DBRNet: Advancing Individual-Level Continuous Treatment Estimation through Disentangled and Balanced Representation

Thank you for your valuable insights and the recognition of the improvements in our work. Your feedback as an ICLR reviewer, with experience from NeurIPS, is greatly appreciated.

Regarding your concern about the use of 800 epochs for every model, we agree with your point. To address this, we have implemented an early stopping technique across all models to prevent overfitting and underfitting in this ICLR version. This modification is detailed in our code. Furthermore, we have specifically highlighted this change in blue on page 13 in the Implementation Details section of our revised manuscript.

We trust that these adjustments adequately address your concerns. We are dedicated to integrating your constructive feedback into the revised version of our paper. Once again, we extend our gratitude for your insightful comments.

8.Clarification on TR

As you rightly pointed out, TR represents targeted regularization. As you mentioned, TR is designed for ATE / ADRF estimation. Furthermore, to obtain ATE and ADRF, the papers [2-3] (which proposed TR) actually first calculate the individual treatment effect and then average them to derive the ATE and ADRF. We conjecture that thoes approaches may also lead to better individual treatment effect estimation. Otherwise, the papers [2-3] might not achieve improved ATE/ADRF results through averaging if individual treatment effect were inaccurately estimated. Therefore, we believe it would be interesting to compare these with our methods. Moreover, including more baseline methods also makes the results more convincing.

9.Clarification on Discrepancy Loss

And we agree with you that the KL divergence is used to measure the discrepancy between two distributions of representations. Typically, in our paper, we use the KL divergence loss, which slightly differs from the original KL divergence. Here is the detailed PyTorch implementation of the KL loss that we use: https://pytorch.org/docs/stable/generated/torch.nn.KLDivLoss.html KL Divergence Loss. Thanks for your question. In response, we have added a section in Appendix D, highlighted in blue, to further clarify KL divergence. Additionally, we have included a sentence in the methods section to guide readers to this new Appendix section.

We hope that our response addresses your concerns adequately, and we are committed to incorporating your valuable feedback into the revised version of our paper. Thank you once again for your insightful comments.

[1] Schwab P, Linhardt L, Bauer S, et al. Learning counterfactual representations for estimating individual dose-response curves[C]//Proceedings of the AAAI Conference on Artificial Intelligence. 2020, 34(04): 5612-5619.

[2] Shi C, Blei D, Veitch V. Adapting neural networks for the estimation of treatment effects[J]. Advances in neural information processing systems, 2019, 32.

[3] Nie L, Ye M, Nicolae D. VCNet and Functional Targeted Regularization For Learning Causal Effects of Continuous Treatments[C]//International Conference on Learning Representations. 2020.

1.Include more MISE results

We are grateful for your insightful suggestion regarding the emphasis on MISE. Initially, we had prioritized AMSE as the primary metric due to its popularity. However, after carefully considering your valuable suggestion, we agree that focusing on MISE is indeed more appropriate for our paper. To reflect this, we have thoughtfully reordered the tables to give precedence to MISE over AMSE. Additionally, we have revised the displayed metric in Fig. 3 according to your suggestion. We have also refined the description of our results to highlight the MISE findings more prominently. All these modifications have been highlighted in blue for ease of review.

2.Implementation about the MISE

Thank you for your reminder. We have updated the code to include the implementation of the MISE. Additionally, we would like to clarify that our test dataset (data used to compute MISE and AMSE) is not biased. To approximate the AMSE and MISE, we apply all $t$ values existing in the current dataset to each unit. Consequently, one unit is tested on all available $t$ values, ensuring that the treatment assignment is not influenced by selection bias. Given this unbiased dataset, we believe that using all real $t$ values in the dataset is preferable to equally sampled points in $\mathcal{T}$. This approach better represents the actual $t$ distribution, as opposed to generating equal-interval $t$ values.

We have carefully reviewed the paper you suggested. In their approach (Equation 1 on page 3), they also proposed to use all $t$ values in the dataset. However, in their implementation, they employ Romberg integration, as you mentioned. We conjecture this might be related to their method, which involves dividing the treatment equally into several strata and assigning a specific prediction head for each. Romberg integration, in such case, is a more suitable metric for their method as it ensures accurate predictions for each head. Nevertheless, in our paper, we respectfully argue that using the actual $t$ values from the dataset may be a better choice for our methodology.

