Venue: NeurIPS 2021 Conference

Reviews:

final_score: rating: 4: Ok but not good enough - rejection
review_content: summary: This work proposes counterfactual maximum likelihood estimation (CMLE), a new training objective for suppressing the spurious effect of confounding variables. The authors derive two types of upperbound formulation for interventional log-likelihood (i.e. implicit CMLE and explicit CMLE). Using natural language inference (NLI) and image captioning as the intervention modeling tasks, the proposed method demonstrated superior performance in terms of human-perceived performance.
main_review: Pros
- The proposed method performed superior performance in terms of human evaluation for NLI and image captioning, compared to simple MLE baselines.

Cons
- In contrast to the effort that went into deriving the CMLE objective, the experiments seem to lack some important factors as below.
- Lack of baseline models: the aim of this paper is counterfactual estimation (both NLI and image captioning experiments were set up as counterfactual estimation tasks). However, the authors fail to include any existing works related to counterfactual estimation (or treatment effect estimation) such as [1-8].
- Strange choice of datasets: Most existing counterfactual estimation studies use both simulated datasets and real-world dataset. The former is especially used because simulated datasets contain both factual and counterfactual samples, therefore the model can be tested to see if it actually learned the intervention effect (i.e. treatment effect) properly. However, in this work, the authors employ rather unconventional NLP datasets to test their method. If the authors would like to claim their work as a counterfactual estimation model, they should test their model on simulated datasets as well, rather than only relying on human perception of how appealing the generated outputs are.

References
1. Fredrik Johansson, Uri Shalit, and David Sontag. Learning representations for counterfactual inference. In International conference on machine learning, pp. 3020–3029, 2016.
2. Uri Shalit, Fredrik D Johansson, and David Sontag. Estimating individual treatment effect: general- ization bounds and algorithms. In Proceedings of the 34th International Conference on Machine Learning-Volume 70, pp. 3076–3085. JMLR. org, 2017.
3. Ahmed M Alaa and Mihaela van der Schaar. Bayesian inference of individualized treatment effects using multi-task gaussian processes. In Advances in Neural Information Processing Systems, pp. 3424–3432, 2017.
4. Sheng Li and Yun Fu. Matching on balanced nonlinear representations for treatment effects estimation. In Advances in Neural Information Processing Systems, pp. 929–939, 2017.
5. Jinsung Yoon, James Jordon, and Mihaela van der Schaar. Ganite: Estimation of individualized treatment effects using generative adversarial nets. International Conference on Learning Repre- sentations (ICLR), 2018.
6. Liuyi Yao, Sheng Li, Yaliang Li, Mengdi Huai, Jing Gao, and Aidong Zhang. Representation learning for treatment effect estimation from observational data. In Advances in Neural Information Processing Systems, pp. 2633–2643, 2018.
7. Bryan Lim, Ahmed Alaa, and Mihaela van der Schaar. Forecasting treatment responses over time using recurrent marginal structural networks. In Advances in Neural Information Processing Systems, pp. 7493–7503, 2018.
8. Bica, I., Alaa, A.M., Jordon, J. and van der Schaar, M., 2020, September. Estimating counterfactual treatment outcomes over time through adversarially balanced representations. In International Conference on Learning Representations.
limitations_and_societal_impact: N/A
review_title: null

final_score: rating: 6: Marginally above the acceptance threshold
review_content: summary: This paper applies methodology from CATE estimation to do maximum likelihood with respect to samples from the interventional distributions Y|do(T),X, which they call Counterfactual MLE (CMLE). They provide two algorithms, Implicit CMLE and Explicit CMLE. The implicit variant uses the CATE generalization bounds from Shalit's CATE generalization bounds paper to get bounds on the likelihood from the desired counterfactual sampling distribution. The Explicit variant writes bounds in terms of the distribution T|Y,X. The two methods are applied to natural language inference and image captioning tasks. The authors suggest that this methodology and the surrounding literature on causally-inspired prediction should play a large role in the standard approach of deep learning in order to avoid shortcut learning / relying on spurious correlations.
main_review: 1. In the intro, it is not clear why you introduce a graph that does not have an arrow from X to T but you call X a confounder. I will ask a series of subquestions on this topic: 

- I understand that in general you are concerned with some spurious correlations. However, the *Precise* context in which the red X->T arrow appears was not totally clear in the paper. Y is a common child of X,T so conditioning on Y correlates X and T. But when do we condition on Y? We would usually not do this when predicting Y. 

- Separately, you mentioned X may contain some confounders (mutual parent of T,Y). Wouldn't that necessitate a regular (black) arrow from X to T? Why is that not in the graphical models? 

