Learning Representations of Instruments for Partial Identification of Treatment Effects
causal inference;partial identification;instrumental variables;treatment effect;representation learning
Yes
No ethics review needed.
I have no further questions.
This paper, to my knowledge, provides a novel solution to a well motivated problem. It provides thorough theoretical results and adequate empirical evaluation. The writing quality and organization is excellent. The availability of high dimensional instruments is common in many settings beyond the medical domain, so I believe the potential for impact is high.
This paper provides a method for the partial identification of treatment effects when potentially high-dimensional instruments belonging to a broad class of domains are available. To overcome the potential of overly conservative bounds, it proposes a discrete embedding scheme for the instruments. It provides theoretical results for the validity of the proposed bounds and for estimator efficiency. It provides an empirical evaluation of the method using a well motivated simulated data generating process.
A discussion on potential applications outside of medicine may help to increase the visibility of this work. Perhaps by extending Appendix B.
Yes
No ethics review needed.
- Even the experiements in the high dimensional settings had only 20 dimensional instruments. I am not familar with Mendelian randomization with SNPs, so I wonder if this falls into the normal range of such applications. 
- Is the bound from Theorem 1 sharp?
- I appreciate the clear comparison with existing works. 
- The paper provided clear description of a neural implementation of the proposed approach, and there is some innovation in the custom loss function.
This paper proposes a partial idetification approach of the conditional average treatment effect (CATE) that allows for arbitrary instruments. In particular, the proposed appraoch first maps the intstruments to a discrete representation space, and then leverages partial identification results for discrete intruments to bound the CATE. The representation mapping is learned by minimizing the length of the bounding interval while stabilizing finite sample performance. The authors also provided a neural implementation of the proposed method and performed simulation experiments.
Overall, the theoretical contribution of the paper appears limited (some of them are very straight forward applications of the existing results for discrete instruments) and may benefit from further exploration.
- The paper only provided finite samle guarantees for the second stage nuisance functions, but not for the final bounds, which might be more useful (for e.g. guaging the quality of the estimation) and easier to interpret. For instance it would be nice to have some theoretical results on the coverage (or scaled coverage - coverage/length of interval) of the estimated bounds.
- The number of partitions ($k$) is an important hyperparameter, but the paper did not provide anytheoretical results on how the estimation error or the tightness of the bounds would scale with $k$.
Yes
No ethics review needed.
Marks will be adjusted according to the replies. Below are some feedback/questions:
1. What is the point of building bounding estimators? As mentioned in the paper, existing literature focuses on point estimators. Indeed, we can build the confidence interval based on the point estimator. It is well-known that these are two concepts, but it is odds to build bounding estimators present in the paper.
2. Theorem 2 gives the asymptotic properties of the nuisance estimators $\hat{\mu}$ and $\hat{pi}$ when $\phi$ is arbitrary. It would be better to study the asymptotic properties of the nuisance estimators due to optimal $\phi^*$ after Eqn. (8).
3. It is strange to have $N_b$ in Algorithm 1 (see lines 387, 388).
4. The auxiliary guidance loss is not clear enough. It would be better if the authors could provide an explicit formula for the loss similar to bandwidth minimization loss and regularization loss.
5. The size of $k$ should affect the bounded estimators. Please demonstrate a scientific way to choose $k$. In the existing experiments, authors study results for different $k$. In any case, it seems that increasing $k$ would give better results. It should not be correct in general.
6. Could you provide the results of the following experiment:
assuming linear generative model, nonlinear ML methods are used to estimate the nuisance functions and then construct the corresponding bandwidth;
assuming a nonlinear generative model, linear ML methods are used to estimate the nuisance functions and then construct the corresponding bandwidth.
7. Would the constructed bounding estimators be doubly robust?
This paper investigates the conditional average treatment effect (CATE), assuming the presence of unobserved confounders. Further, researchers encounter complex instrument information (e.g., continuous/high-dimensional), which makes the computation hard in many circumstances. The authors aim to develop estimators that can provide reliable analysis of the above assumptions. Unlike the existing literature, the authors establish bounding estimators of the target quantity and provide theoretical studies of the constructed estimators. A merit of the paper is that it is well-written, so readers can easily follow its notions.
Reliable estimation of treatment effects from observational data is crucial in many disciplines and is a challenge when unconfoundedness assumption in the causal inference literature is violated. In this paper, the authors leverage arbitrary instruments to estimate bounds on the conditional average treatment effect (CATE). First, the authors propose a novel approach for partial identification by mapping instruments to a discrete representation space such that valid bounds on the CATE are yielded. Second, the authors derive a two-step procedure that learns tight bounds using a tailored neural partitioning of the latent instrument space. Thus, instability issues due to numerical approximations or adversarial training are avoided. Third, the authors provide theoretical studies on the proposed approach. Finally, the authors perform extensive experiments to demonstrate the effectiveness across various settings.
There are some notational problems in the paper. For example:
1. Notational problems in Eqn. (10).
2. According to Eqn. (8) (or Eqn. (14)), $\phi$ should be a representation map, and $\Phi$ should be a set of all representations. It is quite confusing to write $\Phi(Z)=l$ (e.g., see line 323). 
3. Please also state the explicit form of the constants $c$, $d$ in Theorem 2.
Please recheck the notations to avoid any confusions.
Yes
No ethics review needed.
See Weaknesses part.
1.	The study addresses an intriguing and valuable problem in causal inference.

