE methods (including [7]) regardless of which performs better than the others.
# Clarification of Misunderstandings

We would like to point out some misunderstandings of Reviewer hZrx and clarify several important facts before replying to their specific comments:

**[Fact 1]**: The paper does NOT propose a new CE method. Instead, there are two proposed things: One is the proposed OT-based p-SHAP, used for feature attributions for refining counterfactual explanations. The other is a versatile mechanism to refine/sparsify explanations generated by other CE methods. We have clearly stated this in the main contributions of Section 1.

**[Fact 2]**: To our knowledge, this is the first work that provides a unified way for refining/sparsifying explanations generated by existing tabular data CE methods, without assumptions on the machine learning models and the CE methods. We’d happily refer to others’ work for this if there is any.

**[Fact 3]**: Due to [Fact 1], the baselines in this paper are not CE methods. 
1) To demonstrate the validity and effectiveness of COLA, we have provided its empirical results (in Figures 3 and 4, and Appendix H) under different scenarios (i.e. using COLA to refine the generated counterfactuals from different CE methods for different ML algorithms). 

2) To explore the potential and importance of using joint distribution informed by Shapley to refine counterfactuals and demonstrate the proposed p-SHAP, we have provided its empirical results in Table 3.  Our baselines are those different Shapley methods and different joint probability distribution setups. In Table 2, CF-$p_{\text{OT}}$ stands for our proposed OT-based p-SHAP. All the other rows are baselines. We benchmarked our proposed p-SHAP to all the baselines in all the mentioned CE methods stated in lines 368-372.

# Response to "7.[Really Major]"

We disagree with the reviewer about the weakness of the experiment. We have benchmarked our proposed p-SHAP and some other existing Shapley methods (baselines) on 4 datasets, under different scenarios (changing in 5 different CE algorithms and 13 different machine learning algorithms). We believe the experimental results strongly indicated the effectiveness of our proposed COLA. Besides, **the strength of our experimental results has been explicitly acknowledged by Reviewers iyvf, hbCQ, and WJ7H** regarding its exhaustiveness and robustness. 

More detailed responses to the reviewer are as follows. (**Q** and **A** are question raised by the reviewer and answer provided by the authors respectively).

**Q1**: “1. First and the most important weakness is that you need another CFE generation technique to generate a CFEs for a lot of datapoints that you use to compute the joint distribution and then generate a CFE using your technique, is that right? If that is the case, in the paragraph of computation complexity, why do you not include that? Also it is not the case that your technique just takes a CFE from some other technique and refines it, it needs a whole lot of datapoints and CFEs to even start functioning. Please correct me if I am wrong.”

**A1**: **What you said is not correct** for three reasons. 

First, the proposed COLA is not a CE (referred to by the reviewer as “CFE”) algorithm. Instead, it is a unified mechanism to refine (or sparsify) explanations generated by any CE algorithm (See [Fact 1]). It is a sparsification mechanism for other CE methods, yet does NOT rely on one specific CE method.

Second, we have already considered the computation complexity of other CE methods when analyzing the computational complexity. See Lines 348-353 “Complexity of COLA”. Note that $A_{\text{CE}}$ is the CE algorithm in step 1, and  $O(M_{\text{CE}})$ indicates its complexity. 

