Venue: NeurIPS 2022 Conference

Reviews:

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: The paper uses auxiliary labels to detect and mitigate shortcuts. The key idea is that they are able to go from a large set of auxiliary labels to a potentially small set that are actually shortcut labels. The most of the representations building follows from Makar et al. 2022.





strengths_and_weaknesses: The paper is easy to read and makes an important contribution to an important problem. They take clean and useful steps to go from having auxiliary labels that are not necessarily shortcut labels to get to a shortcut labels by using conditional independence tests. This seems to suggest that we can pick up a bunch of labels about the task and use them as V^d. The experiments in the paper are encouraging. Lines 105-113 talking about a specific important problem were useful and informative!


My main issue with this paper is the ability to collect auxiliary labels that satisfy the conditions of $V_c$ in figure 1. My issue is that one can end up collecting auxiliary variables that are causal children of $X^*$. This would mean that s(X) is dependent on these always. This means these potentially invariant and informative features (because they appear in $X^*$) would end up being listed in $\hat{V}_p$. Then, under  means going to $P_0$ will make Y independent on some invariantly relevant features. This would lead to suboptimal error. 

This means that a lot of care could still be required in specifying $V_c$, which would require domain knowledge or some knowledge of shortcuts. That said, I do believe the paper points out a useful next step to do when one is able to get a list $V_d$ that does not specify any $X^*$ related features.

I have other issues with the claim of the ability to handle high-dimensional $V_d$. See questions.


There's a few papers that have related causal/anticausal factorizations and learning that could maybe go in the related work because they also handle high-dimensional shortcuts or do not require exact knowledge of the shortcut features: causal sufficiency based representation learning https://arxiv.org/abs/2109.03795, equation 1 seems to like the family here and high-dimensional spurious features  https://arxiv.org/abs/2107.00520, the causal diagram is used along with environments but not spurious features https://arxiv.org/abs/2006.07500, use augmentations to build robust models https://arxiv.org/abs/2111.12525


===== Update after rebuttal

The authors have addressed my concerns. I'm updating my score accordingly.
questions: 1. Selecting the auxiliary labels seems to be as hard as finding spurious features using expert knowledge. How can I pick auxiliary variables without knowledge?
2. While V^d is allowed to be highdimensional, and then try to find a subset by testing each V separately. Conditional independence testing is supposed to be hard when things get high-dimensional (queue the advent of CRTs https://arxiv.org/abs/2104.10618 etc.). Can the authors comment on if and why they believe this may not be an issue? Is KCIT particularly suited here?

related issue: 

Finding s(X) in equation 2 seems to require building a model with a high-dimensional output (if V^d is allowed to be high-dimensional). Was this easy in practice? How large can V^d get before this step seems a large error?

3. Can the authors address the main concern from above? Giving an example would be greeat here.
limitations: See questions and weaknesses.
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: The paper proposes a method for (1) idetifying shortcuts among a set of candidate shortcuts and (2) training a predictor that is invariant to these shortcuts. The method is based on assumptions about the causal relationships between the target variables $Y$, observed inputs $X$ and the candidate spurious attributes $V^{d}$, and comes with theoretical guarantees. The authors perform experiments on two semi-synthetic vision datasets.
strengths_and_weaknesses: I want to note that I am not an expert on causal inference, so I did not verify all the details of the mathematical derivations.

**Strength 1.** The paper is well-written and the presentation is clear. In particular, Section 3 is written in a way that it can be understood by non-expert readers, which I appreciate: the authors provide examples associated with different types of causal structures.

**Strength 2.** The proposed method tackles a challenging setting where the list of shortcuts is not known a priori, and has to be identified from a broader range of candidate shortcuts.

**Strength 3.** The experiments show that all the components of the proposed method are actually useful, and the method cannot be trivially simplified.

**Strength 4.** The authors describe the details of the proposed procedure carefully, including how the cross-validation is performed.

**Weakness 1.** The proposed method is quite complicated and involves a lot of moving parts. As far as I understand, you need to (1) train a predictor $s(x)$ that predicts the attributes $V^d$ from $X$; (2) train a predictor $\eta(v^p_i, y_i)$ in order to obtain example weights to achieve independence between $Y$ and $V^p$; (3) train a feature representation $\phi(X)$ and classifier $h(x)$; (4) perform multiple independence tests during shortcut identification, feature representation learning and validation. Given the complexity of the procedure, it is likely that it may not work out of the box on a new problem. 

