Venue: NeurIPS 2021 Conference

Reviews:

final_score: rating: 7: Good paper, accept
review_content: summary: The work proposes a causal effect estimation method in presence of unobserved confounding, building on proximal causal learning. It starts from an existing two-stage regression approach for tractably solving the proximal causal learning problem and extends it to handle high-dimensional and non-linearly related data using neural networks to learn adaptive features which are used as input to the regression approach.
main_review: This work lifts the limitation of using linear or fixed kernel-based function classes in proximal causal learning, showing how to use neural networks which provide a more expressible and data-adaptive function class. The past approach based on two-stage regression is described in great detail, and the proposed modifications are clear. While the changing the method from static kernel-based features to adaptive neural network-based features is conceptually close to the approach of [32,18], the work demonstrates the significant technical effort required to make the change. The estimation method is shown to be consistent given assumptions on estimation of the regression functions in two stages and Rademacher complexity of the function classes used. The experiments show significant improvement from using neural networks.

My first concern is the artificial nature of the two experiments. The demand design task, while being realistic, simulates both the covariates and outcomes. Experiment on dSprite uses more realistic covariate distribution but the task itself (which is estimating the causal effect of an image on a synthetic outcome function) does not seem realistic or modelled after some real world application. I recognise that these are good benchmarks for testing the proposed methods that account for high-dimensional features. I would have appreciated demonstration of the method on a real world dataset or a synthetic one modelled after a task of practical interest and designed using realistic data distribution (in contrast to the demand design task).

My second concern is the limited motivation provided for the confounded off-policy evaluation problem which seems to be of practical value. But the description and possible applications of the problem is not very detailed. This can be improved by adding more example applications which are suitable to be modelled as confounded off-policy evaluation problem.

Questions:

Experiment setup:
How did the authors control the degree of complexity of confounder-treatment/outcome or outcome-treatment functions and dimensions of the three? Is it the case that Demand task has a  complex outcome function while dSprite task has complex confounder- treatment/outcome functions.

The method assumes continuous treatments, line 88, whereas in many practical settings we are concerned with quantifying treatment effect between two levels of the treatment. Does it extend to binary treatments? If not, then what is the difficulty on handling binary treatments?

Can you please provide example applications where the complexity of the datasets necessitate adaptive features?

Theoretical results:
The consistency results are left in terms of the Rademacher complexity of the function classes used. However, to justify the use of neural networks through these results, could you please comment on the Rademacher complexity of possibly a restricted class of neural networks? For example, a 2 layer ReLU network https://arxiv.org/abs/1805.12076. 
Additionally, please discuss whether the Rademacher complexities can be shown to vanish and at what rate, even in some restricted class of neural networks. 
Without these, the theoretical results are disconnected from the proposed method.

Method:
Can deep kernel learning (e.g. https://arxiv.org/abs/1511.02222) be a practical way of achieving adaptivity to data in the kernel-based methods [3,18]? Are there difficulties in learning such kernels for causal effect estimation tasks which in turn justify the proposed approach?

---
Author response addressed my concerns on experiments on realistic dataset and ideal application settings.
limitations_and_societal_impact: Consider adding limitation on only handling continuous actions.

Suggestions:

Average treatment *effect* is defined typically as the contrast between potential outcomes at two treatment levels and not for a single treatment level as in line 88. Consider rewording to average potential outcome or a similar name.

The experiment setup for demand design experiment states it as a prediction task line 277. Instead, please consider posing it as a causal effect estimation task to justify the need for removing confounding bias.

Assumptions 4,5,6 directly referenced in the Proposition 1 without introducing the nature of these assumptions. Please add a few words e.g. saying these are regularity conditions on conditional expectation functions or that these are not structural but functional assumptions.
Similarly, for Assumptions 7,8.

The approximation for computing gradient w.r.t. theta_W as mentioned in line 171 can be clarified in the update equations in Algorithm 1.

Line 97, may be easily included -> can be, since Appendix D extends the proposed method, as I understand.

Line 284, clarify what figure in this phrase mean “treatment is each figure”.

