Title: DeCaFlow: A deconfounding causal generative model
Venue: NeurIPS 2025
Accepted: yes
Keywords: hidden confounders

causal identifiability

causal query

latent variable model

counterfactuals
Abstract: We introduce DeCaFlow, a deconfounding causal generative model. Training once per dataset using just observational data and the underlying causal graph, DeCaFlow enables accurate causal inference on continuous variables under the presence of hidden confounders. Specifically, we extend previous results on causal estimation under hidden confounding to show that a single instance of DeCaFlow provides correct estimates for all causal queries identifiable with do-calculus, leveraging proxy variables to adjust for the causal effects when do-calculus alone is insufficient. Moreover, we show that counterfactual queries are identifiable as long as their interventional counterparts are identifiable, and thus are also correctly estimated by DeCaFlow. Our empirical results on diverse settings—including the Ecoli70 dataset, with 3 independent hidden confounders, tens of observed variables and hundreds of causal queries—show that DeCaFlow outperforms existing approaches, while demonstrating its out-of-the-box applicability to any given causal graph.


Peer reviews:
{"IS_META_REVIEW": false, "comments": "SUMMARY:\nThe paper introduces deconfounding causal flows an extension to causal normalising flows that uses and VAE-style approach to estimate causal queries under hidden confounding. The paper introduces novel indentifiability results that open promise correct estimates on a wide range of causal queries. The experiments support the performance of the proposed method compared to relevant baselines making this a promising method for causal practitioners.\n\nSTRENGTHS AND WEAKNESSES:\n+ The paper tackles the interesting problem of causal inference under hidden confounding providing novel theoretical insights as well as a practical method that should be applicable to a wide range of real-world tasks.\n+ The paper is well written and thoroughly explains the approach and significance. (I did however, not check the correctness of the proofs or appendix)\n\n- The empirical results could be stronger by testing this method on more real-world datasets without replacing the ground-truth functional relationships. The paper could easily produce additional causal benchmarks by hiding confounders for evaluation, turning a fully observed causal benchmark into one with hidden confounders.\n- Could be a bit clearer on the functional limits on CNFs before the conclusion.\n- It’s unclear how the hyper parameters of the models are chosen and how a practitioner should go about using this method.\n\nQUESTIONS:\n- Can this deal with differences of which variables are available during training and inference?\n- A strong requirement here is to perfectly fit the data distribution. How hard is this in practice? How hard is it to estimate if you correctly capture the distribution while only having access to finite samples?\n- How do you chose a prior over z? What’s the impact of this?\n- L 235 - 4. How do you go about measuring “enough information”?\n- How are the hyper parameters chosen? B.3 almost sounds like it’s been chosen given test set performances.\n- How come you can achieve almost 0 ATE error but significantly higher CF error if the identifiability of ATEs mean identifiability of CFs?\n- Why are you replacing the data generating processes rather than simply taken real world causal datasets and drop confounders to estimate the correctness under hidden confounding?\n\nLIMITATIONS:\nmostly", "TITLE": "Official Review", "RECOMMENDATION": 4, "REVIEWER_CONFIDENCE": 3, "CLARITY": 2, "IMPACT": 3, "ORIGINALITY": 3, "DATE": "2025-07-01"}

{"IS_META_REVIEW": false, "comments": "SUMMARY:\nThis work presents deconfounding causal normalizing flow (DeCaFlow), a framework that extends causal normalizing flows (CNFs) to the case when hidden confounders are present. When a causal graph is given, CNFs are autoregressive normalizing flows that parametrically model the generative mechanisms and allow us to answer causal queries among other applications. DeCaFlows are similar, however they are equipped to handle hidden confounders as well, under some assumptions. The framework assumes access to the underlying causal graph and iid observations, and essentially builds a generative model and a deconfounding model, which are jointly trained using a variant of the standard ELBO loss.\n\nThe paper shows that DeCaFlows satisfy many desiderata, such as identifiability results for causal queries such as do operations or interventional queries (even though we have hidden confounders). However, these results apply under various assumptions on the causal structure of the query and infinite data regime. Finally the technique is validated via experiments on semi-synthetic data and the Ecoli70 gene dataset, and it outperforms prior techniques on standard metrics such as MAE. The counterfactual fairness-prediction application is also interesting. The target audience are people interested in causal inference.\n\nSTRENGTHS AND WEAKNESSES:\n## Strengths:\n\n- The problem of building normalizing flows in the presence of hidden confounders is important and relatively less studied, so this work is a useful step towards this direction.\n\n- The paper is well-written, and related work seems to be cited well. The proof techniques are very interesting, generalize prior works and the experiments probe different aspects such as misspecification.\n\n## Weaknesses:\n\n- While the identifiability results are interested, I'm unable to gauge how restrictive the assumptions are, e.g. in proposition A.2. It'd be nice if the authors could comment on this.\n\nQUESTIONS:\nNone\n\nLIMITATIONS:\nLimitations have been discussed.", "TITLE": "Official Review", "RECOMMENDATION": 5, "REVIEWER_CONFIDENCE": 2, "CLARITY": 4, "IMPACT": 3, "ORIGINALITY": 4, "DATE": "2025-07-02"}