Third, our proposed COLA does NOT need many data points and CEs to work. In fact, it also work with one single factual data point and one corresponding CE data point. This is exactly the case of CF-$p_{\text{Ect}}$ stated in the last row of Table 2, where each factual data point is known to be aligned with another exact counterfactual data point. As we can see from the corresponding results in Figure 4, COLA functions well in this case. The concrete number of the used data points depends on the used CE method.
Yes
No ethics review needed.
Specific suggestions (please feel free to ignore these if I didn’t understand things well):
- In order to make this methodology widespread and for reproducibility, I don’t know if the authors considered converting their code (in the supplemental material) to a Python package or creating a Python class? I am not sure if the editor should require this for publication?
- Typo on row 196? “First p-SHAP degrades to RB-SHAP”, shouldn’t it be B-SHAP?
- Typo on row 474? Word alignment misspelled?
- Perhaps clarify on row 231 that it is the tightest Lipschitz upper bound, not necessarily the tightest upper bound.
- The paper attempts to contribute to important theoretical explainability literature, in addition to connecting to real-world demands to make model explanations more actionable. This is a growing demand in several areas of society, especially with current and incoming AI regulation.
- The authors thankfully write for a broader audience without being too verbose. Although most of the paper’s contribution is presented starting in Section 4, the content before this section provides several points of entry and the exact amount of revision a reader needs to understand their framework. I personally learned from their exposition.
- The method is mostly sound and tries to be as generic as possible (e.g., as p-SHAP is a generic formulation), and the authors provide intuition for most of their steps. Overall, the paper seems well-polished and organized, lacking only a few important adjustments. 
- A clear algorithm is defined, consisting of a collection of widely used algorithms, and its computational complexity is derived, which is informative for scalability. 
- Their methodology is tested in a wide variety of settings, i.e., using four different divergence functions, four different datasets, comparing COLA to five other CE algorithms, and utilizing 12 different classifiers. This is useful to demonstrate the robustness of their method compared to others.
The paper titled "Refining Counterfactual Explanations with Joint-Distribution-Informed Shapley Towards Actionable Minimality" proposes a framework for improving counterfactual explanations (CE) in machine learning models. Current CE methods often include unnecessary feature changes, making them difficult to apply in practical scenarios. The approach proposed in this paper seeks to minimize these changes while maintaining the validity of the counterfactual exercise, making CE more actionable for both users and stakeholders, particularly in terms of simplified and actionable decision-making.

*Major contributions of the paper include:*
1. The setup of a well-defined problem for finding CE with minimal feature changes (Equation 1).
2. The development of the algorithm "COunterfactuals with Limited Actions (COLA)" to find the solution to the previous point.

*Sub-contributions that are incorporated into the definition of COLA:*
- The definition of a generic Shapley framework (p-SHAP), which nests several other commonly used Shapley frameworks for computing feature importance and allows for incorporating the distributional connection between factual data $x$ and counterfactual data $r$, i.e., their joint distribution $Prob(x,r)$, in its computation.
- They show that p-SHAP correctly measures the causal behavior of shifting $x$ towards $r$ (Theorem 4.2).
They propose Optimal Transport (OT) techniques to recover $Prob(x,r)$, given $x$ and $r$, which can be incorporated into p-SHAP for CE. The OT guarantees tighter bounds on the distance between factual and counterfactual, $D(f(x), y^*)$, under the assumption that the model $f$ is Lipschitz continuous and $y^* = f(r)$ (Theorem 4.1).
- They derive the computational complexity of COLA.

The authors combine a collection of algorithms in order to construct COLA. Each of the algorithms is listed below:

a. FIND $r$: For a counterfactual $y^*$ and a factual $x$, find $r$ within an $\epsilon$ radius of $x$ to minimize the distance $D(y^*, f(r))$.

b. COMPUTE $Prob(r,x)$: Once $r$ is found, use it to estimate the joint density $Prob(x,r)$, (mostly) with OT.

c. COMPUTE p-SHAP values: Once $Prob(x,r)$ is obtained, use it to estimate p-SHAP values $\phi$ between $x$ and $r$.

d. OBTAIN THE CE: Using $\phi$, together with $Prob(x,r)$ and $r$, edit $x$ minimally in order to obtain the CE of $y^*$ from $x$, called $z$.