2.	The writing is clear and accessible, making complex concepts easier to understand.
This paper introduces a method for estimating treatment effects from observational data despite violations of unconfoundedness. It presents a two-step procedure using high-dimensional latent instruments to derive valid bounds on the Conditional Average Treatment Effect.
1. The method appears to be a straightforward combination of existing techniques, lacking clear theoretical innovation.  

2. Although the paper highlights the advantage of utilizing high-dimensional instruments, there are limited experiments involving such instruments in the evaluation phase.  

3. The experimental results show no substantial improvements, casting doubt on the method's effectiveness.  

4. While the authors discuss the lack of comparison implementations, it would strengthen the argument to adapt baseline methods to the current setting and compare their performance with that of the proposed method, making the results more persuasive.

5. The final loss function includes two hyperparameters, making it crucial to conduct a sensitivity analysis to evaluate the method's robustness. However, the absence of such experiments raises concerns about the reliability and generalizability of the proposed approach.

6.  The assumption that all observed variables are confounders may be stringent and difficult to satisfy in practical scenarios.

7. The two-stage method presents several limitations, such as potential inefficiencies in estimation and sensitivity to the parameters selected at each stage, which may compromise the overall robustness of the results.
We develop a novel method for partial identification of treatment effects by tailored representation learning of instruments
@inproceedings{
anonymous2024learning,
title={Learning Representations of Instruments for Partial Identification of Treatment Effects},
author={Anonymous},
booktitle={Submitted to The Thirteenth International Conference on Learning Representations},
year={2024},
url={https://openreview.net/forum?id=Q5CLpqbrFM},
note={under review}
}
Reliable estimation of treatment effects from observational data is important in many disciplines, such as medicine. However, estimation is challenging when unconfoundedness as a standard assumption in the causal inference literature is violated. In this work, we leverage arbitrary (potentially high-dimensional) instruments to estimate bounds on the conditional average treatment effect (CATE). Our contributions are three-fold: (1) We propose a novel approach for partial identification through a mapping of instruments to a discrete representation space so that we yield valid bounds on the CATE. This is crucial for reliable decision-making in real-world applications. (2) We derive a two-step method that learns tight bounds using a tailored neural partitioning of the latent instrument space. As a result, we avoid instability issues due to numerical approximations or adversarial training. Furthermore, our procedure aims to reduce the estimation variance in finite-sample settings to yield more reliable estimates. (3) We show theoretically that our procedure obtains valid bounds while reducing estimation variance and we perform experiments to demonstrate the effectiveness across various settings. Overall, our procedure offers a novel path for practitioners to make use of potentially high-dimensional instruments (e.g., as in Mendelian randomization).
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causal inference partial identification instrumental variables treatment effect representation learning
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Learning Representations of Instruments for Partial Identification of Treatment Effects
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