Learning causal representations from observational and interventional data in the absence of known ground-truth graph structures necessitates implicit latent causal representation learning. Implicit learning of causal mechanisms typically involves two categories of interventional data: hard and soft interventions. In real-world scenarios, soft interventions are often more realistic than hard interventions, as the latter require fully controlled environments. Unlike hard interventions, which directly force changes in a causal variable, soft interventions exert influence indirectly by affecting the causal mechanism. However, the subtlety of soft interventions impose several challenges for learning causal models. One challenge is that soft intervention's effects are ambiguous, since parental relations remain intact. In this paper, we tackle the challenges of learning causal models using soft interventions while retaining implicit modelling. We propose ICLR-SM, which models the effects of soft interventions by employing a causal mechanism switch variable designed to toggle between different causal mechanisms. In our experiments, we consistently observe improved learning of identifiable, causal representations, compared to baseline approaches.
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Summary
This paper studies weakly supervised causal representation learning with soft interventions. It assumes that pairs of observations are provided that differ by a soft intervention on one variable in the latent space. Additionally, the intervention target (and the total number of latent variables) are given. Identifiability up to element-wise transformations assuming linear mixing and known intervention targets (among other assumptions) is shown. Experiments on synthetic data compare the proposed method to ILCM, beta-VAE and D-VAE. An improved D and C score in the DCI framework is shown. An experiment on semi-synthetic image data is shown.
Strengths
- The method extends previous work on weakly supervised CRL and generalizes it from hard to soft interventions, which is an important step for bringing CRL closer to real-world applications, since CRL methods often suffer from restrictive assumptions. - Also, I appreciate the effort of testing this CRL approach to datasets which are more similar to real-world image datasets.
Weaknesses
- The mathematical notation is poorly defined and difficult to follow: objects aren't well-defined and notation inconsistently or unusually used. See questions below. - L136-137: "a diffeomorphic solution function [...] deterministically maps a value for exogenous variable [...] to a value for causal variable [...]" That's incorrect. There can be such a map from the set of all exogenous to all endogenous, but not per variable. Consider $X:= U_X; Y:= X+U_Y$, where $U_X$, $U_Y$ are exogenous. In general, there is no deterministic map from $U_Y$ to $Y$. - Even though the DCI framework for evaluation of the learned representation is cited, only two of the metrics (D and C) are used, whereas Informativeness (I) is omitted without comment. That seems suspicious to me. - The synthetic experiments test a rather simple setting on few data generating processes. The observation dimension is 4 (same as latent dimension) and the mixing is linear (as far as I can tell). We have seen in previous work (e.g. [2]) that the complexity of the mixing function is a crucial element in the recoverability of the latents. For example, the more nonlinear the function, the harder it is to recover latents. Furthermore, only 10 data generating processes are tested. That seems quite limited, given that the dimensions of the data is so small. **Minor:** - L133: "decoder function" is a bit of an odd choice for something that relates to the ground-truth data generating process. Usually, this is a part of a model. "Mixing function" would be more appropriate. - There is a period missing in L251. - L345: There is a follow-up version of DCI that takes more aspects of the learned representations into account [1]. It could be considered for the next iteration if time permits. - L363: "As mentioned in [27, 25], causal graphs are sparse and in the G5 case, where the graph is fully connected, the proposed method cannot identify the causal variables well." The two references **do not say that causal graphs are sparse**. You may refer to the sparse mechanism shift hypothesis, which says that changes between environments are assumed to stem from changes in few mechanisms of the causal graph. This is a statement about sparse changes, not sparse graphs.
