Venue: ICLR 2021 Conference

Reviews:

final_score: rating: 5: Marginally below acceptance threshold
review_content: Solid theoretical results are provided to confirm the doubly robustness of the treatment estimator and outcome estimator. This paper is well-written, however, I still have some concerns about the contributions. 
1.	The author claimed that confounder is one challenge for treatment effect estimation. Some existing deep learning methods resort to balanced learning or reweighting. For the continuous treatment, how the proposed method addresses the confounder factors?
2.	Another big concern is the varing coefficient neural network. Why the VCnet designed to be dependent of treatment information? The dependence is not theoretically discussed in this paper.
3.	The experimental results are not convincing for me. Only two baselines are compared with the proposed method. Also the sufficient theoretical discussion is given which however is mainly about the doubly robust estimators. But the design of VCnet needs the numerical results to confirm its effectiveness for ADRF.

review_title: This paper aims at estimating average dose-response curve (ADRF) and propose to design a new varying coefficient neural network and a doubly robust estimator for ADRF. 

final_score: rating: 6: Marginally above acceptance threshold
review_content: This paper is to develop a varying coefficient neural network to estimate average dose-response curve (ADRF).  Although this paper has several interesting results, the paper is full of many typos and small errors.  The current paper needs substantial improvement. Here are some detailed comments. 

1. The introduction section is not well written since the logic does not flow very smooth. 
2. The motivation for （1）can be improved. You miss period in (1).  
3. In Theorem 2, please not use (1)-(6) to itemize the assumptions, since you use them to denote the equations. 
4. In the proof of all theorems, there are some obvious mistakes inside. 
review_title:  Varying Coefficient Neural Network with Functional Targeted Regularization for Estimating Continuous Treatment Effects

final_score: rating: 9: Top 15% of accepted papers, strong accept
review_content: This problem is well-motivated --- estimating dose-response is a challenging and practically important problem.
The paper is extremely well written.  It explained complex (poor written) ideas in the semiparametric literature clearly. 
The comparison against existing works is clear.
The theory, as far as I can tell, is sound. It improves the existing results in targeted regularization and can be adapted to analyze one step TMLE.
The experiment shows that the model outperforms existing benchmarks on the task it set out to do. 

My main suggestion to improve the paper is to use some datasets that actually have continuous treatment in evaluating the method.  In particular, I would be interested in seeing an application of the methods on real-world datasets. That being said, while it will improve the paper, it's probably asking too much for an 8-page conference submission. I believe the paper at its current state is sufficient for acceptance.

I want to thank the authors for writing such an elegant paper. I really enjoyed reading it. 
review_title:  This paper focuses on the problem of estimating average dose-response curve from observational data. The paper proposes 1) varying coefficient neural network, a network designed for continuous treatment; 2) functional targeted regularization, a doubly robust estimator of the whole ADRF curve.

Meta-review: The paper designs a new way (in some sense a new perspective) on how neural networks can be used to model intervention variables when the goal is to estimate ADRF.  Basically, the idea is to emphasize the importance of the intervention variable by ensuring that it appears not just in every layer but also in every neural of a neural network.  

Reviewers mostly agree that this is a good paper with varying degrees, although there are some criticisms on e.g., assuming away the confounders.  However, I believe the authors address the criticisms of R4 satisfactorily. 

Overall I find the idea new and interesting and the experimental results strong, hence I happily recommend accepting the paper.

I do have a few quips myself and some comments that may help the authors to further improve the paper.

1. Re: the design that models each parameter as a spline. 
This is equivalent to introducing additional parameters (coefficients for spline basis) and adding a fixed linear layer (spline basis themselves) to every layer of the neural networks. t is taken as an input in all layers thus it makes sure that the model prioritizes on learning the impact of t. 

2. If you use a B-spline basis (that comes with kernels of bounded support), then the proposed method is very similar to stratifying the data according to different bins of t, and then fitting a separate model for each t. The only difference is that the different bins are now smooth kernels and they overlap somewhat. As a side note,  the authors should clearly write out how they are choosing the knots to specify the basis functions. Otherwise the paper will not be reproducible. 

3. I am not sure how this method would compare to naive (non-deep) baselines. Maybe this was considered in a prior work? If not, then I tend to side with Reviewer 4 that the evaluations are mostly ablation studies and they are not really comparing to representative work in this domain. Given that there is a large body of work on this before deep learning takes over, it is important to somehow compare with the right baselines.


Decision: Accept (Oral)