*Numerical Results:*
- The authors test their algorithm using four different datasets, where the task is classification. They show that the algorithm is feasible and achieves $z$ with empirically minimal changes compared to five other CE algorithms, with minimal or zero misalignment $D(f(z), y^*)$, across 12 different classifier models.
- In simpler setups, the authors compare COLA’s performance in terms of finding the $z$, measuring its performance $D(f(z), y^*)$, while comparing it to the optimal theoretical performance. Although not achieving optimality for some scenarios, COLA sometimes still outperforms CE methods that use exact alignment.
*PRESSING ISSUES*
- COLA has a well-defined procedure to compute $z$. It seems clear from Theorem 5.1 that $z$ would satisfy the constraints from Equation 1, but it is not clear how the chosen $z$ from COLA is actually optimal, i.e., why is it minimizing, or closer to minimizing, the problem in Equation 1, given that the last algorithm in COLA to find $z$ does not minimize any function. Even if it is not optimal, as suggested by Figure 4, the paper would benefit from having a clearer narrative of why COLA is closer than other methods to optimal, considering the minimization problem in Equation 1.
- The connection between $p-SHAP$ and $p_{OT}$ in Section 4 can be improved. This is the part that seems to be able to benefit the most from clarity and extra sentences connecting these two different topics and situating them in the bigger goals of the paper. A few suggestions:
    - When introducing the OT problem in this section, the reader might benefit from having a sentence or two mentioning what the goal of OT is, in addition to its purpose in p-SHAP. This is somewhat done in row 209, but I believe it would be clearer if it comes earlier in the previous paragraph.
    - It would be great to have a clear explanation/insight in the paper about why $A_{prob}$ does not necessarily require knowledge of how $r \sim \mathcal{D}$ is generated in order to achieve good CE performance.
    - In the “Theoretical Aspects of p-SHAP”, it would be helpful to know more precisely why using OT for obtaining the joint distribution $Prob(r,x)$ helps later with minimizing $D(f(z),y^*)$. This connection doesn’t seem to be precise as it is.
    - Theorem 4.1 is labeled as “p-SHAP towards CE”, but the theorem is much more a result of OT + Lipschitz continuity of $f$, and its direct connection to p-SHAP seems to be missing.

*OTHER*
- The paper provides so many entry points for the reader, and it would be nice to also have the definition of “Exact Alignment” and “Feature Alignment (FA) performance” at least once in a footnote.
- Perhaps writing a sentence at the beginning of Section 3, and/or at the end of Section 2, so the reader knows what to expect in the transition from Section 2 to Section 3, and how they fit in the big picture of the paper.
- Row 472: Result III could benefit from having a sentence entry point to situate the reader as to why this is important and how it fits in the big picture of the paper. Furthermore, another sentence would be useful to provide insights on why $CF-P_{OT}$ outperforms $CF-P_{Ect}$.
- Please add titles to the x-axes of Figures 3 and 4, either in the image or in their descriptions.
Yes
No ethics review needed.
Reordering the writing would help readers make sense of the contributions in a single pass. The inclusion of SHAP seems arbitrary - and although demonstrated to work well - it is unclear why other methods are not included.
The paper presents a new problem perviously unreported in the literature, and solves it effectively. The empirical findings seem to be robust and diverse. The paper presents the proposed method adequately and displays the improvements it provides through exhaustive experiments.
The paper presents a post-hoc modification of a set of counterfactual explanations. It does so with the aim of reducing the modification-costs of the counterfactual explanations found. To do so, it employs a new variant of the common SHAP feature attribution technique, which explicitly includes both in-distribution and counterfactual-distribution data in the SHAP baseline prediction computation. The feature attributions so obtained are used to modify the existing set of counterfactual explanations, and it turns out that this modification reduces the costs associated with the counterfactuals.
The writing could be clearer. The paper introduces and repeatedly uses terms without defining them: "exact alignment" (line 25, 197, etc; finally explained only on line 308), "well-performed action plans" (line 98), etc. It would be useful to define the terms at the time of their first use.

I do not understand the "decoupling" phenomenon mentioned in line 85-86, and the reference to the later demonstration was lost (or I may have missed it). Perhaps more exposition and an explicit reference to where in the paper to find this "later" would be helpful.

The "counter-intuitive finding" described in lines 101-105 remained difficult to parse until I had reached the end of the paper, because "associating" and "alignment" had not been defined yet. These terms can be defined and explained earlier in the paper, so that the findings become easier to understand in a first read. The abstract could also be amended similarly to ensure that it is easier to understand.

