Venue: NeurIPS 2021 Conference

Reviews:

final_score: rating: 6: Marginally above the acceptance threshold
review_content: summary: In this paper, the authors proposed methods to encourage structural similarities in the potential outcomes (POs) under different treatments when learning the conditional average treatment effects (CATEs). Specifically, three sets of different structure/model modifications were proposed on top of the existing TNet/TarNet model by utilizing regularizations or shared hidden units under different treatments. Proposed methods were evaluated on various simulated data. 
main_review: The proposed methods are structure modifications to existing methods for learning CATEs. The modifications are fairly straightforward, utilizing regularization or shared hidden units in neural networks. These techniques are commonly used in neural network models, so the contribution mainly lies in the application area for learning CATEs under the inductive bias assumption.

The proposed methods are valid and appropriate to address the research question. This paper is in general well organized. Extensive simulation studies were conducted. If the true POs share a common structure, the proposed methods are useful in improving the estimation for CATEs by borrowing strengths and encouraging a simpler model structure. My main concern is the soundness of the assumption and how the proposed models perform under violation of the assumptions. Also, how to test the assumption and whether people should proceed with this line of methods when there is no prior knowledge of POs need to be examined.

Additional comments and questions:

In the simulations, all settings assumed some common structure between the two POs. As a sensitivity analysis, I wonder how would the models perform if the two POs do not share any structure or parameter? In this circumstance, would the penalization parameter that encourages similarity to be chosen close to 0 by cross-validation? 

Can the authors talk about how would people check the assumptions that the POs are similar, and whether or not to encourage a similar structure between POs in learning CATEs when there is no prior knowledge?

Also, I wonder do the authors compare the accuracy in inferring the optimal treatments under different methods? MSEs of CATEs were reported. But sometimes a more meaningful question is whether the treatment recommendation direction is correct, and such result can be informative to viewers. 

limitations_and_societal_impact: The authors should discuss more on the limitation and societal impact when the inductive bias for encouraging similarity between POs is not correct. How much would this impact the estimation and treatment recommendation should be evaluated. Potential remedies and proper guidance on whether this line of methods should be utilized should be discussed.
review_title: null

final_score: rating: 6: Marginally above the acceptance threshold
review_content: summary: This paper considers the problem of estimating the conditional average treatment effect (CATE) of a binary treatment with some potential outcomes of interest (either continuous or binary). Simply put, in, e.g., a medical scenario, CATE would measure the expected delta in administering some drug vs. not for a particular patient X. The main challenge of this problem is that Y(0) and Y(1), the outcomes given the value of the binary treatment, are never observed at the same time, so estimating CATE is not a standard supervised learning problem, where Y(1) - Y(0) can be observed for the same input X. One can estimate both Y(1) and Y(0) separately, but the errors add. 

The key insight of this work is that the difference, $\tau(x) = \mathbb{E}[Y(1) - Y(0) \mid X = x]$, is often of a much simpler form than either $\mathbb{E}[Y(1) \mid X = x]$ or $\mathbb{E}[Y(0) \mid X = x]$, due to inherent similarities in Y(1) and Y(0). To account for this, this paper investigates and compares several end-to-end learning strategies that encode inductive bias for shared/similar structure---namely, (1) regularization, (2) reparameterization, and (3) shared multi-task architectures.
main_review: === Strengths ===

- The paper is very well written and provides extensive evaluation and discussion/comparison of past work. 
- In general, the problem that the paper focuses on is interesting and important.
- It is nice to see *some* real world evaluation (Twins dataset), with the understanding that this is imperfect and hard to come by.
- Empirically, the strategies proposed by the authors (in particular, FlexTENet) seem to show consistent improvements over competing baselines.
- The proposed strategies are simple and easy to implement within most frameworks, and should be easy to adopt.

=== Weaknesses ===

- From a technical standpoint, the contributions of this paper are fairly limited. The inductive biases for shared/similar structure are, for the most part, well-known (at least in the multi-task learning community). This is not inherently bad---there remains value in the analysis. The wording of lines 61-70 is a bit confusing though, as shared structure inductive bias has already been a quite common "dimension" for improving MTL estimators (not just the architectures used). The use in CATE estimation specifically may be a bit less prevalent.

