Paper: Trend/Seasonality based Causal Structure for Time Series Counterfactual Outcome Prediction (ICLR-2024)

Reviewer comment (Theory):
**[Unclear]** The authors argue that existing methods introduce a certain degree of selection bias since the balance representations act as confounders for both treatment and outcomes. However, this paper still uses the same independent constraints (Eq. (4) in (Hassanpour & Greiner, 2020), IPM loss in (Shalit et al., 2017)), contradicting their own statement.

Author response:
The proposed causal structure employs a decomposed approach to learn the trend/seasonality representations, and the selection bias is minimized by making the causal representations be independent of the treatments. As a result, the proposed causal structure achieves better performance than the balanced representation algorithms (e.g., CRN and Causal Transformer).

Reviewer comment (Theory):
**[Completeness 1]** The problem settings in this paper are incomplete. The causal relationship between x, a, and y in the time series is not clear. Will the outcomes at time t+1 be influenced by all the historical data? Would using only past P time steps data lead to unmeasured confounding bias? Does the causal relationship between covariates X change over time? I suggest the authors to provide a causal diagram of the time series to further clarify the problem settings. Additionally, in the problem settings section, what is the impact of trend and seasonality on the causal relationship?

Author response:
Thank you for your comment. We agree with Reviewer WhEV that the causal diagram between input, treatment, and outcome will clarify the problem settings. Furthermore, we will also provide the detailed implementations of the data generation processes in the main text or appendix.

Reviewer comment (Experiments):
[**Experiments**] This paper decomposes representations as Causal Trend and Causal Seasonality. However, how can we evaluate and demonstrate this? The experiments in the paper do not provide evidence for these statements.

Author response:
As denoted by other reviewers, there are not enough theoretical justification of trend/seasonality decomposed representations in the manuscript. We will present theoretical analysis and experimental results to support the issue in the future. In addition, the causal seasonality representations can be plotted using t-SNE graph to validate the issue.

Reviewer comment (Theory):
The major motivation for adapting the decomposition method is that the balanced representation approach produces selection bias. Yet, the decomposition method, as shown in Fig. 1, has a causal trend $T_t$, which is also a confounder. In the balanced representation approach, the representation is trained not to be predictive of the treatment. However, in the proposed approach, the confounder $T_t$ is trained to be predictive of the treatment. It is hard to argue which approach has a greater selection bias. If some theoretical analysis or visualization of the latent space could provide some insights into this issue, the argument in this paper would be more convincing.

Author response:
Thank you very much for your review!

We highlight below the difference between our work and the balanced representation approaches. 
The conventional balanced representation approaches learn a balance representation using the domain adversarial training framework to reduce the selection bias. On the other hand, the proposed causal structure learns the trend/seasonality decomposed representations, and the selection bias is minimized by making the causal representations be independent of the treatments. As a result, the proposed causal structure achieves better performance than the balanced representation algorithms (e.g., CRN and Causal Transformer).

Furthermore, we agree with Reviewer WboM regarding why minimizing the discrepancy could make the seasonality independent of the treatment. We will present theoretical analysis and experimental results to support the issue in the future. In addition, the causal seasonality representations can be plotted using t-SNE graph to validate the issue.

Reviewer comment (Theory):
It is argued that the imbalance loss as in Eq. (11-12) could learn seasonality representations with no information about the treatment. This is not obvious and it needs more explanation regarding why minimizing the discrepancy could make $S_t$ independent of the treatment.

Author response:
Furthermore, we agree with Reviewer WboM regarding why minimizing the discrepancy could make the seasonality independent of the treatment. We will present theoretical analysis and experimental results to support the issue in the future. In addition, the causal seasonality representations can be plotted using t-SNE graph to validate the issue.

Reviewer comment (Evaluation):
In experiments, no measure of uncertainty is provided. It is suggested to also report one of the following: standard deviation, confidence interval, or p-value.

Author response:
In the experiments, we will add the standard deviation as the measure of uncertainty, and we will clarify the real data experiment results. Thank you for your suggestion.

Reviewer comment (Experiments):
It is unclear how the real dataset is used. Since counterfactual outcomes do not exist in real data, it is not clear what the "real" columns in Table 2 refer to.

Author response:
In the experiments, we will add the standard deviation as the measure of uncertainty, and we will clarify the real data experiment results. Thank you for your suggestion.

Reviewer comment (Theory):
Why the proposed method could lead to reduced selection bias given that the imbalanced representation approaches explicitly remove the dependency of treatment on the learned representation?

Author response:
We highlight below the difference between our work and the balanced representation approaches. 
The conventional balanced representation approaches learn a balance representation using the domain adversarial training framework to reduce the selection bias. On the other hand, the proposed causal structure learns the trend/seasonality decomposed representations, and the selection bias is minimized by making the causal representations be independent of the treatments. As a result, the proposed causal structure achieves better performance than the balanced representation algorithms (e.g., CRN and Causal Transformer).

Reviewer comment (Theory):
Why minimizing the discrepancy could make $S_t$ independent of the treatment?

Author response:
Furthermore, we agree with Reviewer WboM regarding why minimizing the discrepancy could make the seasonality independent of the treatment. We will present theoretical analysis and experimental results to support the issue in the future. In addition, the causal seasonality representations can be plotted using t-SNE graph to validate the issue.