**Weakness 2.** Experiments only compare the variations of the proposed method, standard training with weight decay and group weighting. I understand that the paper tackles a unique setting, but it would be good to include other baselines such as Group DRO (given that shortcuts are known) or methods such as Just Train Twice, even if the comparison is not entirely fair. Group DRO could possibly provide an upper bound on the robust classifier performance with identified shortcuts.

**Weakness 3.** Experiments are all done on semi-synthetic problems. Both problems use artificially added black patches as one of the shortcuts. It would be nice to see a more realistic application of the proposed method.

**Typos**:
- line 7: interprability 
- line 92: are are
- line 166: two tests that enables
- line 170: in principal
- line 281: the that

questions: **Question 1.** In line 104, could you please clarify what you mean by $P_s(V^6) P_s(Y) \ll P_s(V^p, Y)$? Does the $\ll$ here mean "absolutely continuous with respect to" or  "much lower"? In the latter case, one probability measure cannot be much lower than another one everywhere, as they have to both integrate to $1$?

**Question 2.** In proposition 1 you say that you require $Y$ to be independent from $V^p$ but in the interpretation in line 140 you say $X$ independent from $V^p$. Is this a typo?

**Question 3.** In definition 1, what is $f$? Should it be $g'$?

**Question 3.** You mention "overlap" several times in the paper, e.g. in line 103 and line 148. What exactly do you mean by overlap? 

**Question 4.** Could you please comment on the similarity of your work to iCaRL [1]? 

**Question 5.** Once the shortcuts are identified, do I understand correctly that you could apply some of the standard methods in the spurious correlation literature to learn a robust predictor? For example, Group DRO?

**Question 6.** How did you select the strength of $L_2$ regularization for the $L2$ method? It appears that it performs poorly even in-distribution on Waterbirds.

[1] *Invariant Causal Representation Learning for Out-of-Distribution Generalization*;
Chaochao Lu, Yuhuai Wu, José Miguel Hernández-Lobato, Bernhard Schölkopf
limitations: No issues.
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: This paper aims to deal with the shortcut learning to alleviate distribution shift problem by leveraging the causal structure of a problem. The paper first defines several models and concepts including the casual DAGs, generalization risk, P-specific shortcuts, etc. Then, it identifies a sufficient subset of shortcuts with the help of two properties stated in section 4. Afterward, it builds risk invariant predictors on the given identified set. Experiments on two datasets demonstrate the effectiveness of their method. 

strengths_and_weaknesses: strength:
(1) The paper provides an idea that robustness to a large set of distribution shifts can be achieved by ensuring the invariance to a small set of shortcuts.
(2) The paper further develops a method to identify the small set of shortcuts. 

weakness:
(1) The author proposed a two-step method to build risk invariant predictors, however there lacks statements on the impact of the accuracy of step 1 on step 2. Such as, in section 3, the author assume that Vp is a subset of Vd. How will it affects the robustness of the predictors when it is violated? Since this method is based on a group of complex assumptions, I believe that such results is needed(no matter theoretical or experimental).

(2) The experimental results are indirect to demonstrate the contribution claimed by the authors. The authors claim that their methods are able to identify shortcuts, while in both experiments there lacks an actual result to illustrate it, and merely overall AUROCs on different settings are offered.
(3) It seems that both experiments are synthetic, so it is a little not convincing. 
questions: (1) In equation(1), it seems the target set of distributions is calculated from a specific DAG. Whether the arguments and results below relies on a correct DAG?
(2) In section 6.1, it says "our approach is able to correctly identify the two true auxiliary labels which mark the true shortcuts in all 10 simulations". Is there any detailed result?
limitations: Yes
review_title: null

Meta-review: metareview: The reviewers agreed the paper is a worthwhile contribution in a growing area of identifying and removing shortcuts for robustness to distributional shift. Please take the reviewers feedback into consideration for the camera-ready.
confidence: Certain
Decision: Accept