- While it may be true that this shared structure inductive bias may be useful, it seems hard to systematically tune the regularization strengths, $\lambda$. This is especially true in the real world, where development data will be mostly unavailable, and the true underlying setting (shared structure or not) will be unknown. In the worst case, it seems that strategies (1) and (3) with too high of a regularization could severely underestimate CATE (i.e., the models collapse together)? How should these weights be chosen?

=== Justification for score ===

Overall, the paper is well-written and provides an interesting survey of several reasonable inductive-bias inducing techniques for CATE estimation. The technical novelty of the paper, however, is fairly limited, and its experimental findings are not that surprising given what we know from MTL literature, which makes it borderline. That said, its presentation and analysis could still make a potential contribution to the treatment effect estimation community. 

=== Minor comments ===
- It would be helpful to introduce the CATE estimation problem more formally (as done in Section 2) earlier in the introduction. This would help ground readers less familiar with PO frameworks.
limitations_and_societal_impact: I do not foresee any major limitations and/or societal impacts. How to choose regularization strengths would be the main implementation question/limitation.
review_title: null

final_score: rating: 8: Top 50% of accepted NeurIPS papers, clear accept
review_content: summary: This paper contributes an investigation of the inductive biases of various neural network architectures in the context of conditional average treatment effect estimation. Specifically, the authors put forth the hypothesis that $\mu_0(x) = E[Y|X=x, W=0]$ and  $\mu_1(x) = E[Y|X=x, W=1]$ have similar structure and thus $\tau(x) = \mu_1(x) - \mu_0(x)$ *can* be simpler than either $\mu_w(x)$. 

The authors investigate three approaches: (1) a two path (one per treatment) neural network, where the parameters $\theta_w$ of both paths are regularized to be point-wise close, (2) reparametrization whereby they explicitly learn a $\mu_0$ and a $\tau$ and set $\mu_1$ as $\mu_0 + \tau$, and (3) the authors' proposed approach (FlexTENet) where there are "private" functions $\mu_w$ for each treatment $w$ and a "shared" subspace in each layer. 
main_review: Thanks to the authors on the hard work on this paper. It is obvious that they have put in time and thought to address the concerns of previous reviewers (ICML 2021).  The paper is ready for publication in my opinion, especially considering the wealth of additional experimental evidence in the appendix. CATE is hard, and having promising neural network architectures is important.

The work is largely clear and well-written. A few questions:

(1) The section that actually describes FlexTENet starts on line 229. I found it lacked the details I was expecting. Some pseudocode or math in the appendix would be helpful. It's not clear exactly what the arrows mean in Figure 2.3. When 2 orange arrows go into the same block, does that mean the inputs are concatenated? That is, the private $\theta$ are always being mixed with the shared $\theta$?

(2) A lot of this work is presented as being built on the idea that $\tau$ may be easier to estimate than $\mu_w$. However, I am unclear as to when this would actually be the case in practice. For example, if the true $\mu_w$ was a decision tree, then $\mu_1 - \mu_0$ would be a difference of two decision trees, which is more complex than either one. From what I can tell, your toy example in Figure 1 is a lot of the justification of this idea. Can you justify it further? Perhaps using data from the twin study? Also, just because the experimental results are promising, does that mean you've found evidence of the hypothesis that $\tau$ is simpler than $\mu_w$?

(3) In lines 401 and 402 you wrote "The former seems to be the best choice ... when ... $\mu_0$ is simpler than $\mu_1$." Is it possible to fit 2 variants of the reparametrization model, where $h_0$ estimates $\mu_0$ in one case and $h_1$ estimates $\mu_1$ in the other case, and then choose the better one as part of the hyperparameter optimization? Would this approach significantly improve the reparametrization model model? After all, one or the other will be more complex in practice, although they could be of very similar complexity. Does the reparametrization model fail when $\mu_0$ and $\mu_1$ are of comparable complexity?
limitations_and_societal_impact: Yes.
review_title: null

Meta-review: This paper presents a novel framing and approach to the problem of conditional average treatment effect estimation, and validates it on synthetic data and a small sample of natural data. Reviewers generally found it to be a technically-simple but interesting contribution, and raised only minor concerns.
Decision: Accept (Spotlight)