DFITE: Estimation of Individual Treatment Effect Using Diffusion Model

1. Lack of discussion on why diffusion models can tackle unmeasured confounding.

I think a huge missing part here is to justify why diffusion model can tackle causal inference problems and unmeasured confounding. This could be improved by re-organizing the paper a bit. Instead of directly coming up with diffusion model, it is helpful to first explain why generating synthetic unmeasured confounding can be useful, and how. Then, one can talk about why diffusion model is a useful tool in doing so. In particular, there appears to be no "causal" thinking across Section 3. I even cannot see what the unmeasured confounder is in the expressions. Is it $x^{(T)}$? Why can we learn it from data given that we never observe them? Is that because there are observable implications of a correct unmeasured confounder that we can leverage in the training? What does the variational lower bound mean? Why maximizing the log likelihood gives a good sampler for unmeasured confounding? Also, though section 4 appears at the end of theory & method, maybe it is more appropriate as a motivating point.

2. Missing details of the experiments.

Though the experiments are thorough, and given the provided codebase, I believe the methods are solid. But due to missing details I am confused how the performance is evaluated, such as how do we get the ground truth, and how is the ground truth defined.

3. Writing quality and clarity.

In general the quality of writing can be improved in this paper. Besides the above points on presentation, there are also many typos and broken sentences, which I point out in the Questions section.

1. Writing could be improved. For example, for every single-line equation, the word "where" should not be capitalized.

The authors need to discuss when the unobserved confounders can and cannot be accurately inferred from the observed variables. Real data examples can be helpful to illustrate this and inform the readers when they encounter this problem in practice. Additionally, the rationale for using the diffusion model to infer the latent unobserved confounders and why the diffusion model could potentially offer an advantage compared to other methods needs more discussion in the Introduction section. Also, whether and why the diffusion model can recover the true unobserved confounder was not clear. Why this process offers more information than just using X in the ITE model was not clear either, as the unobserved latent confounder was solely inferred from X. Lastly, the experiment results do not fully justify the utility of learning the unobserved confounder for learning ITE and the benefit of the diffusion model. Detailed comments can be found in the questions.

1. The writing is extremely poor, making the reviewer wondering whether the draft was proofread before submission:

• $\epsilon_{PEHE}$ and $\epsilon_{ATE}$ undefined before used in abstract
• in 2nd paragraph: "(e.g.,medicine)" --- missing space --- and "(e.g., demographic characteristics )" --- one extra space before ")".
• in 2nd paragraph: "DR", which the reviewer assumed to be "doubly robust", is again used before definition

It is not the reviewer's responsibility to proofread the paper and it is highly recommended that a careful revision is needed before resubmission.

2. Additionally, the review of existing work and motivation are unclear from the introduction:

"...and accordingly to infer the ITE in an unbiased settings..." What is an "unbiased setting"? Does it mean the estimator is unbiased?

"VAEs make substantially weaker assumptions in generating the structure of the hidden confounders Louizos et al. (2017), which could restrict the model’s flexibility." Why a weaker assumption leads to more restrictive method?

"For examples, GAN-based methods could be unstable in modeling ITE due to the adversarial losses. VAEs make substantially weaker assumptions in generating the structure of the hidden confounders Louizos et al. (2017), which could restrict the model’s flexibility. In order to address these challenges, in this paper, we propose to generate the unobserved confounders using diffusion model."

Based on the above review of existing work, it is very, very unclear why the proposed diffusion method can handle the issues (and not to mention that those issues are not stated clearly at all).

I don't stand by the theoretical justification for using diffusion model to generate unobserved confounder. It does not align with the causal graph you proposed in Figure 1, in which $Z$ and $X$ are conditionally independent given $\eta$. Thus, generating $z$ by using $\mu_\theta$ plus noise makes no sense to me.

Besides, the factorization in the proof of the ELBO replies on the bayesian network for the generating process to be either $\eta -> x^{(0)} -> x^{(1)} ... -> x^{(T)}$ or $\eta <- x^{(0)} <- x^{(1)} ... <- x^{(T)}$, which is also unjustifiable to me.

The motivation for using diffusion model is also very doubtful. It is very unclear to me why one would use it to diffuse covariates vector, which in most real-world cases aren't even fully continuous, let alone having Gaussian noises, and in some case aren't even available in high-dimension. The simulation cases you proposed aren't really realistic to me for that reason. Although it is mentioned in one sentence in the introduction, it's still very much unclear to me why diffusion model is preferred over an VAE approach and why the assumption that the covariates are generated from a denoising process is preffered over no assumption.

In a bigger picture, on the scope of missing data imputation, prior work [1] has already proposed using diffusion model to impute missing data, and has advanced the "impute-then-generate" framework you're using to directly account for the uncertainty of missing data in the learning process, and the drawback of "impute-then-generate" framework was illustrated.

Overall, the contribution of this paper is flawed and unsubstantial in my opinion.

[1] Ouyang, Yidong, et al. "MissDiff: Training Diffusion Models on Tabular Data with Missing Values." arXiv preprint arXiv:2307.00467 (2023).