It is unclear to me why the proposed SHAP variant performs better than other SHAP variants, or indeed why would SHAP feature attributions be a good way to perform post-hoc optimisations on generated counterfactual explanations at all. The paper presents the proposed method adequately and displays the improvements it confers, but I'm unsure why this is the case. Any intuition or ideas that the authors have about this would be good to include. While additional experiments aren't strictly necessary, I am curious about how non SHAP based methods would perform. I have not looked at the code directly, but if the results are easily replicable, this might lead to rapid future work in this area, providing more understanding of the phenomena reported in the paper.
Yes
No ethics review needed.
I have stated all the questions in the weakness section of the review. The paper needs to really strengthen its experimental results section. I would expect something like a table, where the columns are the various metrics along with a CFE is evaluated, like validity, proximity, sparsity, distance of training data manifold, adherence to causal constraints, and the time to generate the CFEs (including dependence on any other technique) and the rows to be a large set of baselines. Only when the numerical results demonstrate the superiority of COLA, can the supporting theory, theorems, and the claims of near-optimal performance be useful.
The paper establishes an excellent mathematical framework to generate CFEs such that they change the smallest number of features from the original datapoint. This framework connects CFEs with Feature attribution technique SHAP.
The paper proposes an algorithm to compute CFEs for datapoints such that a minimal number of features are changed, thereby generating sparse CFEs.
There are several weakness in the paper, I list them as follows. The authors only need to address the ones marked as major for the rebuttal (if they like to):
1. Line 51: "some CE algorithms assume differentiable models, whereas others are designed specifically for tree-based or ensemble models" -- this is misleading, as many CE algorithms work for black-box ML models, you can find them in the Verma et al. survey paper. 

2. [Major] Line 79: "Three major challenges remain in addressing this problem". The next three lines do not sounds like challenges at all. The first one says that one CE algorithm will not suffice (which is not true as past work have proposed algorithms that work for generating sparse CEs), the second one about not assuming anything about the model (this is not novel several works have done this), and the third is about how feature attribution techniques can be misleading (which is obvious because they are not optimized to be used as CE, a feature that is marked as important by some FA method does not necessarily mean that it is an effective way to change the prediction). Please state the challenges (if there are any).

3. Line 124 $M_{c_{ik}}$ is not defined which makes understanding Eq 1(d) and 1(e) hard. Also how does having $c_{ik}$ = 0 allows no change in its value? I don't see that being implied from the equation

4. B-SHAP and RB-SHAP have different background distributions and it is clear to the community about the advantages and disadvantages of each. You define CF-SHAP, but never state what trade-off does one expect when using background distribution from CF distribution instead of the training distribution. Please explain what should one expect from such a FA method. 

5. Line 197, correct the typo from RB-SHAP to B-SHAP.

6. The first paragraph of section 4 is obvious, it is just a generalization of the notations from Equations 4-6, I don't think there is a need to give so much attention and explanation for it. 

7. [Really Major]. You mention a lot of details about the optimal transport thing to compute the most sparse CE, and do a really good job at explaining Algorithm 1 in Section 5. At this point, I am excited and was anticipating some great experimental results because you spent such a large part of the paper establishing strong mathematical grounds for generating CFEs and even proved some theorems, but the experimental section is **extremely weak** and does not convince me at all about the relevance of the propose technique. 
       1. First and the most important weakness is that you need another CFE generation technique to generate a CFEs for a lot of datapoints that you use to compute the joint distribution and then generate a CFE using your technique, is that right? If that is the case, in the paragraph of computation complexity, why do you not include that? Also it is not the case that your technique just takes a CFE from some other technique and refines it, it needs a whole lot of datapoints and CFEs to even start functioning. Please correct me if I am wrong. 

       2. The experimental results are very weak for the following reasons:
              **a.)** Result 1 in Section 6 (lines 415 - 421) are not useful when a datapoint does not achieve the desired classification. In other words, if a datapoint does not achieve y* classification (which makes it a valid CFE), there is no point in mentioning the sparsity of that, because it is an invalid and not useful CFE. Therefore the third column in Table 3 is not useful at all. 

