Paper: Natural Counterfactuals With Necessary Backtracking (ICLR-2024)

Reviewer comment (Presentation):
Knowledge about the causal graph looks like a strong assumption to me, but I know that this is assumption is quite common the causality domain. However, I miss a little bit the relation to machine learning -- i.e. how exactly this might be applied to arbitrary machine learning systems. This is somehow mentioned in Appendix D, but I was wondering whether it might be beneficial, in order to make the paper more accessible to a larger community, to elaborate more on this in the main paper.

Author response:
**Q2. Knowledge about the causal graph looks like a strong assumption to me, but I know that this is assumption is quite common the causality domain. However, I miss a little bit the relation to machine learning -- i.e. how exactly this might be applied to arbitrary machine learning systems. This is somehow mentioned in Appendix D, but I was wondering whether it might be beneficial, in order to make the paper more accessible to a larger community, to elaborate more on this in the main paper.**

Thanks for the helpful suggestion. Your critical point is well taken. It is certainly a limitation of our work and most of the related work that the causal information needed for such methods is not always available. Still, we believe counterfactual reasoning fundamentally relies on causal understanding. If machine learning aims also to harness counterfactual reasoning, it has to somehow incorporate causal knowledge or assumptions, either by building in background knowledge or by automated causal discovery. In this connection, it is worth noting that learning of causal structures from observational data, though still fraught with challenges, has made a number of impressive advances in recent decades.

To acknowledge this important critical point, we have incorporated a discussion within Sec. 6 (Conclusion and Discussion) of the main paper. Thanks again for the suggestion.

Reviewer comment (Presentation):
Broken reference in Section 2 second line?

Author response:
**Q3. Minor Issues.***

We are very grateful for your careful review of our paper. We have addressed and resolved all the problems you spotted, and your valuable feedback is highly appreciated.

Reviewer comment (Writing):
Sometimes the authors write "non-backtracking" and sometimes "nonbacktracking" -- I am not a native speaker but the first one looks more correct to me.

Author response:
**Q3. Minor Issues.***

We are very grateful for your careful review of our paper. We have addressed and resolved all the problems you spotted, and your valuable feedback is highly appreciated.

Reviewer comment (Presentation):
V-SCM Reference in A.2 on page 12 is broken?

Author response:
**Q3. Minor Issues.***

We are very grateful for your careful review of our paper. We have addressed and resolved all the problems you spotted, and your valuable feedback is highly appreciated.

Reviewer comment (Novelty):
How does your work differ from 'Backtracking Counterfactuals'? https://arxiv.org/abs/2211.00472.

Author response:
***Question: How does your work differ from 'Backtracking Counterfactuals'? https://arxiv.org/abs/2211.00472".***

Thank you for this important question. Due to the space constraint, we did not discuss this question in detail in the main text but left it to Sec. C of the Appendix. In our paper, we term the "Backtracking Counterfactuals" in your question as **prior-based backtracking counterfactuals**. In addition to the discussion in Sec. C, we also raised some concerns regarding prior-based backtracking counterfactuals in Sec. B of the Appendix.

We outline below the key differences between our natural counterfactuals and prior-based backtracking counterfactuals:

**Prior-based Backtracking Counterfactuals** [1]:
This approach involves backtracking to all exogenous variables, which amounts to requiring that interventions are applied only to these variables. The measure of similarity between the actual and counterfactual worlds is based on a predefined prior distribution. Exogenous variable values in the counterfactual world are sampled from a posterior distribution given the actual world's values and the desired counterfactual value.

**Natural Counterfactuals**:
Our method involves backtracking with a 'naturalness constraint' when an intervention on the target variable $A$ is implausible. This process aims to minimize changes and backtracking. It backtracks only when it is necessary to maintain "naturalness". If a direct intervention on $A$ is plausible, our approach aligns with non-backtracking counterfactuals.


**Differences Between Them:**

**(1) Intervention Approach and Resulting Changes:**

Prior-based Backtracking Counterfactuals: These counterfactuals directly intervene on noise/exogenous variables, which can lead to unnecessary changes in the counterfactual world. Consequently, the similarity between the actual data point and its counterfactual counterpart tends to be lower. In short, prior-based backtracking counterfactuals may introduce changes that are not needed. 

Natural Counterfactuals: In contrast, our natural counterfactuals only engage in necessary backtracking when direct intervention is infeasible. This approach aims to ensure that the counterfactual world results from minimal alterations, maintaining a higher degree of fidelity to the actual world.

**(2) Counterfactual Worlds:**

Prior-based Backtracking Counterfactuals: This approach assigns varying weights to the numerous potential counterfactual worlds capable of effecting the desired change. The weight assigned to each world is directly proportional to its similarity to the actual world. it is worth noting that among this array of counterfactual worlds, some may exhibit minimal resemblance to the actual world, even when equipped with complete evidence, including the values of all endogenous variables. This divergence arises because by sampling from the posterior distribution of exogenous variables, even highly dissimilar worlds may still be drawn.

Natural Counterfactuals: In contrast, our natural counterfactuals prioritize the construction of counterfactual worlds that closely emulate the characteristics of the actual world through an optimization process. As a result, in most instances, one actual world corresponds to a single counterfactual world when employing natural counterfactuals with full evidence.

**(3) Implementation Practicality:**

Prior-based Backtracking Counterfactuals: 
The practical implementation of prior-based backtracking counterfactuals can be a daunting challenge. To date, we have been prevented from conducting a comparative experiment with this approach due to uncertainty about its feasibility in practical applications. Among other tasks, the computation of the posterior distribution of exogenous variables can be a computationally intensive endeavor. Furthermore, it is worth noting that the paper [1] provides only rudimentary examples without presenting a comprehensive algorithm or accompanying experimental results. 

Natural Counterfactuals: In stark contrast, our natural counterfactuals have been meticulously designed with practicality at the forefront. We have developed a user-friendly algorithm that can be applied in real-world scenarios. Rigorous experimentation, involving four simulation datasets and two public datasets, has confirmed the efficacy and reliability of our approach. This extensive validation underscores the accessibility and utility of our algorithm for tackling specific problems, making it a valuable tool for practical applications.

In response to your feedback, we have incorporated a discussion on these key differences into Sec. 6 (Conclusion and Discussion) of the main paper (highlighted in red) and expanded the explanation in Sec. C of the Appendix, covering all three types of counterfactual reasoning discussed in our paper.

[1] Julius von Kugelgen, Abdirisak Mohamed, and Sander Beckers. Backtracking counterfactuals. arXiv preprint arXiv:2211.00472, 2022.