Mitigating Unobserved Confounding via Diffusion Probabilistic Models

Main weakness

1. This paper tackles the challenging problem of estimating the CATE under unobserved confounding. However, without additional assumptions (e.g., instruments), it is impossible to get identification of CATE or unbiased estimation, regardless of the latent variable model used. Therefore, it is impossible to solve the task of unobserved confounders in causal inference with the diffusion model as the paper claimed for its contribution.

Current research in causal inference discusses partial identification and sensitivity analysis with unobserved confounding settings, e.g. [A Neural Framework for Generalized Causal Sensitivity Analysis]. Authors should explore these directions more.

Other weakness

2. The paper lacks a thorough literature review on using diffusion models for CATE and counterfactual estimation. Specifically, it fails to cite and differentiate itself from closely related works, such as [Interventional and Counterfactual Inference with Diffusion Models] and [Diffusion Causal Models for Counterfactual Estimation]. Despite the identifiability of the proposed method in this paper, it does not adequately discuss how its approach compares to other existing methods which also use diffusion models for the same task.

3. The variational lower bound presented is trivial, essentially involving a simple replacing notation from standard diffusion models. Not necessarily counts as a contribution.

4. In terms of experimental results, the proposed method performs similarly to TARNet, and in some cases, even worse.

In summary, the paper does not address the issue of identifiability as it claims and also lacks a literature review on using diffusion models for CATE estimation.

Weaknesses / Questions

1. Could you provide more discussion on $\eta$, including its physical meaning and how it works for recovering $z$? And it is unclear why we can learn $p(\eta|x)$ correctly. If so, why can't we directly learn $p(z|x)$ correctly as $z,\eta$ are all the direct parents of $x$​ in the assumed causal graph?
2. My biggest concern is the lack of identifiability of $z$​​ (e.g., iVAE [1]), which means that the proposed method can not guarantee the correctness of learned representations. Additionally, it could be better to provide the MCC results ($\hat z$ and $z$).
3. It could be better to provide more discussion on the experimental results.
   1. Since ACIC and IHDP datasets contain all observed confounders, why can the proposed method outperform existing methods?
   2. In the Sim-z dataset, $x$ and $z$ are independent (which does not follow the assumed causal graph), is it possible to recover $z$ by using $x$?
   3. The only dataset following the assumed causal graph is the Sim-$\eta$, however, it seems that it only achieves a similar result to TARNet.
4. It could be better to compare with recent methods, e.g., [2,3,4].

Minors (that do not influence my score)

Line 87: likelihoodof -> likelihood of

[1] Khemakhem I, Kingma D, Monti R, et al. Variational autoencoders and nonlinear ica: A unifying framework[C]//International conference on artificial intelligence and statistics. PMLR, 2020: 2207-2217.

[2] Ma Y, Melnychuk V, Schweisthal J, et al. DiffPO: A causal diffusion model for learning distributions of potential outcomes[J]. arXiv preprint arXiv:2410.08924, 2024.

[3] Zhang W, Liu L, Li J. Treatment effect estimation with disentangled latent factors[C]//Proceedings of the AAAI Conference on Artificial Intelligence. 2021, 35(12): 10923-10930.

[4] Guo X, Zhang Y, Wang J, et al. Estimating heterogeneous treatment effects: Mutual information bounds and learning algorithms[C]//International Conference on Machine Learning. PMLR, 2023: 12108-12121.

1/ It appears to me that the proposed method is a straightforward application of a diffusion model, used to infer unobserved confounders. I believe it can be directly applied to methods that address unobserved confounders, such as CEVAE.

2/ The inference of unobserved confounders is based on variational inference, which could be unidentifiable unless further assumptions are made. This is known as posterior collapse and is well documented in:

• Wang, Y., Blei, D., & Cunningham, J. P. (2021). Posterior collapse and latent variable non-identifiability. Advances in neural information processing systems, 34, 5443-5455.

Can the authors show that the latent confounders are identifiable with the diffusion model?

In general, I believe that the causal effects in this case is unidentifiable unless the authors limit their work with specific assumptions as discussed in CEVAE:

• Louizos, C., Shalit, U., Mooij, J. M., Sontag, D., Zemel, R., & Welling, M. (2017). Causal effect inference with deep latent-variable models. Advances in neural information processing systems, 30.

3/ The causal quantity of interest in this paper is CATE, defined in Section 2.1. This quantity is only conditional on the observed confounder $x$. To estimate this quantity, we need to block the backdoor through $z$. It is unclear how they blocked it. Did you sample $z$ from the diffusion model and use these samples to block the backdoor? In that case, the concern goes back to point 2/ above -- we cannot recover the latent confounders due to posterior collapse.

4/ Since the unobserved confounder $z$ is learned from the observed confounder $x$, this could be a big problem if they are 'independent'. How can you infer $z$ from a variable $x$ which are independent of it?

5/ Concerns regarding the datasets used in experiments:

• IHDP data is randomised and all confounders are observed. Why do we need to infer unobserved confounder?

• From the simulation of Sim-z (Eq. 12), $z$ and $x$ are independent. It means that you cannot infer $z$ from $x$ since there is no correlation/causal relationship between them. This concern is related to point 4/ above.

This raises a significant concern regarding the experimental comparison on these two datasets.

6/ In Eq. 8, $\Phi(\cdot)$ is a function of the observed confounder $x$. However, in Eq. 10, it is a function of $x$ and $z$. Can the author(s) explain why there are such differences? Isn't the input to $\Phi(\cdot)$ should be a fixed vector?

7/ Table 1 should be Figure 1?

The computational cost of the diffusion process itself might be a concern, especially for large-scale real-world datasets. Further discussion on the computational complexity and potential bottlenecks of the diffusion process would be beneficial for understanding its practical applicability.