- Finally, usually spurious correlations are defined as a correlation between the outcome and some variable that we do not want to predict with. This can arise when they have a common child that is conditioned on, or a common parent that is unobserved. Then, people worry about spurious correlations because the correlation may not hold in new populations / test sets. Can you elaborate on the precise meaning of spurious correlation, conditioning on which variables makes it happen, why do you assume it is bad if a model takes advantage of the correlation (eg some assumption about this correlation not holding in the test data)


2. Why do you call ptheta(T|X,Y) in eq. (2) the "interventional distribution" and call it the "observational distribution" in line 223? By interventional do you mean "distribution over possible interventions (treatments)" and likewise by observational do you mean "distribution that determines which Yt we observe"? I would maybe rephrase both of these since "interventional distribution" is usually used for p(outcome|do(treatment))"

3. I would suggest omitting some vague descriptions/adjectives/adverbs such a "much easier" in 228 and "potentially complicated" in 229 or rephrase with more precise terms.

4. Implicit CMLE: it's pretty unclear what is the contribution from the Shalit generalization bounds paper versus what you do on top of it. Can you try to restructure so that you can make that more clear? Do I understand that the main step here is to bound the MLE objective where expectation is over interventional distribution p(Y|do(T),X), and do I understand this bound is achieved by re-arranging the terms in the Shalit generalization bound?

5. Explicit CMLE: when you assume you can estimate  P(T|Y,X) can you provide more info on what making this assumption implies? And if there is any insight on what to expect when it is misestimated?

5. M-1 samples versus tuning gumbel-softmax's temperature parameter. I'm really not sure which is worse. I suggest a dedicated synthetic experiment where you compare these two methods (does gumbel-softmax work well enough).

6. More generally, I think the omission of synthetic experiments is one of the main weaknesses of the paper. The setup has so many moving parts (estimating IPMs, learning auxiliary models, gumbel-softmax). It's so important to isolate the effects of any of these steps and the effect on the entire objective/procedure when any one of these step is wrong. For example, you could try a controlled simulation where the p(T|Y,X) model perfectly matches the ground truth.

side note not factoring into my review: for unobserved confounders, I would check out the recent work on proxy variables. There they discuss observed children of confounders and it may be a useful basis for extensions.

To summarize, these should be improved:
- writing clarity about X->T edge
- writing clarity about contributions over Shalit bounds (e.g. we re-arrange their equation (XYZ) to get our .....)
- synthetic experiment should be added to test individual parts of the setup.

limitations_and_societal_impact: Yes
review_title: null

final_score: rating: 6: Marginally above the acceptance threshold
review_content: summary: The paper tackles the problem of spurious correlations caused by observed confounders and offers two potential solutions: implicit and explicit counterfactual maximum likelihood estimation. Specifically the paper deals with the setup of predicting the outcome Y of some action T on X and considers X to potentially be a confounder. The paper compares the performance of the proposed methods to on a natural language inference and an image captioning task and shows improvements in terms of human evaluation but little difference in terms of automatic evaluation.
main_review: Pros:
- The paper tackles the important problem of deep learning models picking up spurious correlations and proposes an interesting approach to dealing with this problem.
- The causal angle to reducing spurious correlations is currently being studied from various angles and seems to be a promising direction to handle this problem.

Cons:
- The paper assumes full observability of the confounder, that the exogenous variables are observed and only models a very specific causal model with three variables. This greatly limits the applicability of this work to the general problem of reducing reliance on spurious correlations.
- The general problem setup of the causal relations and the observability of exogenous variables seems like it lacks some clarity.
- The main benefits of the method seem to only be observable under the setting of human evaluation. It would be useful to turn to more standard benchmarks or at least similar set ups that test domain generalisation to other types of spurious correlation. The usual benchmarks such as coloured MNIST or ideas from e.g. [2] do not fit the assumed causal model though.  

Detailed comments:
- Line 61: differnce -> difference
- The paper assumes the exogenous variable to be included in X - as such it can be argued that the paper does not actually consider counterfactuals but rather only interventions. Throughout the paper the definition of counterfactuals is not precise.
- Section 3.2 mentions that neural networks are invertible as long as the activations functions are invertible. This is not exactly true as not every weight matrix is invertible, e.g. check out [1] for more on this.
- Section 4.1 mentions that CMLE significantly outperforms the other baselines the adversarial test set. This is not possible to judge without any confidence intervals. 
- The evaluation of the MLE with augmentation in section 4.2. seems flawed as the augmentations introduce noisy data which can be assumed to deteriorate the performance.
- The implicit CMLE seems similar to ideas in [2]. Is this correct? It would be good to discuss the relationship to this work.

