Venue: NeurIPS 2022 Conference

Reviews:

final_score: rating: 6: Weak Accept: Technically solid, moderate-to-high impact paper, with no major concerns with respect to evaluation, resources, reproducibility, ethical considerations.
review_content: summary: This paper is on disentangling the effects of single interventions from jointly applied interventions, given observational data and the joint interventions. In particular, this paper shows that the causal effect of single interventions is generally unidentifiable, but it is identifiable for the so-called symmetric ANMs, where there is no direct causal connection among the treatment variables. Moreover, this paper proposes a practical method to estimate the causal effect of single interventions.
strengths_and_weaknesses: Strengths:
The motivation is clearly stated at the beginning of the paper, and the overall organization is good. The studied problem is new to me.

The paper gives both theoretical identifiability results and practical estimation methods.

Weaknesses:
The authors give the identifiability in rather strong assumptions. One is that if there is no direct causal connection among the treatment variables for ANMs, then the causal effect of single interventions is identifiable. The other is that for general ANMs, the causal effect of the sink treatment variable is identifiable. It could be interesting to investigate weaker identifiability conditions. 

In addition, in some cases, we may want to know the identifiability of a subset of the interventions, so it would be also interesting to see the identifiability conditions for the causal effect of a subset of interventions. 

questions: If only some of the treatment variables are influenced by hidden confounders, then what will the identifiability conditions be? Can they become weaker?
limitations: The authors did not discuss the limitations and potential negative societal impact of their work.
review_title: null

final_score: rating: 6: Weak Accept: Technically solid, moderate-to-high impact paper, with no major concerns with respect to evaluation, resources, reproducibility, ethical considerations.
review_content: summary: The paper considers estimating the causal effect of a single intervention when multiple interventions are applied at the same time.
The paper characterizes several cases where the single intervention's effect can be identified. 
In particular, the paper considers the identifiability characterization under non-linear structural models, unobserved confounders, and interactions among interventions. The paper also designs an algorithm that learns the causal effect by combining observed data and interventional data.

strengths_and_weaknesses: Strengths:

* The paper extends previous works of linear structural models to allow non-linear dependence. The paper also takes into account unobserved confounders---a fundamental challenge in causal inference.

* The paper employs observational data to augment interventional data. This is impactful because there are usually more observational datasets available, and often in large scale.  

Weaknesses:

* The identifiability discussed in the paper relies on the multivariate normal assumption. This may not always be satisfied in practice. For example, some variables may be binary and do not follow Gaussian distributions.


questions: * It would be very helpful to discuss the necessity and sufficiency of the identifiability conditions. 

* It would be very helpful to provide some theoretical insights of the proposed algorithm. 

* It would be very helpful to discuss how the identifiability conditions could be verified/checked on a real dataset.

limitations: Yes.
review_title: null

final_score: rating: 6: Weak Accept: Technically solid, moderate-to-high impact paper, with no major concerns with respect to evaluation, resources, reproducibility, ethical considerations.
review_content: summary: Assuming $C \perp U$ and $X_i \perp X_j \mid C, U$ ($i \not = j$) in Figure 2(c), this paper provides identification proofs under non-linear continuous structural causal models with additive, multivariate Gaussian noise. The estimation is identifiable from the conjunction of two data regimes: (1) the observational distribution, and (2) any intervention distribution on a set of treatments. Then, this paper extends the Expectation-Maximization-style iterative algorithm to disentangle causal effects.
strengths_and_weaknesses: This paper claims that disentangling the effects of single interventions from jointly applied interventions is a challenging task. Thus, they assume $C \perp U$ and $X_i \perp X_j \mid C, U$ ($i \not = j$) in Figure 2(c). In this setting, is it still a challenge to disentangle the effects of single interventions? I will adjust my score according to the authors’ responses to my comments.

**Strengths**
- This paper considers a interesting problem in Multiple Treatment Effect and provide identification assumption. 
- Theoretically, this paper provide that learning the effect of a single-intervention from both observational data and sets of interventions is not generally possible, but provide identification proofs demonstrating that it can be achieved under non-linear continuous structural causal models with additive, multivariate Gaussian noise. 

**Weaknesses**
- Additive multivariate Gaussian noise assumption is not a general condition, which is rarely satisfied in practice. 
- In Experiment Sectoin, the regression method is not a representative baseline in causal inference.
- In the observed data, disentangling single-treatment effect does not seem to be a challenge. We can analyze the single-treatment effect one by one and treat all other variables as confounders.