Questions
- L136: $i$ isn't defined, I suppose it's the index of the causal variables. However, later it's defined as an element of the intervention targets. Which one is it? - L138: What is $\mathcal{S}$ is it a set of functions $\mathcal{E}_i\to\mathcal{Z}_i$ (as suggested by the first statement in the sentence) or is it a map $\mathcal{E}\to\mathcal{Z}$? - L187: Previously, $s_i$ was introduced as a function $\mathcal{E}_i\to\mathcal{Z}_i$ (L136), now it seems to be a function $\mathcal{E}\to\mathcal{Z}_i$. Which one is it? - L204: What does this equation mean? How come you are using the same function but with a different set of arguments? What does it mean when one argument disappears? - Equation 2: Is the Taylor expansion necessary here, or is the expansion used elsewhere? To me, the LHS can be transformed to the RHS in any case, since $R_i$ is just some variable that is introduced for the difference. If it's not used elsewhere, I would suggest removing it since it's only a distraction and doesn't add to the method or understanding. - Assumption 3: I'm confused by the approximate relation. Either $g$ is linear and has no intercept term ("truly linear"), then $g(\tilde{z}) g(z)=g(\tilde{z} - z)$; or it has an intercept term (affine), then the difference between LHS and RHS can be arbitrarily large and thus writing approximately equal is inappropriate. - Assumption 3: What exactly is the assumption? Is it that $g$ is linear? The rest seems to (more or less) follow from linearity and the statements made before. - L325: "loc and scale networks are changed in post intervention", but from Equation (7) it seems only loc is changed? - Equation 7: Are the loc parameters during data generation generated by random neural networks? Do they have the same architecture as the network that estimates those parameters? - The experiment code seems to indicate that the following seeds were selected for synthetic experiments: "nature_seed=5 # 1, 2, 5, 6, 7, 8, 9, 10, 11, 12" Why were seeds 3 and 4 omitted? - I struggle to understand both the evaluation of the experiments in 5.3. Why weren't the same DCI metrics compared here?
Rating
3
Confidence
3
Soundness
2
Presentation
2
Contribution
2
Limitations
- As far as I can tell, no latents were uncovered (theoretically or experimentally) for either nonlinear mixing or unobserved intervention targets. Therefore, it seems to me, it should be mentioned that the results are for the linear case and weakly supervised. The title and abstract make the impression as if the more general CRL problem with paired observations is solved.
Summary
This paper proposes a new approach **ICRL-SM** that performs implicit causal representation learning (mapping from noise to latent variables) by using causal mechanism switch variable to model the soft intervention effects. ### References [1] Burak Varıcı, Emre Acartürk, Karthikeyan Shanmugam, Abhishek Kumar, and Ali Tajer. Score- based causal representation learning with interventions. arXiv:2301.08230, 2023. [2] Burak Varıcı, Emre Acartürk, Karthikeyan Shanmugam, Abhishek Kumar, and Ali Tajer. Score- based causal representation learning: Linear and general transformations. arXiv:2402.00849, 2024. [3] Julius von Kügelgen, Michel Besserve, Wendong Liang, Luigi Gresele, Armin Kekic ́, Elias Bareinboim, David M Blei, and Bernhard Schölkopf. Nonparametric identifiability of causal rep- resentations from unknown interventions. In Proc. Advances in Neural Information Processing Systems, New Orleans, LA, December 2023. [4] J. Brehmer, P. De Haan, P. Lippe, and T. Cohen. Weakly supervised causal representation learning. In Advances in Neural Information Processing Systems, volume 35, pages 38319– 38331, 2022.
Strengths
The idea of implicitly modeling causal effects using switch variables is very interesting. The experiments have shown promising performance on synthetic and high-dimensional image datasets compared to several baselines.
Weaknesses
1. My most significant concern is that this paper is generally not well written and, thus, pretty hard to follow. For example, the calligraphic letter $\mathcal{Z}$ was used throughout to denote both causal variables (e.g., line 137) and its domain (e.g., line 139). 2. The assumption of a diffeomorphic causal mechanism is pretty strong. I am aware that [4] made a similar assumption. Yet, it is not a very common assumption for latent causal models in other causal representation learning literature (e.g., [1, 2, 3]). 3. Line 278: The Gaussianity assumption of the causal and exogenous variables might be hard to satisfy in realistic settings.