             **b.)** Several baselines are mentioned in lines 368-372, but none of them are used in the experimental results section? Why? Aren't these the baselines that you need to compare against to show that your technique is better than them atleast in the one metric you are targeting (which is sparsity)? Instead what you do in Table 3 is compare against 5 variations of your own proposed method. Sure one of your own method is better than the other 4 you mention, that does not tell me anything about how does COLA compare to previous techniques. Please let me know if you disagree. Therefore Result 2 is not useful. 

             **c.)** The baselines considered in the paper (the results for which are not reported atleast in the main paper), are outdated and several new techniques have been proposed that are better at all metrics than DiCE and KNN, for e.g. see Amortized Generation of Sequential Algorithmic Recourses for Black-box Models. 

            **d.)** An underlying and unstated key assumption in the formulation of the paper is that sparsity is the most important metric to consider when generating CFEs. This is atleast not agreed upon by the community, see the list of metrics proposed in Verma et al. survey paper.
Yes
No ethics review needed.
How well would this method generalize to different multiclass and regression settings?
This paper addresses the important task of making counterfactual explanations actionable by minimizing unnecessary feature changes.

The authors offer a detailed theoretical basis for their methodology with clear explanations and motivations. 

By sharing their code and giving computational details, the author makes the approach more accessible and transparent.

The results seem robust and the counterintuitive finding that relying solely on exact alignment between factual and counterfactual data can be suboptimal is interesting.
This paper addresses the challenge of creating valid and actionable counterfactual explanations by minimizing unnecessary feature changes. The authors introduce the COLA framework, which computes a joint distribution between observed and counterfactual data to inform Shapley values for feature attributions. This joint-distribution-informed approach allows them to refine the counterfactual explanations without imposing restrictions on model types or algorithms to compute the counterfactuals.
The approach is computationally demanding, mainly due to the optimal transport (OT) calculation, which may limit its scalability in large datasets. (which the authors acknowledge.)

While OT provides a probabilistically informed alignment, it may only sometimes yield the optimal feature attributions for all tasks, as it lacks task-specific tuning and causal considerations. However, the authors denote this as future work.

The approach is primarily evaluated on binary classification and tabular data, leaving its effectiveness on multiclass or regression and other data types (e.g., images, text) scenarios unexplored.
@inproceedings{
anonymous2024refining,
title={Refining Counterfactual Explanations With Joint-Distribution-Informed Shapley Towards Actionable Minimality},
author={Anonymous},
booktitle={Submitted to The Thirteenth International Conference on Learning Representations},
year={2024},
url={https://openreview.net/forum?id=hQ2TUZmse1},
note={under review}
}
Counterfactual explanations (CE) identify data points that closely resemble the observed data but produce different machine learning (ML) model outputs, offering critical insights into model decisions. Despite the diverse scenarios, goals and tasks to which they are tailored, existing CE methods often lack actionable efficiency because of unnecessary feature changes included within the explanations that are presented to users and stakeholders. We address this problem by proposing a method that minimizes the required feature changes while maintaining the validity of CE, without imposing restrictions on models or CE algorithms, whether instance- or group-based. The key innovation lies in computing a joint distribution between observed and counterfactual data and leveraging it to inform Shapley values for feature attributions (FA). We demonstrate that optimal transport (OT) effectively derives this distribution, especially when the alignment between observed and counterfactual data is unclear in used CE methods. Additionally, a counterintuitive finding is uncovered: it may be misleading to rely on an exact alignment defined by the CE generation mechanism in conducting FA. Our proposed method is validated on extensive experiments across multiple datasets, showcasing its effectiveness in refining CE towards greater actionable efficiency.
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Explainable artificial Intelligence Feature attributions Counterfactual explanations
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interpretability and explainable AI
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Refining Counterfactual Explanations With Joint-Distribution-Informed Shapley Towards Actionable Minimality
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