Minor
Line 27 confouder, line 195 frm, line 336 DFIV
review_title: null

final_score: rating: 6: Marginally above the acceptance threshold
review_content: summary: This paper presents a novel method: deep feature proxy variable. It applies a neural network to PCL, allowing non-linear relationships between variables. The authors prove the consistency of the method and demonstrate how this method can be applied to off-policy evaluation. The authors test the methods using two simulation studies, showing that DFPV outperforms existing methods. 
main_review: Overall, I enjoyed reading this paper. I believe some analysis on the usability of the method could make the paper more impactful. I would a consider increasing my score if the authors address the concerns.

pros
- The paper is clear and well written. It’s clear in its notation and setup. It also clearly stated the limitations of the theoretical contribution.
- The paper is well researched and motivated. It provides a crisp overview of proximal causal learning. It articulates the challenges in PCL and provides a reasonable solution.
- The experiments are reasonably designed. The authors provide detailed records of the experiment and source code. 

Area of improvements
- The captions in figure 3 and 4 are not clear. Why is DFPV so high variance?
-  I would be interested in knowing the performance of DFPV on a relatively simple data generating process. What sort of behaviour would DFPV exhibit in that case? 
- I would like an analysis about when we should use DFPV in contrast to the parametric methods.

limitations_and_societal_impact: The authors addressed the limitation of the theoretical performance, showing that the method works well in practice. I would like to see an non-trivial failure case of the method.
review_title: null

final_score: rating: 6: Marginally above the acceptance threshold
review_content: summary: The paper proposes an algorithm that operationalize the proxy variable
strategy for causal identification. It builds on existing approaches
(Deaner [3] and Mastouri and Zhu et al. [18]) and additionally
consider adaptive features as in Deep Feature Instruemtal Variable
method [32]. The key idea is to consider features parameterized by
neural nets, and alternate between learning $V$ by minimizing the
empirical loss and learning the parameters of the feature maps. The
paper shows that the additional flexibility of the features helps the
proxy variable method achieve better out of sample performance and
smaller errors in empirical studies.
main_review: The paper proposes an algorithm that operationalize the proxy variable
strategy for causal identification. It builds on existing approaches
(Deaner [3] and Mastouri and Zhu et al. [18]) and additionally
consider adaptive features as in Deep Feature Instruemtal Variable
method [32]. The key idea is to consider features parameterized by
neural nets, and alternate between learning $V$ by minimizing the
empirical loss and learning the parameters of the feature maps. The
paper shows that the additional flexibility of the features helps the
proxy variable method achieve better out of sample performance and
smaller errors in empirical studies.

Both the theoretical and empirical results of the paper make sense.
The methods and the results of the paper build closely on the two
stage formulation of Deaner [3] and Mastouri and Zhu et al. [18] and
the adaptive feature idea in Deep Feature Instruemtal Variable method
[32]. I have a few major questions.

The paper claim that Assumption 1 and 2 (the completeness assumption
on the unobserved confounder) are sufficient for causal
identification. In particular, the paper says that: Assumption 3,
which was needed in the original proxy variable paper (Miao et al
2018), is not necessary. Can the authors explain the intuition here?
Why is it not necesary here? The proof of Miao et al 2018 does rely on
this assumption. Moreover, do these completeness conditions in
Assumptions 1 and 2 have observable implications? Do they imply the
conditional of the proxy given treatment is complete in any ways? Or
do they have provably *no* observable implications? These observables
implications are important for causal estimation in principle.

Further, the completeness assumptions  plays a key role for
identification in the proxy variable strategy. They are not regularity
conditions. Rather, the completeness conditions are quite strong; they
are used to guarantee the solution to the integral equation is unique.
(Solutions to integral equations are not unique in general.) Despite
the importance of these identification assumptions, nowhere in the
algorithm are these completeness conditions enforced. As above, even
though the completeness assumption of Assumptions 1 and 2 are about
unobserved confounders, they may have observable implications and
shall be enforced in the proposed algorithm. (Or we should prove that
there exist *no* observable implications.) Without enforcing these
conditions, the causal estimation can in general by biased.

Finally, the paper could benefit from a discussion on the connections
to other recent work on proxy variables, which also discussed
practical estimation approaches to proxy variables that may be
compatible with the adaptive feature idea:

Miao, W., Hu, W., Ogburn, E. L., & Zhou, X. (2020). Identifying effects of multiple treatments in the presence of unmeasured confounding. arXiv preprint arXiv:2011.04504.