[1] Kingma, Diederik P., and Prafulla Dhariwal. "Glow: Generative flow with invertible 1x1 convolutions." arXiv preprint arXiv:1807.03039 (2018).
[2] Makar, Maggie, et al. "Causally-motivated Shortcut Removal Using Auxiliary Labels." arXiv preprint arXiv:2105.06422 (2021).
limitations_and_societal_impact: See other comments.
review_title: null

final_score: rating: 7: Good paper, accept
review_content: summary: In this work, authors propose the Counterfactual Maximum Likelihood Objective CMLE, where the parameters of the statistical model are inferred by maximizing the likelihood of the data under the interventional distribution, as opposed to the observational data. For the assumed model X -> Y <- T and X -> T, where X is the covariate, T is the treatment and Y is the outcome, the objective is to learn the parameters \theta that predict Y|X=x,T=t using just the causal link T->Y and not the spurious features in X=x. Ideally, if one could intervene on T and set do(T=t), it is possible to collect data where the outcome is observed upon the intervention done on T. Then maximizing the following likelihood: (CMLE objective) \argmax_\theta \sum_t E_{X|t}  E_{Y|x,t} p_\theta(Y|X=x,do(T=t)) would give us the MLE estimate of the parameter \theta under the set of interventional distributions do(T=t), thereby eliminating any effect of the spurious features in X on the prediction of the outcome label Y. The paper proposes two upper bounds for the above CMLE objective: i) Implicit MLE: focuses on obtaining better representations of the covariates X, such that the distribution of these representations is similar (by Wasserstein distance) for every value of T; and ii) Explicit MLE: where counterfactual examples are generated during training. Expectations in the theoretical derivations of the above upper bounds, can be estimated by Monte Carlo evaluations using only the observational data. Results are provided on two downstream tasks where models often rely upon spurious correlations: i) Natural Language Inference (NLI); and ii) Image Captioning (IC).
main_review: - The empirical results on NLI and image captioning seem fairly convincing, especially the human evaluations. But the improvements in automated metrics don’t seem very significant. 
- The paper is mostly clear and easy to understand. But, I would recommend the authors to improve the notation schema for Explicit MLE while providing an intuitive explanation for the upper bound.
- Since Explicit MLE does much better on human evaluation for both NLI and IC, it is unclear if practitioners should use Explicit MLE over Implicit MLE for all downstream tasks which require OOD generalization. It would be useful to be aware of at least one setting where Implicit MLE is useful. Although the authors conjecture a plausible explanation, the true reasoning behind this phenomena is not investigated in this work. Undoubtedly, it would be useful for the community to have a better understanding of why modeling the representations of X to be invariant under different treatments is not helpful---especially since multiple works have been proposed along these lines. Is the reason for this purely statistical, wherein the computation of the Wasserstein distance in high dimensions is inefficient or is it more fundamental, i.e. does the upper bound not closely track the CMLE objective to begin with?
- The theoretical derivations for the upper bounds seem correct. But, both upper bounds are in expectation, i.e. the authors don’t provide probabilistic tail bounds. This is especially important since even though the final optimization objective is an unbiased estimate of the upper bound, the statistical error is very high for those in high dimensions. 
- The authors have provided full access to the code for both NLI and IC tasks. The implementation details have also been made fairly clear.
limitations_and_societal_impact: Most of the concerns I laid above could be addressed in an expanded limitations section. I think if you condense your introduction section, you'll have a bit more space to expand your discussion. Parts of your broader impact discussion in the Appendix can also be brought here once you have more space.
review_title: null

final_score: rating: 7: Good paper, accept
review_content: summary: This paper proposed to use counterfactual maximum likelihood estimation to learn deep learning models that are less susceptible to spurious correlation relationships. In particular, it proposes two general algorithms, Implicit CMLE and Explicit CMLE, for learning causal predictions of DL models under observational data. The proposed method shows improvement over the regular MLE method in two real data sets.
main_review: Overall, I think this is a high quality paper with solid works done. Let me summarize my comments in some different aspects:

1. Originality: the proposed algorithm is novel and the idea itself is very interesting.

2. Clarity: this work is well-presented in general. With intuitive explanation following each formula/theorem.

3. Significance: The method itself is very general. The two real data experiments are very enlightening and I think the proposed method has great application potential in more real life tasks.
limitations_and_societal_impact: Yes
review_title: null

Meta-review: We thank the authors for their engaging submission on an important topic of research. 

A major shared concern of the reviewers is the lack of baseline methods in the empirical study.  While the related work section describes the state of existing invariant learning algorithms, the authors make no direct comparisons in the experiments.  And while there may be no directly comparable algorithm, the wealth of causal representation learning algorithms enumerated by reviewer S8oA could still be used to form predictions that highlight the key differences of the CMLE framework. 

Still though, this work introduces and empirically investigates a new objective for learning invariant representations.  With the additional simulation study and reviewer responses, this work was viewed favorably by most reviewers.  We encourage to the authors to incorporate insights from the simulation study into the manuscript.  
Decision: Accept (Poster)