-----------------------
I thank the authors for addressing my comments. I increase my score to 6.


questions: 1. This paper claims that disentangling the effects of single interventions from jointly applied interventions is a challenging task. Thus, they assume $C \perp U$ and $X_i \perp X_j \mid C, U$ ($i \not = j$) in Figure 2(c). In this setting, is it still a challenge to disentangle the effects of single interventions?

2. Under additive multivariate Gaussian noise assumption, can we use traditional methods for single treatment analysis? That is, we can focus on a single treatment variable $X_i$ and treat other treatments $\{X_j\}_{j \not= i}$ as confounders. 

3. Does this paper require prior knowledge of the structural equations?  The reasons for uniform distribution over [-2,+2] and [-1,+1] are?

4. The estimation is identifiable from the observational distribution. Why would this paper identifies causal effects from intervention distribution? To be honest, the acquisition of experimental data is also a problem.

5. As the baseline for this paper, I think some causal algorithms for distribution modeling should also be considered, such as GANITE (Yoon et al., 2018), SCIGAN (Bica et al. 2020), CEVAE (Louizos et al., 2017), and Intact-VAE (Pengzhou et al., 2022)...

6. In the presence of unmeasured confounders (unconfoundedness assumption is violated), can the causal effect of a single intervention variable be accurately estimated under non-linear continuous structural causal models with additive, multivariate Gaussian noise? 
limitations: I do not foresee any major limitations and/or societal impacts.
review_title: null

final_score: rating: 5: Borderline accept: Technically solid paper where reasons to accept outweigh reasons to reject, e.g., limited evaluation. Please use sparingly.
review_content: summary: In this paper, the authors aim to disentangle the single intervention's effect with the observational data and interventional data upon **many variables** simultaneously, in the presence of latent confounders. The authors suppose the additive noise model, and propose two cases when the effect can be disentangled, one is the case when all the treatment variables are in exact causal order and we want to identify the causal effect of the treatment variable at the last of the order on the outcome, in Theorem 1, the other is the case when there are no causal relations between the treatment variables, in Theorem 2. Further, the authors present the method to disentangle the effect by EM algorithm.

strengths_and_weaknesses: Strengths: 

(+) The problem of disentangling single intervention's effect is interesting.

(+) In total, the paper is clearly written.

Weaknesses:

(-) According to my understanding, to the problem of disentangling single intervention's effect, the most interesting part is not to give some cases when the disentangling can be finished, but when the disentangling cannot be finished. A sufficient and necessary condition for the ANM model is interesting and novel. The current paper only presents two cases when the single intervention's effect can be identified. A deeper study is expected.


(-) In this paper, it is not allowed that some covariate $C$ is caused by the treatment variable, as Line 121. I think the authors should make it clear that it is an assumption in this paper. In general SCM framework, there are not such assumptions that the causal directions between covariates and treatments are from covariates to treatments.

(-) The formalization of the problem on Line 133 is not quite good. The intervention can be upon more than two variables, but in the format here there are only two intervention variables.

(-) I think it will be better if the authors can further clarify the motivation of the disentangling from interventions upon many variables. In the view of theory, Lee et al. 2020 have given the sound and complete result for the non-parametric identifiability with arbitrary experiments. The manuscript can be seen as a special case when we (1) consider ANM; (2) assume covariates cause both treatment and outcome; (3) Gaussian noise. I am not saying it is not good, I can understand that by this way there are some advantages in computation. But considering that the theoretical results in the manuscript are not complete, it is vital to argue for the importance of their results or methods in reality.
questions: I am not quite sure whether the examples in the first paragraph are convincing. For example, people are targeted by multiple concurrent campaigns in computational advertising, or patients that possess many commodities may have to be simultaneously treated with multiple prescriptions. In these cases, our goal is usually to know how to intervene to make the people buy our commodity, or how to do to make patients restored from sickness. Why do we identify the single intervention's effect?
limitations: The authors should make it clear that it is an assumption that covariates $C$ are not allowed to be caused by the treatment variable.
review_title: null

Meta-review: metareview: The authors describe a method to estimate the effect of an intervention on a single variable X_j in a setting where data from interventions on multiple variables is available. This data is combined with observational data to arrive at an identification formula. The procedure relies heavily on (a) assuming that the noise / confounding is additive (b) that there is no causal relationship between the covariates and to lesser extent on (c) a Gaussianity assumption. The identification strategy is based on a neat idea, and it is refreshing to read about novel identification results that make use of both observational and interventional data. However, it is unclear how robust the procedure is under small violations of the assumptions. Furthermore, in many applications, some of the covariates might be categorical. This is problematic under the additive confounding assumption. To summarize, this paper presents an interesting idea that allows combining evidence from observational and interventional data. In its current form, the setting is likely too artificial to be directly relevant for practice.
confidence: Less certain
Decision: Accept