Wang, Y., & Blei, D. (2021, July). A Proxy Variable View of Shared Confounding. In International Conference on Machine Learning (pp. 10697-10707). PMLR.

Miao, W., & Tchetgen Tchetgen, E. (2018). A confounding bridge approach for double negative control inference on causal effects (supplement and sample codes are included). arXiv preprint arXiv:1808.04945.
limitations_and_societal_impact: The paper could benefit from a more elaborate discussion on its limitations. Is the use of adaptive features free lunch?
review_title: null

final_score: rating: 7: Good paper, accept
review_content: summary: This work extends known Proxy Causal Learning methods that aim at learning the causal effect of treatment in cases where unobserved confounders are assumed yet there is observable information in form of proxy variables to these confounders.
In particular, authors extend the theory to allow deep neural nets to be used as building blocks of the two stage regression proposed by Mastouri et al instead of RKHS. The paper also explains how to use the method to perform off-policy evaluation in a bandit setting where arms are confounded. Synthetic experiments are also reported to compare the performance with a few baselines of the same family.
main_review: Originality:
- the two main original contributions seem to be the theory that enables deepnets in place of RKHS and the explanation of how to do OPE with the method 

Quality & Clarity:
- I appreciate the summary of related works which makes it easy to refresh one's memory before diving in the main development
- The notation and mathematical developments are relatively easy to follow thanks to a nice introduction of details and assumptions when they are needed
- I appreciate also that the corresponding proofs in appendix are detailed enough to follow and that required a dedicated effort from the authors
- I'm not completely convinced by some of the arguments, especially on why we need deepnets (see below)
- I'm not convinced that the experimental setup is providing evidence for that either (see below)
- there are a few typos (l242 Propositionn) but it doesn't affect reading

Significance:
- I understand in principle that the work enables application of PCL to more complex settings, even though I think the authors don't make an especially good argument on why it is required (the running argument in my head being that it might be the next natural thing to do in the field if deepnets were not tried before)
- the OPE reduction is usable for all PCL methods and thus might be interesting for this community which means for a large number of potential application domains where off-policy is interesting or the only option possible

limitations_and_societal_impact: I would be keen to read a developed argument about some of the claims in the discussion phase. I believe it could firm up my mind on the significance of the proposed method.

- l32: authors indicate that ref 7/9/33 (BART, CFRNet, ...) have too restrictive assumptions; in what sense exactly ? if they are too restrictive can you give a small example explaining the limitations ?
- l42: authors indicate that ref 14/17 provide "little theory" to guarantee recovery of causal effect - could you elaborate and point out what is missing in your opinion and how your work differs ?
- l60: authors seem to imply that deepnets can learn more complex functions than RKHS - is that right ? if so in what sense ? are the cases where it makes a difference significant from an application perspective ?
- l101: the proposed setup assumes the existence of both outcome- and treatment-inducing proxies - isn't that a bit restrictive ? esp. compared to latent variables methods like the Deconfounder or ref 14/17 ?
- l207: did you try to measure such Rademacher complexities to compute this bound in practice (and verify its empirical tightness) ?
- in Sec 4, it seems to me the proposed setups are maybe more complex than it should. Esp. the Demand experiment equations seem a bit random and not very realistic (just try to imagine the shape of the curve from the equations in your head ?). At this point I can't make up my mind if the setup was designed to be so arbitrary that deepnets would be the only viable modeling option or if it resembles anything realistic.
- in the same idea I'd like to see what the method does when the setup is simpler. I believe it is part of the authors duty to study the limits of their method and the regimes where it is recommended to use it or not.
- the choice of CEVAE as the only baseline not from the CPL family is not very well motivated and I wonder of other methods could have been tried as well ?
- Ideally, I would like to have pointers on the performance of these baselines in the same setup in different papers to make sure the baseline methods perform as expected (i.e. why another benchmark ?)
review_title: null

Meta-review: The expert reviewers all appreciated the paper and agree it provides a useful new method and that the paper should be accepted. The reviewers appreciated the authors' response which better highlighted the significance of the contribution, including the relevant applications and what is lacking in previous work. The authors are expected to address the points raised by reviewers in a final version, including incorporating the additional clarifying discussion in their responses.
Decision: Accept (Poster)