From: ICLR.cc/2023/Conference/Paper2666/Authors
title: Submission Withdrawn by the Authors

From: ICLR.cc/2023/Conference/Paper2666/Authors
title: Response to Reviewer kPrL (3/3)
comment: **4. Analysis and justification on drifted data generation setting:**

To justify the setting for generating drifted data, the Gaussian noise we used follows a normal distribution $\mathcal{N}(\mu,\sigma)$. For each test instance, the random noise has different mean $\mu$ as it is drawn from a uniform distribution. On the other hand, we provide additional experiments by varying the upper bound of the uniform distribution for ${\mu}$ (e.g., $\mu_{1}\sim\mathcal{U}(0, 0.25)$, $\mu_{2}\sim\mathcal{U}(0, 1)$, $\mu_{3}\sim\mathcal{U}(0, 1.5)$) and take different variance $\sigma\in$ {$0.1, 0.25$} at the domain corruption level 1/3. We have appended our experiments on different Gaussian noise magnitudes in Appendix 8.4.2, and the test results with different settings are provided in the following:

|Model |$\mu_{1}\sim\mathcal{U}(0, 0.25)$, $\sigma=0.1$|$\mu_{2}\sim\mathcal{U}(0, 1)$, $\sigma=0.25$|$\mu_{3}\sim\mathcal{U}(0, 1.5)$, $\sigma=0.25$|
|-----|--------|--------|--------|
|TARNet| 0.775 ± .04| 0.777 ± .04| 0.789 ± .04|
|$\text{VEGAN}_{\text{II}}$ | 0.395 ± .02| 0.443 ± .02| 0.498 ± .04|

Table 5. $\sqrt{\epsilon_{\text{PEHE}}}$ of out-of-sample prediction on ACIC dataset with different noise setting.

|Model |$\mu_{1}\sim\mathcal{U}(0, 0.25)$, $\sigma=0.1$|$\mu_{2}\sim\mathcal{U}(0, 1)$, $\sigma=0.25$|$\mu_{3}\sim\mathcal{U}(0, 1.5)$, $\sigma=0.25$|
|-----|--------|--------|--------|
|TARNet |0.211 ± .03| 0.253 ± .03| 0.285 ± .03|
|$\text{VEGAN}_{\text{II}}$ |0.231 ± .02| 0.230 ± .02 |0.265 ± .02|

Table 6. $\epsilon_{\text{ATE}}$ of out-of-sample prediction on ACIC dataset with different noise settings.

We compare the full version of VEGAN with TARNet as all the other baselines built on top of TARNet are equally the same in terms of lacking the functionality to handle noised test set due to our defined domain corruption.  When the noise magnitude increases, the prediction errors of both methods increase, but VEGAN holds a consistent and significant improvement margin compared with TARNet's results. 

**5. Combining stage 2 adaptation with existing method:**

In response to your concern, we integrate the second stage adversarial plug-in into the most representative model TARNet. The experiment results are presented in the following:
|Model |CL=1/20|CL=1/8|CL=1/5|CL=1/3|
|-----|--------|--------|--------|--------|
|TARNet| 0.813 ± .05| 0.738 ± .04| 0.798 ± .05| 0.754 ± .04|
|TARNet-Plugin| 0.540 ± .01| 0.545 ± .02| 0.526 ± .02| 0.554 ± .02|

Table 7. $\sqrt{\epsilon_{\text{PEHE}}}$ of out-of-sample prediction on ACIC dataset with different corruption levels.

|Model |CL=1/20|CL=1/8|CL=1/5|CL=1/3|
|-----|--------|--------|--------|--------|
|TARNet |1.45 |2.12| 4.55 |6.34|
|TARNet-Plugin |2.21 |0.29 |1.90 |2.29|

Table 8. Variation $\Delta$(\%) of the out-of-sample $\sqrt{\epsilon_{\text{PEHE}}}$ w.r.t. the in-sample one on ACIC dataset across increasing domain corruption level.

Our improved verion of TARNet is denoted as TARNet-Plugin. As the results suggest, the benefit of the stage 2 adaptation for training/test set will be enlarged under higher corruption level. When the adversarial plug-in is in use, it can effectively help TARNet reduce model volatility under runtime domain corruption, as the volatility of the TARNet-Plugin is stabilized at around 2\% on the corrupted test set.

**6. Unconfoundedness assumption for ITE/CATE:**

We actually do not need unconfoundedness for the definition of ITE/CATE, and it is  needed for making valid ITE/CATE estimations. Thanks for pointing it out, and we have corrected this in our updated manuscript.

**7. Presentation:**

Thanks for identifying those language issues. We have revised our paper accordingly, and have done a thorough proofreading on the updated manuscript.

**References:**

Jeroen Berrevoets, Fergus Imrie, Trent Kyono, James Jordon, and Mihaela van der Schaar. To impute or not to impute?–missing data in treatment effect estimation. arXiv preprint arXiv:2202.02096, 2022.

Andrew Jesson, S ̈oren Mindermann, Uri Shalit, and Yarin Gal. Identifying causal-effect inference
failure with uncertainty-aware models. Advances in Neural Information Processing Systems, 33:
11637–11649, 2020.

Imke Mayer, Erik Sverdrup, Tobias Gauss, Jean-Denis Moyer, Stefan Wager, and Julie Josse. Doubly robust treatment effect estimation with missing attributes. The Annals of Applied Statistics, 14(3): 1409–1431, 2020.

Uri Shalit, Fredrik D Johansson, and David Sontag. Estimating individual treatment effect: gener-
alization bounds and algorithms. In International Conference on Machine Learning, pp. 3076–
3085. PMLR, 2017.

From: ICLR.cc/2023/Conference/Paper2666/Authors
title: Response to Reviewer kPrL (2/3)
comment: **3. Reason for 0-padding missing variables:**

The theoretical justification on using 0-padding instead of padding with non-zero values or dropping the corrupted attribute has been provided in our response to *Clarity of runtime domain corruption's definition*. In addition, in the revised version, we have further tested the efficacy of utilizing data imputation (Mayer et al., 2020; Berrevoets et al., 2022) as an alternative to 0-padding,  where the results are presented in our updated manuscript in Appendix 8.7, and here we present the experiment results on the ACIC dataset with imputation-enhanced baselines (noted with IMP) in Table 3 and 4 as follows:

|Model |CL=1/20|CL=1/8|CL=1/5|CL=1/3|
|-----|--------|--------|--------|--------|
|TARNet|0.813 ± .05 |0.738 ± .04| 0.798 ± .05| 0.754 ± .04|
|TARNet-IMP   |0.807 ± .04| 0.728 ± .04| 0.783 ± .04| 0.763 ± .04|
|$\text{CFR}_{\text{WASS}}$   |0.730 ± .04 | 0.655 ± .03 | 0.738 ± .04 | 0.644 ± .04      |
|$\text{CFR}_{\text{WASS}}$-IMP  |0.722 ± .04| 0.640 ± .03| 0.710 ± .04| 0.679 ± .04      |
|SITE  |1.482 ± .08| 1.361 ± .08| 1.365 ± .09| 1.586 ± .10      |
|SITE-IMP   |1.322 ± .08| 1.210 ± .07| 1.358 ± .08| 1.268 ± .08      |
|$\text{Dragonnet}_{\text{Base}}$  |2.250 ± .02| 2.192 ± .02| 2.142 ± .02| 2.063 ± .02      |
|$\text{Dragonnet}_{\text{Base}}$-IMP  |2.232 ± .02| 2.162 ± .02| 2.097 ± .02| 2.117 ± .02      |
|$\text{Dragonnet}_{\text{TR}}$  |2.517 ± .02| 2.456 ± .02| 2.406 ± .02| 2.342 ± .02      |
|$\text{Dragonnet}_{\text{TR}}$-IMP  |2.485 ± .02| 2.407 ± .02| 2.343 ± .02| 2.393 ± .02 |
|CEVAE |0.646 ± .02| 0.629 ± .02 |0.594 ± .02 |0.581 ± .03|
|CEVAE-IMP| 0.626 ± .02| 0.601 ± .02 |0.577 ± .02| 0.568 ± .03|
|$\text{VEGAN}_{\text{I}}$   | 0.466 ± .01| 0.489 ± .01| 0.488 ± .01| 0.501 ± .01      |
|$\text{VEGAN}_{\text{II}}$   |0.490 ± .01| 0.493 ± .01| 0.471 ± .01| 0.455 ± .00      |   

Table 3. $\sqrt{\epsilon_{\text{PEHE}}}$ of out-of-sample prediction on ACIC dataset with different corruption levels (CL).     


|Model |CL=1/20|CL=1/8|CL=1/5|CL=1/3|
|-----|--------|--------|--------|--------|
|TARNet |1.45 |2.12 |4.55 |6.34|
|TARNet-IMP| 2.18 |3.45 |6.34 |7.06|
|$\text{CFR}_{\text{WASS}}$ |0.41 |0.61 |2.38 |3.45|
|$\text{CFR}_{\text{WASS}}$-IMP |1.5 |2.88 |6.08 |6.86|
|SITE |3.49 |3.03 |6.47 |10.68|
|SITE-IMP |2.44 |4.42 |5.96 |9.37|
|$\text{Dragonnet}_{\text{Base}}$| 0.09 |2.23| 4.59 |7.74|
|$\text{Dragonnet}_{\text{Base}}$-IMP |0.49 |3.65 |6.38 |5.70|
|$\text{Dragonnet}_{\text{TR}}$ |0.64 |1.76 |3.76| 6.17|
|$\text{Dragonnet}_{\text{TR}}$-IMP |0.44 |3.41 |5.87 |4.62|
|CEVAE |7.71 |10.01 |12.00| 16.76|
|CEVAE-IMP |8.21 |9.24 |11.57| 14.82|
|$\text{VEGAN}_{\text{I}}$ |0.64 |0.81 |0.61| 2.72|
|$\text{VEGAN}_{\text{II}}$ |0.20 |1.60 |0.42 |0.22|

Table 4. Variation $\Delta$(\%) of the out-of-sample $\sqrt{\epsilon_{\text{PEHE}}}$ w.r.t. the in-sample one on ACIC dataset across increasing domain corruption level.

As the results and our analysis suggest, imputation only offers limited help when the corruption rate is low, and is less effective compared with our two-step domain adaptation. Furthermore, attribute imputation is rendered impossible in scenarios where an attribute is completely missing for all instances, making 0-padding a more versatile and generalizable approach for runtime domain corruption.

From: ICLR.cc/2023/Conference/Paper2666/Authors
title: References
comment: **References:**

Jeroen Berrevoets, Fergus Imrie, Trent Kyono, James Jordon, and Mihaela van der Schaar. To impute
or not to impute?–missing data in treatment effect estimation. arXiv preprint arXiv:2202.02096,
2022.

Andrew Jesson, S ̈oren Mindermann, Uri Shalit, and Yarin Gal. Identifying causal-effect inference
failure with uncertainty-aware models. Advances in Neural Information Processing Systems, 33:
11637–11649, 2020.

Christos Louizos, Uri Shalit, Joris M Mooij, David Sontag, Richard Zemel, and Max Welling.
Causal effect inference with deep latent-variable models. Advances in neural information pro-
cessing systems, 30, 2017.

Imke Mayer, Erik Sverdrup, Tobias Gauss, Jean-Denis Moyer, Stefan Wager, and Julie Josse. Doubly
robust treatment effect estimation with missing attributes. The Annals of Applied Statistics, 14(3):
1409–1431, 2020.

Uri Shalit, Fredrik D Johansson, and David Sontag. Estimating individual treatment effect: gener-
alization bounds and algorithms. In International Conference on Machine Learning, pp. 3076–
3085. PMLR, 2017.

Claudia Shi, David Blei, and Victor Veitch. Adapting neural networks for the estimation of treatment
effects. Advances in neural information processing systems, 32, 2019.
Stef Van Buuren and Catharina GM Oudshoorn. Multivariate imputation by chained equations,
2000.

Olga Troyanskaya, Michael Cantor, Gavin Sherlock, Pat Brown, Trevor Hastie, Robert Tibshirani, David Botstein, and Russ B Altman. Missing value estimation methods for dna microarrays. Bioinformatics, 17(6):520–525, 2001.

Liuyi Yao, Sheng Li, Yaliang Li, Mengdi Huai, Jing Gao, and Aidong Zhang. Representation
learning for treatment effect estimation from observational data. Advances in Neural Information
Processing Systems, 31, 2018

From: ICLR.cc/2023/Conference/Paper2666/Authors
title: Response to Reviewer kPrL (1/3)
comment: We thank the Reviewer kPrL for your helpful and valuable feedback. We address the raised concerns as follows: 

**1. Clarity of runtime domain corruption's definition:**

The domain corruption is twofold, one is distribution shift, and another is missing values. For your interpretation of the latter case, we would like to further clarify how we deal with missing/inaccessible variables. Specifically, we do not discard the missing/inaccessible variables from the input, which will cause dimensionality reduction on the input. Instead, we keep the dimensionality of target domain dataset the same as the source domain dataset, and pad 0 to entries that correspond to missing variables. Please note that in Challenge 3, we have specified the input vector $\textbf{x}$ only contains multi-hot categorical features and non-zero numerical features (this can be achieved via common preprocessing steps like rescaling, exponential, normalization, etc.). In short, in our definition, domain shift happens when covariate distribution shifts, while domain corruption is caused by the co-occurrence of domain shift and missing values. Then, using 0-padding for runtime domain corruption will make practical sense -- although in a traditional numerical view it statistically causes domain shift. This is because all known variables are assigned non-zero values, while all missing variables (at individual-level) takes the value of 0 and hence will be naturally filtered out in the latent space after being projected via a weight matrix. 

Also, our special way of handling missing variables is a more feasible solution in real applications, as for each runtime instance $\textbf{x}$, it may have an arbitrary set and combination of attributes corrupted. Our definition and experimental setup have reflected the same scenario. Since it is impractical to assume any prior knowledge on which attributes will be missing for all runtime input instances, 0-padding is a more flexible and scalable approach for learning domain-invariant latent representations with a shared feature extractor. In contrast, if the unavailable dimensions of $\textbf{x}$ are removed, then we will have to train dedicated feature extractors for differently corrupted input vectors to the same latent space. In our updated manuscript, we have provided more descriptions accordingly to further clarify and justify our problem setting in Section 1.

**2. Suggested baseline:**

Thanks for suggesting an additional comparison to Jesson et al. (2020). In our updated manuscript, the Bayesian TARNet (BTARNet) (Jesson et al., 2020) model has been included in our experiments. Generally, the results do not deviate much from TARNet  (Shalit et al., 2017) that BTARNet is based upon. It is worth pointing out that Jesson et al. (2020)'s method works on identifying the out-of-distribution (OOD) samples and excluding them during test time, which is a foundationally different from our settings where OOD samples are aimed to be predicted. In the following experimental results given below, we align BTARNet to our task and include the treatment effect prediction for all samples:

|Model |CL=1/20|CL=1/8|CL=1/5|CL=1/3|
|-----|--------|--------|--------|--------|
| TARNet| 0.813 ± .05 | 0.738 ± .04| 0.798 ± .05 |0.754 ± .04|
|BTARNet |0.797 ± .04 |0.754 ± .04 |0.773 ± .04|0.768 ± .04|

Table 1. $\sqrt{\epsilon_{\text{PEHE}}}$ of out-of-sample prediction on ACIC dataset with different corruption levels.

|Model |CL=1/20|CL=1/8|CL=1/5|CL=1/3|
|-----|--------|--------|--------|--------|
| TARNet| 1.45 |2.12| 4.55| 6.34|
|BTARNet |1.88 |2.48| 4.34| 6.96|

Table 2. Variation $\Delta$(\%) of the out-of-sample $\sqrt{\epsilon_{\text{PEHE}}}$ w.r.t. the in-sample one on ACIC dataset across increasing domain corruption level.

As Table 1 and 2 shown, BTARNet does not express much difference from TARNet under our Challenge 3 setting.

From: ICLR.cc/2023/Conference/Paper2666/Authors
title: Response To Reviewer GyRM (3/3)
comment: **7. Missing related work:**

Thanks for suggesting the causal inference papers which handle missing values via imputation. We have included additional discussions in Related Work on their limitations under runtime domain corruption. To compare imputation-based methods with VEGAN, we used the MICE algorithm (Van Buuren & Oudshoorn, 2000)  adopted by Mayer et al. (2020) and Berrevoets et al. (2022) to impute the missing values in the test set. Notably, when the corruption level (i.e., missing rate) reaches 1/3, the MICE algorithm melts down, and we then turn to KNN-based imputation (Troyanskaya et al., 2001) from the corruption level of 1/3. We have updated our manuscript and included the experiments in Appendix 8.7. For your information, we provide the updated experiment results on the ACIC dataset with imputation-enhanced baselines (noted with IMP) below:

|Model |CL=1/20|CL=1/8|CL=1/5|CL=1/3|
|-----|--------|--------|--------|--------|
|TARNet|0.813 ± .05 |0.738 ± .04| 0.798 ± .05| 0.754 ± .04|
|TARNet-IMP   |0.807 ± .04| 0.728 ± .04| 0.783 ± .04| 0.763 ± .04|
|$\text{CFR}_{\text{WASS}}$   |0.730 ± .04 | 0.655 ± .03 | 0.738 ± .04 | 0.644 ± .04      |
|$\text{CFR}_{\text{WASS}}$-IMP  |0.722 ± .04| 0.640 ± .03| 0.710 ± .04| 0.679 ± .04      |
|SITE  |1.482 ± .08| 1.361 ± .08| 1.365 ± .09| 1.586 ± .10      |
|SITE-IMP   |1.322 ± .08| 1.210 ± .07| 1.358 ± .08| 1.268 ± .08      |
|$\text{Dragonnet}_{\text{Base}}$  |2.250 ± .02| 2.192 ± .02| 2.142 ± .02| 2.063 ± .02      |
|$\text{Dragonnet}_{\text{Base}}$-IMP  |2.232 ± .02| 2.162 ± .02| 2.097 ± .02| 2.117 ± .02      |
|$\text{Dragonnet}_{\text{TR}}$  |2.517 ± .02| 2.456 ± .02| 2.406 ± .02| 2.342 ± .02      |
|$\text{Dragonnet}_{\text{TR}}$-IMP  |2.485 ± .02| 2.407 ± .02| 2.343 ± .02| 2.393 ± .02 |
|CEVAE |0.646 ± .02| 0.629 ± .02 |0.594 ± .02 |0.581 ± .03|
|CEVAE-IMP| 0.626 ± .02| 0.601 ± .02 |0.577 ± .02| 0.568 ± .03|
|$\text{VEGAN}_{\text{I}}$   | 0.466 ± .01| 0.489 ± .01| 0.488 ± .01| 0.501 ± .01      |
|$\text{VEGAN}_{\text{II}}$   |0.490 ± .01| 0.493 ± .01| 0.471 ± .01| 0.455 ± .00      |   

Table 1. $\sqrt{\epsilon_{\text{PEHE}}}$ of out-of-sample prediction on ACIC dataset with different corruption levels (CL).     


|Model |CL=1/20|CL=1/8|CL=1/5|CL=1/3|
|-----|--------|--------|--------|--------|
|TARNet |1.45 |2.12 |4.55 |6.34|
|TARNet-IMP| 2.18 |3.45 |6.34 |7.06|
|$\text{CFR}_{\text{WASS}}$ |0.41 |0.61 |2.38 |3.45|
|$\text{CFR}_{\text{WASS}}$-IMP |1.5 |2.88 |6.08 |6.86|
|SITE |3.49 |3.03 |6.47 |10.68|
|SITE-IMP |2.44 |4.42 |5.96 |9.37|
|$\text{Dragonnet}_{\text{Base}}$| 0.09 |2.23| 4.59 |7.74|
|$\text{Dragonnet}_{\text{Base}}$-IMP |0.49 |3.65 |6.38 |5.70|
|$\text{Dragonnet}_{\text{TR}}$ |0.64 |1.76 |3.76| 6.17|
|$\text{Dragonnet}_{\text{TR}}$-IMP |0.44 |3.41 |5.87 |4.62|
|CEVAE |7.71 |10.01 |12.00| 16.76|
|CEVAE-IMP |8.21 |9.24 |11.57| 14.82|
|$\text{VEGAN}_{\text{I}}$ |0.64 |0.81 |0.61| 2.72|
|$\text{VEGAN}_{\text{II}}$ |0.20 |1.60 |0.42 |0.22|

Table 2. Variation $\Delta$(\%) of the out-of-sample $\sqrt{\epsilon_{\text{PEHE}}}$ w.r.t. the in-sample one on ACIC dataset across increasing domain corruption level.

As shown in Table 1 and 2, when the corruption rate is low, using imputation is generally helpful for slightly increasing the prediction performance, but may provide negative impact when more attributes are corrupted (e.g., at a rate of 1/5 and 1/3). At the same time, imputation methods do not make a difference in terms of volatility, as the imputed target domain is still subject to significant distribution shift w.r.t. the training domain, and the volatility of the model increases rapidly as corruption level goes up. To conclude, data imputation has very limited practicality under the domain corruption setting. Furthermore, in scenarios where an attribute is completely missing for all instances (e.g., medical checks that are unavailable in some hospitals, which resembles the rightmost column in Table 2), it is infeasible to impute this attribute for prediction.

From: ICLR.cc/2023/Conference/Paper2666/Authors
title: Response To Reviewer GyRM (2/3)
comment: **4 & 5. Clarity of Eq. 3 and Eq. 4:**

Thanks for pointing out these unclear notations. For the first term $p(y)$ in Eq. 3, $y$ should be a vector $\mathbf{y}=[y_1, y_2, \dots, y_N]$ that hosts all training data's ground truth, to represent the joint marginal distribution. For the second term $\prod_{k=1}^{N}p(y_{k})$, we do not condition it on treatment $t$ as it should be the marginal likelihood to be maximised in MLE. For the condition $t$ in the last term, as we further break down the marginal likelihood $p(y_{k})$ to each of the treatment group, we then condition it on each treatment $t$ to have conditional likelihood $p(y_{k}|t_{k})$, leading to the joint product of conditional likelihood from different treatment groups. To comply with the page limit, we only keep the previous Eq. 4 (now Eq. 3) in our updated version, and revised the previous Eq. 4 (now Eq. 3) to $\log p(\textbf{y})=\sum_{k=1}^{N}\log p(y_k)=\sum_{i=1}^{N_1}\log p(y_{i}|t_{i}=1)+\sum_{j=1}^{N_0}\log p(y_{j}|t_{j}=0)$.

**6. Interpretation of Challenge 3:** 

The necessary condition for domain corruption is the missing (i.e., corrupted) values for arbitrary dimensions of an individual variable vector (with arbitrary number of missing attributes) $\textbf{x}$. That is, for an instance $\textbf{x}$ (e.g., an individual), an arbitrary set of dimensions will be set to 0 during inference while other entries maintain unchanged. The common case will likely to be, for instance, $\textbf{x}=[2, 1, 0, 0, \dots, 3, 0,1.5] \in \mathbb{R}^{d}$ containing missing values which have been encoded to 0 at dimensions 3, 4, and $d-1$ for vector $\textbf{x}$. $\textbf{x}=\textbf{0}$ corresponds to the extreme case where $x_{s'}=0 \text{ for } \forall s'\leq d$ as all attributes/dimensions are missing.

From: ICLR.cc/2023/Conference/Paper2666/Authors
title: Response To Reviewer GyRM (1/3)
comment: We thank the Reviewer GyRM for your thoughtful and constructive reviews, we address the raised concerns as follows:

**Overall response to comments on novelty:**

The TARNet framework (Shalit et al., 2017) is the foundational work that many follow-up methods  Louizos et al. (2017); Yao et al. (2018); Shi et al. (2019) build upon. Our model makes major improvements upon one of TARNet's variants, CEVAE (Louizos et al., 2017), that takes the traditional VAE framework to model the joint distribution of $p(z, x , y, t)$ to recover the treatment effect. Unfortunately, CEVAE is computationally demanding, both theoretically and empirically, as they optimise the KL-divergence straightaway. This is one of the key motivations that we mentioned in the original submission's Section 5, and we propose a GAN-based alternative for computational efficiency. Also, our solution VEGAN models the joint distribution of $p(z, y, t)$ to recover the treatment effect, and hence does not need to waste computation power on the reconstruction of $x$ (as we focus on $y$). Unlike CEVAE, we don't need to add the additional auxiliary models, which are used to model the treatment assignment and treatment effect for test set data, to the training procedures. We have additionally reported the training time per 100 epoch of VEGANs and CEVAE on both datasets in our updated manuscript Section 6.3 Figure 3, where the results respectively showcase 6$\times$ and 7$\times$ reduction on IHDP and ACIC using $\text{VEGAN}_{\text{I}}$, showcasing the efficacy of utilizing GAN in our approach. 

**1. Setting missing attributes to zero and its potential trade-off:**

In our approach, we do encode the missing attributes as 0 and feed them into the model at test time. Please note that, attributes are missing at the instance/individual level, i.e., each individual feature vector $\textbf{x}$ may see a different combination and number of unavailable attributes, thus allowing for personalization. One motivating example is that, in real-world applications, user $A$ might choose not to submit her age information while user $B$ may choose not to indicate her income. During test time, we set the age attribute of user $A$ to 0, the income attribute of user $B$ to 0, while keeping all other available attributes of both users unchanged. This setting is adopted in our original experiments and detailed in Appendix 8.4. Hence, we would like to clarify that one attribute is not straightforwardly set to 0 for all instances, and instances that do have this attribute available will maintain its original value and be used for the prediction. Getting back to your example, 50\% of the instances will have this attribute with value 0, while the remaining 50\% will stay unchanged instead of being approximately dropped. In our updated version, we have made more explanations under Challenge 3 to alleviate potential confusion. 

**2. Marginal posteriors:**

We want to use the same prior to align the treated and control domains, so the term $\text{IPM}(\mathbb{P}^{t=1},\mathbb{P}^{t=0})$ in the upper bound of Theorem 1 could be reduced. We agree that different posteriors for different groups are needed to model their corresponded reconstruction likelihood, but we believe there is a slight misperception on the actual effect of the KL divergence used. This is because in practice it can merely bring closer two posteriors as a regularization term instead of making them an exact match. Besides, we are not going to get identical posteriors as the reconstruction loss is a part of the supervision, resulting in two non-identical posteriors to drive optimal reconstruction likelihood for both treated and control groups. Similar observations on non-identical posteriors can be drawn from another typical domain adaptation metric IPM  (Shalit et al., 2017), which is also used for regularizing two posteriors' discrepancy alongside the reconstruction loss. 

**3. Loss function w.r.t. Theorem 1:**

Our derived upper bound does not apply directly to the Jensen-Shannon (JS) divergence in terms of IPM. We do not choose to use IPM because our method uses the VAE framework, where we found optimizing KL divergence directly is computationally expensive. We thus propose to replace it with GAN, which runs significantly faster in training (as shown in our updated manuscript Section 6.3 Figure 3 compared to CEVAE that uses KL divergence), and essentially provides the same functionality as IPM. Ideally, two similar distributions will have a distance close to 0 in both JS divergence and IPM. In short, we use JS divergence as an approximation to IPM to server the same purpose, while making the optimization more scalable with the VAE framework.

From: ICLR.cc/2023/Conference/Paper2666/Authors
title: Response to Reviewer 5nnQ
comment: We thank the Reviewer 5nnQ for your time and efforts, as well as your valuable comments. We address the raised concerns as follows:

**1. GAN training:**

We agree that GAN training needs a bit more tuning efforts, and we have updated our manuscript and added a stability analysis in the Appendix 8.6. For VEGAN, a higher corruption level brings more challenges in the adversarial training, but we observe an equilibrium state in the majority of the cases. Take the harder 1/3 corruption level in IHDP dataset as an example, both discriminators (for treated/control  and training/runtime adaptations) can quickly converge to the equilibrium by returning an average binary cross-entropy loss (BCELoss) of 0.69 ($-\text{ln}(0.5)\approx 0.69$), which means the discriminators are completely decepted by the feature extractors, and always give 0.5 probability for the samples from each of the groups. A part of the log message from one of our experiment runs is printed below:

---------------------------------------

Experiment: 4/100, Epoch: 81/100, Prediction MSE Loss: 1.4, Generator BCELoss: 0.74, First Discriminator BCELoss: 0.67, Second Disc BCELoss: 0.69, Total validation loss: 1.97

Experiment: 4/100, Epoch: 91/100, Prediction MSE Loss: 1.15, Generator BCELoss: 0.94, First Discriminator BCELoss: 0.66, Second Disc BCELoss: 0.69, Total validation loss: 2.11

Experiment: 4/100, Epoch: 100/100, Prediction MSE Loss: 1.36, Generator BCELoss: 0.74, First Discriminator BCELoss: 0.69, Second Disc BCELoss: 0.69, Total validation loss: 2.08

---------------------------------------

We occasionally have the situation where one of the discriminators outperforms the feature extractor, predominantly the discriminator for treated/control adaptation. After repeatedly executing 100 runs for each setting, we observe that on average, this happens less frequently than 5\% for ACIC dataset and 30\% for IHDP dataset. As such, training VEGAN in an adversarial setting is completely attainable.

**2. Use of real datasets:**

We agree that experimenting on real-world dataset will be more convincing. Unfortunately, to the best of our knowledge, there currently is no open benchmark datasets that are suited to the setting of casual inference under runtime domain corruption. Hence, in our experiments, we adopt two well-established (semi-)synthetic datasets  (Shalit et al., 2017; ACIC, 2019) to maintain a fair comparison. In addition, the adoption of both widely adopted datasets have allowed us to derive more empirical insights by extending their use case to the runtime domain corruption setting.

**References:**

ACIC. Atlantic causal inference conference 2019, Aug 2019. URL https://sites.google.com/view/acic2019datachallenge/data-challenge?authuser=0.

Uri Shalit, Fredrik D Johansson, and David Sontag. Estimating individual treatment effect: gener-
alization bounds and algorithms. In International Conference on Machine Learning, pp. 3076–
3085. PMLR, 2017.

From: ICLR.cc/2023/Conference/Paper2666/Reviewer_GyRM
confidence: 3: You are fairly confident in your assessment. It is possible that you did not understand some parts of the submission or that you are unfamiliar with some pieces of related work. Math/other details were not carefully checked.
summary_of_the_paper: This work studies treatment effect prediction in the presence of both missing values and test-time domain shift, and proposes a GAN-based method, by extending the framework in Shalit et al (2017) to additionally minimize the discrepancy between the covariate distributions at training and test time.  The proposed method appears competitive in experiments on semi-synthetic data.
strength_and_weaknesses: The extended setting of having both missing attributes and domain shift makes sense, and the proposed method appears new.

That being said, the proposed algorithm appears rather incremental (being a straightforward combination of the framework of Shalit et al (2017)), and at the same time lacks justification and explanation for its trade-offs.  Concretely, 

1. The authors handled missing attributes by simply setting them to zero ("Challenge 3"), and then adjusted for domain shift by attempting to match the distributions for the learned representations across the training and test-time domains.  As a consequence, the learned representation will likely (approximately) neglect commonly missing attributes: for the representation to have approximately equal distributions across training and test domains, they must have weak dependency on input attributes that have different distributions across domains.  But as missing attributes have been encoded as zero, this will include attributes that are commonly missing in test time.  I don't think this is always reasonable, and in any case it is a significant trade-off which should have been discussed.  For example, what happens for an attribute that is only missing at test time w.p. 0.5 (and thus could have been utilized to improve prediction precision in the other 50\% of cases)?  Will it be approximately dropped?

2. In Section 4.2 the authors claims the distributions of treatment and control-group representations, which are marginal posteriors of an VAE model, can be matched simply because the VAE ELBO regularize both marginals towards the prior.  This is not a complete justification, as it does not preclude the very likely scenario that the other term in ELBO -- the reconstruction likelihood -- could be further improved by having different marginal posteriors.

3. Theorem 1 only applies if the loss function belongs to the test function class for the IPM of choice.  The authors used the Jensen-Shannon divergence.  Will it apply to the loss function?

I am also concerned about major clarity issues in the manuscript; many equations and mathematical statements are plainly wrong.  To name a few:

* Eq. 3 is incorrect.  The left hand side should be $p(\{y_i\}{\color{red}| \{t\_i\}}) = \prod\_{k=1}^N p(y\_i {\color{red}| t\_i}) = \ldots$.
* Eq. 4 is similarly incorrect.
* If interpreted literally, the statement in "Challenge 3" means that runtime domain corruption occurs when the covariate vector $\mathbf{x} = \mathbf{0}$.

Finally, there should have been some discussions of past work on (average) treatment effect estimation with missing attributes, such as [1-3].  The authors should have also compared with baselines based on imputating the missing attributes, which is a natural alternative.

## References

[1] Qu, Yongming, and Ilya Lipkovich. "Propensity score estimation with missing values using a multiple imputation missingness pattern (MIMP) approach." Statistics in medicine 28.9 (2009): 1402-1414.		
															   
[2] Mayer, Imke, et al. "Doubly robust treatment effect estimation with missing attributes." The Annals of Applied Statistics 14.3 (2020): 1409-1431.

[3] Berrevoets, Jeroen, et al. "To Impute or not to Impute?--Missing Data in Treatment Effect Estimation." arXiv preprint arXiv:2202.02096 (2022).

clarity,_quality,_novelty_and_reproducibility: See above.
summary_of_the_review: I am concerned with the lack of proper justifications and discussion of limitations of the proposed method, as well as the clarity issues.
correctness: 2: Several of the paper’s claims are incorrect or not well-supported.
technical_novelty_and_significance: 2: The contributions are only marginally significant or novel.
empirical_novelty_and_significance: 3: The contributions are significant and somewhat new. Aspects of the contributions exist in prior work.
flag_for_ethics_review: NO.
recommendation: 3: reject, not good enough

From: ICLR.cc/2023/Conference/Paper2666/Reviewer_5nnQ
confidence: 3: You are fairly confident in your assessment. It is possible that you did not understand some parts of the submission or that you are unfamiliar with some pieces of related work. Math/other details were not carefully checked.
summary_of_the_paper: The paper focuses on the problem domain adaptation problem in causal inference. That is, some of the variables of input become unavailable during the inference time. This causes a distribution shift between training and inference and also between the treated and control groups. The authors use Neyman-Rubin potential outcome framework along with two-stage scheme, VEGAN, to handle covariate shift and corrupted variables. They demonstrate the proposed method on two data sets. The results are promising. 
strength_and_weaknesses: Strength:
1) The paper provides the upper bound for the error in the target domain. The bound gives the insight that one should 1) bring down the prediction error on the observational data and 2) reduce the imbalance/discrepancy between the treated and control group and between training and testing data sets. 
2) The authors leverage VAE to handle the curse of dimensionality of z. The ELBO is derived for both the treated group and the control group, which can be extended for multiple groups. Becasue of the use of VAE, the posteriors are regularized and naturally balance the latent distribution for domain adaptation. For the runtime DA, the algorithm aims to minimize the KL divergence between runtime posterior and training posterior. 
3) To mitigate the computational cost from KL divergence, the authors use GAN to implicitly minimize the KL. 

Weaknesses/Questions:
1) How hard is the training? Since adversarial learning is introduced, it might bring the difficulty of the training to achieve the equilibrium. 
2) Although IHDP is a semi-synthetic dataset, it seems that experiments on real datasets would be more convincing. 

clarity,_quality,_novelty_and_reproducibility: The paper is well-written and follows naturally. The idea is clear stated and progressed throughout the paper. The idea is novel and the bound gives insight. 
summary_of_the_review: Overall, the idea to handle DA present in this paper is novel with bounded error. The experiments are interesting but mostly on synthetic data sets. And because of adversarial training, it is unclear on how hard the training goes. 
correctness: 3: Some of the paper’s claims have minor issues. A few statements are not well-supported, or require small changes to be made correct.
technical_novelty_and_significance: 3: The contributions are significant and somewhat new. Aspects of the contributions exist in prior work.
empirical_novelty_and_significance: 3: The contributions are significant and somewhat new. Aspects of the contributions exist in prior work.
flag_for_ethics_review: NO.
recommendation: 6: marginally above the acceptance threshold

From: ICLR.cc/2023/Conference/Paper2666/Reviewer_kPrL
confidence: 3: You are fairly confident in your assessment. It is possible that you did not understand some parts of the submission or that you are unfamiliar with some pieces of related work. Math/other details were not carefully checked.
summary_of_the_paper: This paper presents new counterfactual prediction method, with the consideration of runtime domain corruption. The proposed method deals with confounding bias, selection bias and runtime domain corruption from the perspective of domain adaption (treated vs control groups, and train vs run times), and makes use of variational autoencoder (VAE) and generative adversarial network (GAN) techniques for model optimization. 

The paper also derives a target domain error bound to guide the method design, and evaluates the proposed methods with two datasets with some baseline counterfactual prediction methods.
strength_and_weaknesses: Strengths:
1. The consideration of runtime domain corruption, a very practical issue in counterfactual prediction.
2. The proposal of a unified method which deals confounding bias, selection bias and runtime domain corruption at the same time.
3. Promising results when comparing with the baseline methods.

Weakness:
1. The unclear or misleading definition of runtime domain corruption.
From the text description in Section 1 and the definition of Challenge 3 (runtime domain corruption) excluding the last bit ("x_{s'}=0"), runtime domain corruption sounds like containing two cases in the target dataset/domain: covariate shift (while the set of covariates/features remains the same) and missing/inaccessible variables (no knowledge of a covariate/feature). For the latter case, I understand that the dimensionality of the target domain dataset will be different from the dimensionality of the source domain dataset. However, in the experiments (and the last bit of the definition of Challenge 3, i.e. setting x_{s'}=0), looking at the way how the corrupted data was generated, essentially only covariate shifts are considered since the feature sets of the source and target domains are the same. 

This issue could mislead readers in understanding the claim and contribution of the paper.

2. Experiments
(a) Regarding baselines, the method by Jesson et al. (2020) should be included. Although the authors pointed out in Section 2 that their work has a different focus, a method for dealing with covariate shift was proposed in Jesson et al. (2020) and it was evaluated in terms of the PEHE metric. It is important to include the baseline(s) considering covariate shifts to help readers justify the significance of the contribution.
(b) The reason and impact of setting corrupted features (missing values indeed) to zero (rather than other values or using different ways to represent them) should be discussed.
(c) An analysis should be done on the impact of the different values of the parameters related to generating drifted data on the performance of the different methods, including the standard deviation of the Gaussian random variations on continuous features and the setting of the uniform distribution for \bar\mu; or a justification should be provided on the current values for these parameters.
(d) It would be ideal to plug stage 2 of the proposed method into some existing methods which do not consider runtime domain corruption, to see how the addition improves performance, especially as the authors consider the "plug-in can be potentially applied to other state-of-the-arts". 

3. Accuracy/quality of presentation
(a) Definition of ITE - do we need the unfoundedness assumption for "defining" ITE/CATE?  
(b) There are some minor English problems, e.g. an incomplete sentence in the 2nd paragraph on page 3 "While Dragonnet ..."; the first paragraph of Section 6 "We performance evaluation on ..."

clarity,_quality,_novelty_and_reproducibility: The paper tackles a practical problem of counterfactual prediction, covariate shifts/discrepancy, a problem that has not been well studied in the context of counterfactual prediction. Hence the work is valuable and the proposed approach looks reasonable and promising too. 

There are rooms to improve the evaluation part to better demonstrate the effectiveness of the proposed method and the significance of the contribution, and the clarity of the presentation, especially the specific problem tackled by the paper, can be improved too.

Regarding reproducibility, most of the details are provided. It would be better if justifications/analysis on some details on parameter settings are provided, which should help readers to better understand their impact and choose the suitable values for their problems.
summary_of_the_review: The work has its value and novelty. As detailed in the Strength and Weaknesses section, my main concerns are on the experiments (which have reduced my confidence when assessing the significance of contribution of the proposed method) and the clarity of the statement/claim of the problem tackled in the paper.
correctness: 3: Some of the paper’s claims have minor issues. A few statements are not well-supported, or require small changes to be made correct.
technical_novelty_and_significance: 2: The contributions are only marginally significant or novel.
empirical_novelty_and_significance: 2: The contributions are only marginally significant or novel.
flag_for_ethics_review: NO.
recommendation: 5: marginally below the acceptance threshold