Summary
The paper introduces a novel algorithm for long-term counterfactual forecasting over time through representation learning of historical information and balanced representation learning that predicts the outcome given balanced treatments. The representation learning process combines Contrastive Predictive Coding and Information Maximization, while the training of balanced representation learning involves an adversarial game in the actual outcome and treatment networks.
Strengths
1. The paper introduces a novel algorithm for predicting counterfactual responses over time which outperforms the baselines in both a synthetic and a semi-synthetic dataset.
2. The proposed algorithm is robust.
3. The paper is well-structured and comprehensive, covering theoretical analysis, experiments, ablation studies, and falsifiability tests.
4. The experiment settings are described in detail.
5. Most of the notation is clear and easy to understand.
Weaknesses
1. Is it possible to conduct experiments on real datasets?
2. It appears there is only one synthetic dataset and one semi-synthetic dataset. In the synthetic experiment, is the standard deviation of the errors calculated from experiments with 5 different seeds instead of random settings of the data generating process? Would it be feasible to conduct experiments on multiple synthetic datasets with random settings to obtain error bars, rather than relying on just one synthetic dataset?
3. There don't seem to be any comparisons of time consumption with baselines.
4. The loss functions are constructed based on the lower or upper bound of the mutual information, but there is no discussion or measurement regarding the tightness of the bound.
Questions
1. In equation 1, $U_{t+j}$ in the numerator has one subscript, while $U_{l,t+j}$ in the denominator has two subscripts. Could you please make them consistent? Is $U_{t+j}$ information for one specific individual or an aggregate for all individuals? Is InfoNCE calculated for each individual or as the expectation over all individuals? Given that in equation 1, the subscript is $\mathcal{B}$, is it the individual index
2. Could you elaborate on how Theorem 5.2 influences the construction of the loss function in Equation 7? Specifically, does Theorem 5.2 impact the formulation or design of the loss function described in Equation 7? The authors discuss what we can infer if equality holds from lines 189 to 192, but will equality actually hold? The description in this paragraph suggests that equality can be achieved, yet Proposition 5.1 and Theorem 5.2 indicate positive gaps between the two mutual information measures without specifying the magnitude of these gaps, and the construction of the contrastive loss does not appear to be influenced by Theorem 5.2, as long as Proposition 5.1 holds.
3. Could you explain what is $\gamma$ in equation 7? Is $\gamma$ a similar definition of horizons?
4. In line 202, is there any proof provided regarding "The theoretical existence of such a function"
5. Since the goal is to estimate the counterfactual responses given in the equation at the bottom of page 3, could you explain why we still need to predict the treatments as the conditional expectation is given $ W_{t+1:t+\tau} $? Is this training needed because we want balanced learning? If so, could you explain why selection bias should be avoided given the goal of learning the expectation conditioning on potential treatments?
6. In Theorem 5.3, could you explain why or when the “if” condition holds?
7. Does the balanced learning only work for $W_{t+1}$? Why is it not necessary to extend it to $W_{t+\tau}$ for $\forall \tau\geq 1$?
8. In section 5.3, is $\theta_{R}=[\theta_1, \theta_2]$?
Limitations
The authors have discussed the broader societal impacts.