comments: SUMMARY:
In this paper, the authors extend existing work on Causal Normalizing Flow and introduce DeCaFlow, for "deconfounding causal normalizing flow". The focus of the authors is on scenarios where not all variables of a system are observed and, in particular, where there exists a non-empty set of hidden confounders $\mathcal{Z}$. The goal of DeCaFlow is to be able to answer interventional and counterfactual queries over observed variables $\mathcal{X}$. To this end, they propose to train two models: a deconfounding network (from $\mathcal{X}$ to $\mathcal{Z}$) and a generative network (from the exogenous noise and $\mathcal{Z}$ to $\mathcal{X}$). The authors prove that DeCaFlow correctly solves causal queries between non-confounded variables and provide sufficient conditions for queries between confounded variables.

STRENGTHS AND WEAKNESSES:
Strengths:
- The problem of estimating causal effects between confounded variables is known, interesting, and well-motivated.
- As with Causal Normalizing Flows, DeCaFlow also represents a class of models identifiable from the observational distribution.
- The authors provide in the supplementary materials an algorithm to verify whether a causal query can be identified or not.

Weaknesses:
- The method requires the causal graph between observed variables, which is not trivial to recover in general, in particular under hidden confounding. This problem is not discussed in the paper.

QUESTIONS:
Do the authors have any intuition on how DeCaFlow could be integrated with existing causal discovery algorithms for confounded data?

LIMITATIONS:
yes
TITLE: Official Review
CLARITY: 3
IMPACT: 3
ORIGINALITY: 2
DATE: 2025-07-03

{"IS_META_REVIEW": false, "comments": "SUMMARY:\nThis paper introduces DeCaFlow, a method for causal inference in the presence of latent confounders. \nThe primary contribution is extending causal normalizing flows to the latent confounded case.\n\nGiven a SCM with endogenous variables X and latent confounders Z, this work assumes:\n- Underlying causal graph G is known and acyclic\n- Structural equations f are invertible given Z, and both f and its inverse are continuously differentiable\n- Perfect interventions (do-calculus) over X\n- Access to proxy variables (CI variables informative of hidden confounders) for identifiability beyond what do-calculus provides\n\nThe method is implemented via a latent variable model, where the encoder (X to Z) and decoder (Z to X) are based on normalizing flows.\n\nEvaluations consider 3 settings: two semi-synthetic (real graphs, simulated structural equations) and one real (law school dataset).\n\nSTRENGTHS AND WEAKNESSES:\n# Strengths:\n- Experiments show strong empirical performance, approaching the oracle baseline in both semi-synthetic experiments.\n- The proposed method seems efficient and reasonable -- requiring one training run per dataset (vs. one per query).\n\n# Weaknesses:\n\nA primary weakness of this work is whether the setting is indeed realistic (inherited from causal normalizing flows, upon which this work is based).\n\n1. Invertibility\n\nIn biological datasets (like those used in semi-synthetic experiments), confounders take the form of, e.g. which lab technician conducted the experiment, or the batch index of the cells when being sequenced (later batches are allowed to grow for longer). It is easy to train an inference model to predict these confounders. However, it is not always possible for a generative model to generalize: there may be no predictable pattern to how a new lab technician would act, compared to previous ones.\n\nCould you provide some examples in which invertibility does make sense?\n\n2. Knowledge of G\n\nG is often \"known\" only to a noisy extent. For example, there are multiple versions of the Sachs graph, and feedback loops play a central role in biological systems.\n\nCan you comment on the robustness of your method to errors in G?\n\nQUESTIONS:\n1. In 5.2.1, new SCMs were sampled based on the Sachs graph to ensure that \"the randomized effect of the hidden confounder is perceptible\" [337]. Since the effect size of the original interventions can be quantified (based on the change in target protein activity), is it possible to evaluate the method on (some of) the actual data?\n\n2. The paper is somewhat dense. It would be nice if the main paper included more intuitive explanations throughout. For example: what are proxy variables, how the CNFs are implemented, what do-calculus implies in the context of the illustrative example in Fig 1.\n\n3. Is it necessary to include the ablation study as the first part of results? Moving it to the appendix + citing that the model is not sensitive to increasing $D_z$ could free up space for expanded discussion of [above].\n\n4. Overall, the writing can be made more concise to improve readability. Some limited examples:\n- 103-106 can be split into 2 sentences. \n- 136-137 \"we take [....] and adapt them [...]\" -> \"we adapt CNFs to [...]\"\n- 159-161 -> \"To avoid posterior collapse, we implement [...]\"\n\nLIMITATIONS:\nyes", "TITLE": "Official Review", "RECOMMENDATION": 5, "REVIEWER_CONFIDENCE": 2, "CLARITY": 2, "IMPACT": 2, "ORIGINALITY": 2, "DATE": "2025-07-12"}