3.Clarification on sensitivity analysis

We appreciate your detailed review and have corrected the typo. Furthermore, we have expanded the test range of hyperparameters and included all hyperparameters in the sensitivity analysis. The new results can be found in the revised paper. The figure shows that the re-weighting function and the discrepancy loss ($\beta$) have more substantial influence on the model's performance, which consists with the findings from the previous ablation study. The performance improves notably when $β$ is larger and the re-weighting factor is set to 1.

4.Add more ablation studies for alpha

We agree with you that including all hyperparameters would likely make our analysis more robust. Our initial decision to exclude certain hyperparameters was based on previous studies indicating their minimal impact on results [3], a finding consistent with our preliminary findings. However, as you suggested, exploring this further could be interesting. Therefore, we we have added an ablation study for $α$ and a sensitivity anaylsis for $α$ and $λ$ based on both MISE and AMSE in our revised paper. Due to the space limit we only show the figure based on MISE as you suggested, and we put the result of AMSE in Appendix I. The results confirm our alignment with prior findings: while including this hyperparameter ($\alpha$) does improve performance, the improvement is slight.

5.Baseline Method

Thank you for your suggestion. We would love to add this baseline; however, the code is not open-sourced, and despite our efforts to contact the author, we have not received a response. Should the code be released, we will certainly do our best to include it as a baseline.

6.Clarification on the proof

We agree with your observation. In our paper, we utilize re-weighting to adjust for selection bias, and the provided proof aims to offer theoretical support for this approach. Throughout the paper, we clarify that the proof pertains to the debiasing ability of the re-weighting method rather than balancing. We would like to understand more about your reference to 'balancing' to address any specific concerns you might have.

7.Missing space Problem

We appreciate your detailed review and have already corrected the missing space.

To Reviewer TzGH:

1.Clarification on the law of total probability

Thank you for pointing this out. We realized that the equation and term were confusing, so we have carefully revised them. A new paragraph has been added to Appendix A, which includes our revised equation for continuous settings, highlighted in blue. We have also included additional explanations in the proof section, similarly highlighted. Typically, $t'$ represents all counterfactual treatments of $x$, defined as $t'= \\{t'| t'\in \mathcal{T}, t'\neq t \\}$. The union of $t$ and $t'$ constitutes the universal set of treatments. Therefore, given the probability density function $f(x,t)$ we have, $\mathbb{P}(x,t)+\mathbb{P}(x,t')=\int_{t}f(x,t)dt+\int_{\mathcal{T} / \{t\}}f(x,t)dt =\int_{\mathcal{T}}f(x,t)dt =\mathbb{P}(x)$

2.Estimation of counterfactual distribution, and the technique to deal with the continuous treatment estimation

In our paper, we do not estimate the counterfactual distribution $p(x, t')$; instead, our goal is to estimate the IDRF as shown in Equation 1 $\mu(t, x) = \mathbb{E}[Y(T=t)|X=x, T=t]$. This involves estimating the corresponding $y$ for any given $x$ and $t$. We acknowledge, as you rightly pointed out, that addressing this continuous treatment estimation is a crucial aspect of our work. Typically, we adopt the varying coefficient network [2] (as introduced in Section 3.2 in factual loss) to estimate treatment effects under continuous settings. Thank you for pointing out the confusion of the function of the varying coefficient network. We have added a sentence highlighted in blue in the methods section, to elucidate that.

In binary settings, as demonstrated in the paper by Hassanpour and Greiner [2019b], the common approach is to learn a deep representation of $x$ and then construct a neural network for each treatment to estimate $\mu(t, x)$. However, this method cannot be extended to continuous settings due to the infinite number of treatments, making it impractical to build a neural network for each value of $t$. Therefore, we utilize the varying coefficient network [2] (introduced in factual loss in section 3.2), which enables us to estimate treatment effects under continuous settings. Specifically, the varying coefficient structure uses a function $g_{\theta(t)}(\Delta(x_i), \Upsilon(x_i))$ with varying parameters $\theta(t)$ rather than fixed parameters to predict outcomes $y$ given the treatment $t$ and the corresponding deep representation of covariates $\Delta(x_i), \Upsilon(x_i)$. In this model, the parameters are determined by $t$, allowing us to incorporate the continuous $t$ in outcome estimation and estimate $\mu(t, x)$ without the need to construct a neural network for each value of $t$.

Particularly, we employ a B-spline of degree $p$ with $q$ knots, resulting in $k=p+q+1$ basis functions. Let $**B** =[b_1, b_2, ..., b_k] \in \mathbb{R}^{n\times k}$ denote the spline basis for the treatment $T \in \mathbb{R}^{n\times 1}$. For a single-layer feedforward network with $p$ inputs and $q$ outputs, the function is given by $f_{\theta(t)} = \sum_{i=1}^{k} (b_i \cdot (**X****W**))$, where $**W** \in \mathbb{R}^{p\times q\times k}$ is the optimizable weight matrix.

3.Identifiability of the latent factors

We respectfully argue that our method differs from nonlinear independent component analysis, and our latent factors are fully identifiable through supervised learning. We acknowledge your point that achieving full identifiability in independent component analysis is challenging, as it is inherently unsupervised. While it can separate the latent factors, identifying the semantic meaning of each latent factor is difficult. In contrast, our method leverages supervised learning to ensure that each deep representation learns its corresponding information effectively.

In our paper, we describe three types of deep representations:

1. Instrumental factors $\Gamma(x)$, which are associated with the treatment but not with the outcome except through the treatment.
2. Confounder factors $\Delta(x)$, which are associated with both the treatment and the outcome.
3. Adjustment factors $\Upsilon(x)$, which are predictive of the outcome but not associated with the treatment.

We use instrumental and confounder factors to predict treatment, and confounder and adjustment factors to predict the outcome. The ground truth of the treatment and the outcome, along with the loss function (Equation 2), are used to optimize the learned representations (supervised learning). This approach ensures that different representations only encode relevant information for their respective roles, thereby achieving identifiability. In addition, we attempt to explore whether the representations capture the corresponding factors by utilizing t-SNE to visualize the three deep representations. The results in section 4.5 show that our method has the ability to identify the corresponding factors.

4.Terms' meaning

Thank you for pointing out this issue, which was indeed a typo in the caption of Figure 3. We have now corrected it. The symbol $γ$ represents the weight before the independent loss $L_{ind}$ (as detailed in Equation 2 on page 4) and is one of the hyperparameters. Figure 3 is intended to illustrate the sensitivity of these hyperparameters. TR refers to targeted regularization, a technique that improve the accuracy of treatment estimation [1,2]. We appreciate your observation and have added the full name about this term to enhance clarity.

5.More details about the methods to handle continuous variables

Please refer to our response in answer 2 for the clarification. We hope this addresses your question. Should you have any further queries or require additional information, please do not hesitate to let us know.

We hope that our response addresses your concerns adequately, and we are committed to incorporating your valuable feedback into the revised version of our paper. Thank you once again for your insightful comments.

[1] Shi C, Blei D, Veitch V. Adapting neural networks for the estimation of treatment effects[J]. Advances in neural information processing systems, 2019, 32.

[2] Nie L, Ye M, Nicolae D. VCNet and Functional Targeted Regularization For Learning Causal Effects of Continuous Treatments[C]//International Conference on Learning Representations. 2020.

Dear Reviewer,

Thanks for your assessment and your encouragement of our work. As the deadline for reviewer-author discussion (11/22/23) approaches, we would be happy to take this opportunity to make more discussions about any of our questions or concerns. If our response has addressed your concerns, we would be grateful if you could re-evaluate our paper based on our feedback and new results.

Sincerely,

Authors

• From your definition, it seems $P(X, T')$ is not a distribution anymore as $\int_{support(P(X, T'))}P(x, t')dxdt'= 1-\int_{x}P(x,t)dx<1$, where X and T' are random variables of x and t'.
• Additionally, how do you empirically calculate error CF in Theorem 1 step-by-step. It seems that we need to have a sample from the counterfactual distribution.

Dear authors,

Could you provide rigorous definition of each term and detailed explanation about Theorem 1. It seems that the assumption of P(x, t') for making the reweighting holds can not be defined by following the definition of t' in your proof. t' represents all counterfactual treatments does not imply P(x, t') is a counterfactual distribution. The counterfactual distribution should be P'(X,T), where X and T are random variables.

In this case how can we know the factual treatment t is not allowed in the counterfactual world?