Questions
1. Line 159: (**Terminology**) As far as I know from the causality literature, a **soft intervention** is defined on a distributional level; from this perspective, it is not necessarily correct to assume the values are strictly different pre- and post-interventions for the intervened causal variables. Also, since intervention is performed on a distributional level, one does not observe such ``paired data`` $(x, \tilde{x}, i)$. Instead, one observes the data population before and after intervention $p(x), p(\tilde{x})$ without the same level correspondence (see [1, 2, 3]). 2. Line 162: Is there also a formal mathematical definition for **"sufficient variability"**? 3. Line 181: I would appreciate the authors properly defining the **"switch variables"** upon their first occurrence, especially because the work is based on these "switch variables." 4. Line 244: "Latent Causal Model" is neither defined nor cited.
Rating
3
Confidence
3
Soundness
2
Presentation
1
Contribution
2
Limitations
The main paper did not discuss limitations. The authors pointed them out in the checklist, but I would have appreciated it more if they had adequately addressed the limitations in the main paper.
Summary
This paper presents a novel approach for learning implicit causal representations through switchable mechanisms, specifically designed to handle soft interventions which are more realistic but challenging compared to hard interventions. The authors introduce a causal mechanism switch variable to model the subtle effects of soft interventions and establish the identifiability of causal models under certain assumptions. Their proposed method, ICRL-SM, demonstrates improved performance in learning identifiable causal representations over baseline methods through experiments on synthetic and real-world datasets. The paper contributes a new perspective to causal representation learning with potential applications in various domains where understanding causal relationships from observational and interventional data is crucial.
Strengths
1. A standout feature of this paper is the introduction of a switchable mechanism to model the nuanced effects of soft interventions. Traditional causal inference methods often focus on hard interventions, which are impractical in many real-world scenarios due to the need for stringent control. The paper's approach to incorporate soft interventions through a causal mechanism switch variable is groundbreaking. It allows the model to adapt to changes in causal relationships post-intervention, providing a more realistic and flexible framework for causal representation learning. 2. This paper proposes Augmented Implicit Causal Models, which is an innovative concept that extends the scope of implicit causal representation learning. By integrating the causal mechanism switch variable into the model's solution functions, AICMs can capture the intrinsic characteristics of each causal variable while accounting for intervention effects. This approach sidesteps the need for explicit parameterization of the causal graph, which is a complex and often intractable task. The innovation here lies in the model's ability to implicitly learn the causal structure while directly modeling the effects of interventions.
Weaknesses
1. The method's effectiveness relies on several key assumptions, including knowing the targets for intervention, interventions being atomic (indivisible), and variables following a multivariate normal distribution. These assumptions might not be realistic in many real-world settings where interventions can be complex, and data may not be normally distributed. 2. While the paper's experiments on synthetic and specific real-world (Causal-Triplet) datasets demonstrate the method's potential, it's unclear how well it generalizes to other data types or different domains.
Questions
As the paper itself mentions, the identifiability of causal models can become more challenging with an increase in the number of variables and complexity of causal graphs. The paper could benefit from a deeper analysis of scalability, including how the method performs as the size and complexity of the causal system grow.
Rating
5
Confidence
3
Soundness
3
Presentation
3
Contribution
2
Limitations
No
Summary
This work is in causal representation learning that utilizes interventional data. It involves two types of common interventions: hard interventions and soft interventions. It’s known that soft intervention is more general since it covers hard intervention. But it is also more challenging since parental relations remain. This work proposed identifiability results using a causal mechanism switch variable designed to change between different causal mechanisms by component-wise transformations. Adequate experiments were provided to verify they claim.
Strengths
Pros: 1. Overall, the writing is clear and with good context. 2. Adequate experiments were provided, including real-data experiments. