Dynamic Interference Modeling For Estimating Treatment Effects From Dynamic Graphs

Thank you for your constructive comments. Below are our responses to your concerns.

Summary of Question 1 and Weaknesses 1 and 2: Limitation of the proposed method when there exist hidden confounders.

Response: We had discussed the situation that there exist hidden confounders and some existing works for addressing hidden confounders (such as Deconfounder (Guo et al., 2020)) in the Limitations section of the Appendices. However, the issue of hidden confounders is not the primary focus of our study, which aims to address the new challenging issues: Dynamic interference modeling and ITE estimation under dynamic interference. Considering the complex scenario involving both hidden confounders and dynamic interference might divert readers' attention from our main objectives. Thus, we borrow the assumption that all confounders are observed in covariates, which is made by many studies for ITE estimation under interference, such as GCN-TE (Ma and Tresp, 2021) and HyperSci (Ma et al., 2022b).

To take your comments into account, we conducted experiments to verify the effectiveness of the proposed method in handling hidden confounders. We use the Flickr$_{k_2=1.0}$ dataset (with a parameter $k_2=1.0$), which is provided by the existing work (Deconfounder, Guo et al., 2020) for addressing hidden confounders. Importantly, there exist hidden confounders in this dataset. Results are averaged over five executions, as follows:

Results show that DITE achieves performance comparable to Deconfounder on the Flickr$_{k_2=1.0}$ dataset, which contains hidden confounders. This implies that the proposed DIM layers may have the potential ability to address hidden confounders when such hidden confounders can be captured from the network. This is an interesting phenomenon, which deserves further exploration by building a bridge between networked interference and hidden confounders in the network. Such exploration requires more comprehensive theoretical analysis and additional experiments, which are beyond the scope of our study, which focuses on modeling dynamic interference and estimating ITE under dynamic interference. Therefore, this can be considered as future work.

Moreover, we believe that considering the joint existence of hidden confounders and dynamic interference is a very interesting topic for future research. However, it is a complex and challenging issue that also deserves further exploration.

Action: We will discuss more about this in the part of limitation and future work of the updated version.

Summary of Question 2 and Weaknesses 3: Concerns about the limitation of the proposed method in ITE estimation at future time and authors’ thoughts on estimating future timestamp ITE without future information.

Response: Based on your constructive comments, we discuss two ideas for the issue of ITE estimation without future information. Thank you for the inspiration to explore time-series prediction techniques or generative models to build new models for ITE estimation at future time stamps without using future information. We believe your comment is very helpful for exploring new methods and enhancing the practicality of ITE estimation. We consider the following two ideas:

1. Train several additional RNNs to generate networks and covariates over different time stamps. During training, we can apply a reconstruction loss (such as L2 reconstruction loss) between the output of the RNNs and the networks (or covariates). These additional RNNs should be trained separately from the ${\rm{DITE}}_{\rm{ev}}$ model. Training them jointly might be challenging and time-consuming, as the network’s dimension is typically high and depends on the number of individuals. However, this idea has an obvious disadvantage: Training these models separately rather than jointly in an end-to-end manner often leads to non-optimal parameters for the downstream task.

2. To overcome the disadvantage mentioned in the previous idea, we can incorporate RNNs into the current DITE$_{\rm{ev}}$ to generate interference representations and representations of covariates. In this case, we can apply a reconstruction loss between the interference representation generated by DIM layers and the outputs of the new RNNs during training. A similar strategy can also be applied to the RNNs that generate representations of covariates. This approach allows us to jointly train the new RNNs and ${\rm{DITE}}_{\rm{ev}}$ while avoiding directly generating the network and covariates.

Estimating ITE at future time stamps in the presence of dynamic interference without any future information is an interesting but very challenging task. We will consider more to improve this idea. This needs more consideration about the theoretical analyses, and experimental setup to verify these two ideas for overcoming this challenge. This can be considered as a new topic for future research.

Action: We will discuss more about this in the future work of the updated version.

Weakness 3.1: Its real-world applicability is limited. Accessing complete network dynamics and covariates for all individuals is often infeasible.

Response: As historical information ($<t$) is typically available at time stamp $t$, we can simplify the situation you mentioned to one that discusses whether the information of some individuals on the network is accessible at time $t$. Many existing studies allow using complete information on the network and covariates of all individuals to train their models, such as GCN (Welling and Kipf, 2016), Deconfounders (Guo et al., 2020), and GCN-TE (Ma and Tresp, 2021). However, their applicability is not limited. For example, GCN (Welling and Kipf, 2016) had been widely used in many applications and areas. Following the above works, we make the information on covariates and network accessible at time $t$ for properly addressing the new challenging issues: Dynamic interference modeling and ITE estimation under dynamic interference. Now, we provide a strategy to take your comment into account. When some parts of information on covariates and networks are missing, we can mask the covariates of unobserved individuals and hide the edges connecting to these unobserved individuals in the graphs. In this case, the performance of the model usually decreases and depends on how much information about individuals and the network is provided.

Action: We will discuss the situation when complete network dynamics and covariates of all individuals are not given in the appendices of the updated version.

Weakness 3.2: The algorithm’s runtime on large networks may also pose practical challenges.

Response: There are many existing works for accelerating GNN, such as GraphSAGE, GraphSAINT, and FastGCN, which can be used to reduce computation in the within-time aggregation of proposed methods. Importantly, there usually be a trade-off in performance and efficiency. We aim to address the new issues: Dynamic interference modeling and ITE estimation under dynamic interference. Thus, we prioritize performance in ITE estimation under dynamic interference. When readers want to further accelerate our methods, we recommend that they extend our methods by combining our methods with these existing works for accelerating GNN.

To take your comment into account, we discuss two strategies that can accelerate the within-time aggregation part of our methods in training.

1. Splitting the graph into some sub-graphs when the input graph is large. Then, training our methods on each subgraph.

2. Applying some neighbor sampling mechanisms (e.g., the neighbor sampling mechanism of GraphSAGE) to the within-time aggregation mechanism of our method (as detailed in equation (4)).

As described above, the proposed methods are extendable. We also provide the training time (in minutes) of our methods on corresponding datasets:

The training time of our method is reasonable, even without deliberate acceleration of the within-time aggregation component. If the strategies mentioned above are applied to speed up this part, it may further improve training efficiency.

Action: We will discuss the situation when readers want to accelerate our methods and provide the Table of training time of our methods in the Appendices of the updated version.

Weakness 4: The experiments are conducted on synthetic datasets. To validate the model's utility, evaluation on real-world data would be beneficial.

Response: Our experiments are conducted on semi-synthetic datasets, which is a common choice in most existing works for ITE estimation in the causal area, such as Deconfounder (Guo et al., 2020), GCN-TE (Ma and Tresp, 2021), HyperSci (Ma et al., 2022b), and DNDC (Ma et al., 2021). The ground truth of ITE is hard to collect, as we cannot get the counterfactual outcomes from real-world data. This is a common choice to use semi-synthetic datasets, as conducting RCT to collect the ground truth of ITE is time-consuming and expensive. Thus, using semi-synthetic datasets to conduct experiments is reasonable for research studies in the causal area.

Weakness 5: It remains unclear how the method significantly differs from a non-causal, purely supervised learning setup.

Response: ITE estimation is an important task in causal inference, and different from non-causal learning setup that predicts outcomes only. We had introduced the concept and role of ITE estimation in Section 1 with an example of its application (as detailed in Lines 38 ~ 44), as well as the details of problem setting in Section 3. For more details on the difference between ITE estimation and supervised learning setup, please refer to the survey (Yao et al., 2021).

Thank you for your constructive comments. Below are our responses to your concerns.

Response to Weaknesses:

Weakness 1.1: Assumption 1 implies dependency on the treatment of other users at the same time stamp, but the proposed model does not incorporate this information as input, potentially limiting its alignment with the stated assumptions.

Response: The inputs of $\psi^t$ of our proposed method are $\mathbf{X}^{\leq t}$, $\mathbf{T}^{\leq t}$, and $\mathbf{A}^{\leq t}$ (as detailed in Line 276), where $\mathbf{T}^{\leq t}$ (the description of superscript $\leq t$ is detailed in Line 161 for the original version or Line 165 for the updated version) contains historical treatment assignments and treatments assigned to other individuals at the time stamp $t$.

Weakness 1.2: Moreover, if the model follows the assumption with the treatment as input, it is not clear how the model can be used to in uplift decisions.

Response: We use $f^t_1(\boldsymbol{s}_i^t,\boldsymbol{u}_i^t)- f^t_0(\boldsymbol{s}_i^t,\boldsymbol{u}_i^t)$ to estimate ITE (as detailed in Lines 362 and 363), where ${f^t_1}$ predicts the potential outcome with treatment = 1 and $f^t_0$ predicts the potential outcome with treatment = 0. To model interference, we take treatments as inputs, which follow existing works for ITE estimation under interference, such as GCN-TE (Ma and Tresp, 2021) and HyperSci (Ma et al., 2022b). Moreover, information on observed treatments is also used to train $f^t_1$, and $f^t_0$. If the observed treatment = 1 for a unit at time $t$, the outcome of this unit will be used to train $f^t_1$; If the observed treatment = 0 for a unit, the outcome of this unit will be used to train $f^t_0$, as illustrated in Figure 2(a), detailed in Section 4.3 and Equation (6).

We can estimate ITE at time $t$ and past time stamps (< t) by using our ITE estimator, which can help us to understand the change of individuals, as well as the change of their treatment effect. This can help us to deeply analyze the effect of the treatment, which results in more reasonable decisions.

Action: To take your comment into account, we will add more descriptions for our ITE estimator in the updated version.

Weakness 2: The authors should clarify the size of the training dataset used and provide experimental results on how model accuracy depends on the amount of training data.

Response: We had clarified the ratio of the training set (as detailed in Lines 480 and 481 for the original version of the paper or Line 485 for the updated version) and the size of every dataset (as detailed in the part of Dataset description and Appendix C). Specifically, we use the ratio of 70% data (as detailed in Lines 480 and 481 for the original version of the paper or Line 485 for the updated version) to train all methods.

Based on your constructive comments, we have revised and uploaded a new version of our paper. In the new version, we detailed and highlighted (in red) explanations for your concerns in Sections 4.1 and 4.3, Table 3, Appendices G and J.

Thank you for your constructive comments on the presentation. Below are our responses to your concerns.

Response to Weaknesses:

Weakness 1: The background and introduction sections do not sufficiently explain ITE, particularly in the context of dynamic networks.

Response: We had introduced the role and basic concept of ITE estimation (quantifies the relative change of an individual outcome with/without treatment, as detailed in Lines 43 and 44) by using a commerce case in the first paragraph (detailed in Lines 38~44) of the section of Introduction (i.e., Section 1 in our manuscript). Furthermore, in the second paragraph of the section of Introduction, we introduced that outcomes and information of individuals and networks can change over time in the dynamic graphs, which implies ITE can also change over time. To take your comment into account, we will add some descriptions in Section 1 to emphasize it.

Action: We will add some descriptions to emphasize the dynamics of ITE in the updated version.

Weakness 2: The overall framework diagram for the experiments lacks clarity.

Response: We had introduced the details of the experimental setting (as detailed in Section 5.1). Reviewers EDpc and PQXk point out that the details of experimental settings had already been introduced in the Strengths of their comments. Importantly, the outcome simulation had been introduced detailedly in Equation (7). Considering the outcome simulation is complex and your constructive comment, we will make a diagram for the outcome simulation. Thank you for your constructive comment on the presentation of experiments.

Action: We will add a diagram for the outcome simulation in the updated version.

Weakness 3.1: the main experimental results include only two comparison metrics. Presenting these comparisons in more intuitive charts would also help to better showcase the experimental outcomes.

Response: The metrics used in our paper are widely used in causal inference, there are many existing works that consider these two metrics, such as CFR (Shalit et al., 2017), HyperSci (Ma et al., 2022b), HINITE (Lin et al., 2023), and DNDC (Ma et al., 2021). Thus, they are enough and reasonable for verifying the performance of our methods.

Weakness 3.2: Presenting these comparisons in more intuitive charts would also help to better showcase the experimental outcomes.

Response: We had used histograms to show the results of ablation experiments (as shown in Figure 3) and used line charts to show the results of different hyperparameters (as shown in Figures 4 and 5). Importantly, we clearly highlighted the results with the lowest mean error of those of all methods on the corresponding dataset in boldface in Table 1. Since Table 1 includes ten methods, three datasets, and two metrics, it is challenging to use intuitive charts (e.g., histograms) to represent these results effectively. A small figure would make the results difficult to interpret, while a large figure would occupy excessive space. Separating the results in Table 1 into six large figures would also require a significant amount of space.

Based on your constructive comments, we have revised and uploaded a new version of our paper. In the new version, we detailed and highlighted (in red) explanations for your concerns in Section 1, the part of the description for outcome simulation, Appendix D, and Figures 7 and 8.

Weakness 2 and Question 2: More advanced gnn-based models should be considered.

Response: Although there had been many GNN-based methods compared in our experiments, such as GCN-TE, GCN-TE*, and DNDC, we added two GNN-based methods to take your comment into account, as follows:

1. GAT-TE. As recommended by the comment, we extend GAT to ITE estimation by replacing the GCN of GCN-TE with GAT [R2].

2. NEAT [R3] is designed to estimate ITE under a dynamic environment. However, it only considers how the dynamic network influences the treatment assignment but does not model interference.

The results of GAT-TE and NEAT [R3] are as follows:

On the Flickr dataset.

On the Blog dataset.

On the PeerRead dataset.

Action: We will add these two new baselines in the updated version of our manuscript.

Weakness 4.1: In a closer look at dynamic interference part, a larger t_max should be considered.

Response: Although many experiments had been conducted with different values of $t_{\rm{max}}$ (the size of all time stamps), which reveal the changes in the performance gap between the proposed methods and baselines with different values of $t_{\rm{max}}$, we considered a larger $t_{\rm{max}} = 15$ and conducted experiments on the Flickr dataset to take your comment into account. The results are shown as follows:

Action: We will add these results in the updated version.

Weakness 4.2: Showing the running time of different values of $t_{\rm{max}}$.

Response: The training time (in minutes) of different values of $t_{\rm{max}}$ for DITE are shown as follows:

Results show that the training time increases linearly with $t_{\rm{max}}$.

Action: We will add these results in the updated version.

Reference

[R1] Treatment Effect Estimation Amidst Dynamic Network Interference in Online Gaming Experiments.

[R2] Graph Attention Networks. ICLR 2018.

[R3] A Look into Causal Effects under Entangled Treatment in Graphs: Investigating the Impact of Contact on MRSA Infection. KDD 2023.

Thank you for your constructive comments. Below are our responses to your concerns.

Response to Weaknesses and Questions:

Weakness 1.1: Several works (such as [R1]) focus on solving the dynamic interference in ITE estimation, so the proposed problem is not new.

Response: After carefully reviewing the recommended paper [R1], we found that it tackles a different problem setting from ours. We summarize the differences as follows:

[R1] focuses on the ATE estimation for online games with dynamic networks only, but static covariates and treatments. In contrast, our methods focus on ITE estimation on dynamic graph data that have not only dynamic networks but also dynamic covariates and treatments. Our study introduces a new and more complex challenge: Cross-time interference. Cross-time interference can occur between two individuals who are not neighboring at any time stamp, as shown in Figure 1 and detailed in Section 1 (Lines 81 ~ 83 in the original version or Lines 83 ~ 86 in the updated version). This is a novel and significant challenge. Without properly modeling it, we may end up with wrong ITE estimation, which can result in wrong decision. Moreover, [R1] considers a setting of A/B testing, whereas we consider estimating ITE from observational data, which is inherently more challenging.

Action: We will discuss the differences between our study and [R1] in the updated version.

Weaknesses 1.2 and 3 and Question 1: Concerns about the technical contribution.

Response: Proposing solutions to a new and challenging issue constitutes a significant technical contribution. To overcome the challenges of dynamic interference modeling and ITE estimation under dynamic interference, we make necessary modifications, extensions, and combinations of existing methods. We summarize our technical contributions as follows:

1. DIM Layer for capturing dynamic interference: To address the challenging issue of capturing dynamic interference, we design a new layer: the DIM layer (detailed in Section 4.1). Unlike traditional GNN layers, the proposed DIM layer applies a historical aggregation mechanism before every within-time aggregation (i.e., a single-layered GNN). This step is crucial for capturing cross-time interference. By stacking DIM layers, we are able to model dynamic interference properly. In contrast, traditional GNN methods for dynamic graphs typically use multi-layered GNNs to learn node embeddings at each time stamp and then combine the learned embeddings from all time stamps at once, which can fail to capture cross-time interference properly. For example, results in Table 1 show that the baseline GCN-TE*, which combines the outputs of the final GNN layer at different times only after completing the multiple GNN layers across all time stamps, obtains high errors in ITE estimation. In contrast, our method achieves a lower error in ITE estimation. It is promising to extend DIM layers for other tasks involving dynamic interference in the causal area.

2. T-attention with a sliding window for capturing cross-time interference: To estimate the importance of cross-time interference from different time stamps, we proposed a weighting network: T-attention. This T-attention mechanism is applied to historical aggregation (as detailed in Lines 290 ~ 297 in the original version or Lines 289 ~ 293 in the updated version). To take the scalability issue into account, we apply a sliding window (as detailed in Lines 320 ~ 331 in the original version of the paper or Lines 316 ~ 323 in the updated version) to T-attention and historical information aggregation. This enables the individual to focus on the interference from the most recent time stamps, which often make the most significant contribution to cross-time interference.

3. DITE framework for ITE estimation under dynamic interference: To estimate ITE under dynamic interference, we propose a new framework: DITE (detailed in Section 4).

4. DITE$_{\rm{ev}}$ for capturing graph dynamics: To properly capture the dynamics of graphs, we also propose DITE$_{\rm{ev}}$ (as detailed in Section 4.4), which dynamically evolves the parameters of the model over time by using LSTMs.

Action: We will discuss the technical contributions in the updated version of our manuscript.

Based on your constructive comments, we have revised and uploaded a new version of our paper. In the new version, we detailed and highlighted (in red) explanations for your concerns in Section 2, the part of the description for the baseline, Tables 1, 2, and 4, Figure 5, and Appendices G and I.

We uploaded the revised version of our manuscript based on reviewers' constructive comments, where we highlight the main changes in red. We believe the revision has strengthened the manuscript.

Thank you for your time and consideration!