3.Gap between the loss function and the theoretical analysis

We recognize that there appears to be a gap between the sophisticated loss function and the theoretical analysis. However, we kindly argue that each term in our loss function contributes meaningfully to the theoretical proof. Specifically, some components of the loss function serve to support the assumptions underpinning our proof, as outlined in Assumptions 1-4 in our paper. Their functions are introduced as follows. In Assumption 4, we posit that each latent factor should be independent of each other, where discrepancy loss $L_{dis}$ is used to ensure this. $L_{ind}$ enforces us to encode all information of $t_i$ in $\Gamma(x_i)$ and $\Delta(x_i)$ instead of $\Upsilon(x_i)$, thereby facilitating a more precise and accurate estimation of the weight $w$ (re-weighting before the factual loss). Moreover, the weight $w$ before factual loss is the key of the proof, hence we use the $L_T$ loss to get the accurate weight. Thank you for your suggestion, we have added a paragraph in the Appendix A, highlighted in blue, to clarify the function of each loss in our revised version.

4.More results for sensitivity analysis

We are grateful for your constructive suggestion regarding the addition of more results to enhance the robustness of our experiments. In line with your advice, we have added an ablation study for $\alpha$ (Table 2) and a sensitivity analysis for $\alpha$ and $\lambda$ based on both MISE and AMSE in our revised paper (Figure 3&6). Due to space limitations, we have chosen to only display the figures based on MISE, while the results for AMSE are included in Appendix I. The results show that despite $\alpha$ also contributes to IDRF estimation, its values have a minimal impact on model performance. As for $λ$, which controls the regularization, excluding it leads to a decrease in performance. However, when included, the specific value of $λ$ does not significantly affect the results.

5.Meaning of $Γ(x_i)$ and $Δ(x_i)$ and clarification on KL divergence

In our paper, $X$ represents the entire dataset of covariates, encompassing multiple features, rather than a singular random variable. In the previous given example, within the medical historical data of all patients, $X$ represents all features of all patients. For a specific patient $x_i$, the the patient’s age and gender are the confounder factors $Δ(x_i)$, while the patient’s doctor-in-charge is the instrumental factor $Γ(x_i)$. It is apparent that the doctor-in-charge is independent of the patient's age and gender. We believe that adding this example, as per your suggestion, will elucidate this point more clearly. Moreover, $Γ(x_i)$ and $Δ(x_i)$ generated by our model are not random variables; they are deep representations with a dimension of 50, as generated by three representation networks in our model (Figure 2). We agree with your observation that KL divergence is employed to measure the discrepancy between two distributions of representations. In our work, we specifically use the KL divergence loss, with its detailed implementation available in PyTorch: https://pytorch.org/docs/stable/generated/torch.nn.KLDivLoss.html. Your suggestion is valuable. In response, we have added a section in the Appendix D, highlighted in blue, to clarify KL divergence. Additionally, we have included a sentence in the methods section to direct readers to this new Appendix section.

We hope that our response addresses your concerns adequately, and we are committed to incorporating your valuable feedback into the revised version of our paper. Thank you once again for your insightful comments.

[1] Wu A, Kuang K, Yuan J, et al. Learning decomposed representation for counterfactual inference[J]. arXiv preprint arXiv:2006.07040, 2020. [2] Yao, Liuyi, et al. "A survey on causal inference." ACM Transactions on Knowledge Discovery from Data (TKDD) 15.5 (2021): 1-46.

[3] Kuang, Kun, et al. "Treatment effect estimation with data-driven variable decomposition." Proceedings of the AAAI Conference on Artificial Intelligence. Vol. 31. No. 1. 2017.

[4] Liu, Dugang, et al. "Mitigating confounding bias in recommendation via information bottleneck." Proceedings of the 15th ACM Conference on Recommender Systems. 2021.

[5] Hassanpour, Negar, and Russell Greiner. "Learning disentangled representations for counterfactual regression." International Conference on Learning Representations. 2020.

[6] Shalit, Uri, Fredrik D. Johansson, and David Sontag. "Estimating individual treatment effect: generalization bounds and algorithms." International Conference on Machine Learning. PMLR, 2017.

[7] Bellot A, Dhir A, Prando G. Generalization bounds and algorithms for estimating conditional average treatment effect of dosage[J]. arXiv preprint arXiv:2205.14692, 2022.

To Reviewer cz1b

1.Explanation and soundness of the causal graph

We agree with you that utilizing a concrete example can help readers better understand the causal graph and enhance its soundness, and thus we have added a section in Appendix H (An instantiation of causal graph) and the detailed motivation and intuition for the disentanglement in the method section.(both are highlighted in blue).

The motivation and intuition behind the disentanglement in our study are rooted in causal inference theory, which typically classifies covariates (input features) into three categories: instrumental variables (predictive only of treatment), confounder variables (influencing both treatment and outcome), and adjustment variables (predictive solely of outcome). Furthermore, disentangling $X$ into these three factors is a commonly used approach in causal inference research, as evidenced in [1, 2, 3, 4, 5], allowing for the precise extraction of relevant information.

We presented a detailed example in a medical scenario, as proposed in [1]: We might collect extensive historical data from each patient, including the patients' features $𝑋$ (e.g., age, gender, living environment, doctor-in-charge), treatment of patients $𝑇$ (taking a particular medicine or not), and the final outcome $𝑌$ (cured or not). Among these features, age and gender simultaneously affect the treatment (as a doctor would consider these factors when choosing a treatment) and the outcome (since they can also impact the patient’s recovery rate), hence they are confounding factors $𝐶$. In contrast, the doctor-in-charge would influence only the treatment decision, without affecting the outcome, thus being an instrumental factor $𝐼$. Environment, which only affects the outcome but not the treatment, falls into the category of adjustment factors $𝐴$.

2.Clarification on KL divergence

Thank you for prompting us to clarify our approach to KL divergence. The aim of our causal graph is to demonstrate that covariates can be decomposed into three factors: $Γ(x_i), Δ(x_i), Υ(x_i)$, where $Γ(x_i)$ and $Δ(x_i)$ should be used to estimate $t_i$, while $Δ(x_i)$ and $Υ(x_i)$ should be used to estimate $Y$. Hence, our model structure is already fulfilled this causal graph, and the rest of loss is mainly aim to adjust selection bias.

The disentanglement loss $L_{dis}$ is designed to ensure that these factors are more separated and encode only the relevant information. The purpose of adding an independent loss $L_{ind}$ is to eliminate the selection bias caused by biased treatment assignment. Since we aim to prevent the distribution of the adjustment factor $Υ(x_i)$ from varying across different treatments, so we introduce this term (make the adjustment factor to be independent of $t_i$) to make necessary adjustments. Although many previous papers have proposed similar ideas, most of them focus on binary settings and may therefore adopt different methods [5-7]. This loss function also allows us to encode all information about $t_i$ in $Γ(x_i)$ and $Δ(x_i)$, rather than in $Υ(x_i)$, which aids in making the estimation of $w$ more precise and accurate. Hence, this loss further enhances bias elimination through re-weighting. Secondly, from a practical standpoint, since $Y$ is unknown and is the variable we aim to predict, it is not practical to include a term to measure and minimize the discrepancy loss between two distributions when one of them is unknown. We agree with you using the causal graph structure to justify the $L_{ind}$ may be confusing and we have already modified that part (in section 3.2 Independent loss, highlighted in blue) to clarify the motivation and aim. Thank you again for your suggestion!

[1] Wu A, Kuang K, Yuan J, et al. Learning decomposed representation for counterfactual inference[J]. arXiv preprint arXiv:2006.07040, 2020. [2] Yao, Liuyi, et al. "A survey on causal inference." ACM Transactions on Knowledge Discovery from Data (TKDD) 15.5 (2021): 1-46.

[3] Kuang, Kun, et al. "Treatment effect estimation with data-driven variable decomposition." Proceedings of the AAAI Conference on Artificial Intelligence. Vol. 31. No. 1. 2017.

[4] Liu, Dugang, et al. "Mitigating confounding bias in recommendation via information bottleneck." Proceedings of the 15th ACM Conference on Recommender Systems. 2021.

[5] Hassanpour, Negar, and Russell Greiner. "Learning disentangled representations for counterfactual regression." International Conference on Learning Representations. 2020.

[6] Shalit, Uri, Fredrik D. Johansson, and David Sontag. "Estimating individual treatment effect: generalization bounds and algorithms." International Conference on Machine Learning. PMLR, 2017.

[7] Bellot A, Dhir A, Prando G. Generalization bounds and algorithms for estimating conditional average treatment effect of dosage[J]. arXiv preprint arXiv:2205.14692, 2022.

Hi Reviewer cz1b,

Thank you for your response. We are happy to provide further clarifications as follows.

To elaborate, $\Gamma(x_i)$ and $\Delta(x_i)$ for a specific patient are not singular values; rather, they are combinations of features specific to that patient. For instance, in this example, age and gender (two features) are the confounder variables for the patient, so their combination forms the confounder factors. In real datasets, the complexity of these combinations is often much larger than in this example. For example, if we have a dataset with 50 features, where 20 are instrumental features, 10 are confounder features, and 20 are adjustment features, then the confounder factors for a specific patient would be the combination of those 10 features. However, extracting and representing these combinations for each patient is challenging, which is why we use a neural network in our model. As illustrated in Fig.1, our network learns three separate representations (each with a dimension of 50, representing one factor) from the input. The independent loss is implemented to ensure that each component learns only the information relevant to its specific functionality.

We hope this response clarifies your question. Should you have any further queries or need additional information, please do not hesitate to let us know.

Dear authors,

Please answer my following questions directly and briefly.

1. You seem to use "independence", "disentanglement", and "separation" exchangeably, please clarify their differences.

2. If you say "A is independent of B", what is the definition of "independent" if A and B are not random variables?

3. You say that you want to separate $\Gamma(x_i)$ from $\Delta(x_i)$, but separation does not make sense. Consider A is an n-dim binary vector, and B is XOR(A). Then the divergence between A and B is maximized, but they are not independent of each other.

Dear authors,

In my humble opinion, separation itself does not make sense. According to the Markov property, a graph model (Figure 1(a)) entails independence rather than separation. If I'm wrong, please provide some references about "separation derived from graph".

To Reviewer Wac2:

1.Motivation of using disentanglement in the context of continuous settings

We are grateful for your question. The motivation for using disentanglement in continuous settings is to precisely adjust selection bias. Existing methods often resort to balancing the entire representation, a simple yet brute approach. However, we argue that not all information in the latent representation should be balanced to adjust for selection bias. For instance, while confounder factors in the representation bring selection bias, they also contribute to outcome predictions. Balancing instrumental factors is theoretically implausible since they relate to treatment assignment and should not be identical across treatments. Therefore, indiscriminate balancing of the entire representation of input covariates is not appropriate. Hence, we apply disentanglement techniques to disentangle the three factors for the further precise bias adjustment. We appreciate your suggestion and have added more details about the motivation (highlighted in blue) in both the introduction and the methods sections of our paper.

2.Clarification on KL divergence

Thank you for prompting us to clarify our approach to KL divergence. In our model, both instrumental $\Gamma(x_i)$ and confounder representations $\Delta(x_i)$ are used to estimate the probability of treatment, while confounder $\Delta(x_i)$ and adjustment representations $\Upsilon(x_i)$ are used to predict the outcome. We argue that instrumental and confounder representations are more similar, as are confounder and adjustment representations, since they are optimized for the same goals. Therefore, we only penalize these. To avoid making our model cumbersome, we decided not to include the KL divergence between instrumental $\Gamma(x_i)$ and adjustment representations $\Upsilon(x_i)$ . We have added a section in the Appendix D, highlighted in blue, to clarify KL divergence. Additionally, we have included a sentence in the methods section to direct readers to this new Appendix section.

3.Comparison with other methods

Thank you for sharing these interesting papers! After a careful review, one of them [1] is extensively discussed in the related work and section 3.4 of our paper. The limitations of [1] actually motivated our approach. Specifically, [1] suggests building regression networks on the top of disentangled embeddings for each treatment value in binary settings. However, in continuous settings, building a network for each treatment value is impractical due to the infinite nature of $T$. Moreover, upon revisiting their code according to your suggestion, we note that [1] requires prior knowledge of the probability of each treatment to compute the re-weighting function, making it unsuitable for continuous treatment scenarios. Similarly, the methods in [2] are limited, as they binarize the treatment. The lack of open-source code for [2] further complicates direct comparison. Overall, while these methods employ disentanglement, they address different questions in different settings. We would be eager to compare our method with theirs if they release their code, especially for continuous settings.

We hope that our response adequately addresses your concerns. We are committed to incorporating your valuable feedback into the revised version of our paper. Thank you once again for your insightful comments.

[1] Hassanpour N, Greiner R. Learning disentangled representations for counterfactual regression[C]//International Conference on Learning Representations. 2019.

[2] Wu A, Kuang K, Yuan J, et al. Learning decomposed representation for counterfactual inference[J]. arXiv preprint arXiv:2006.07040, 2020.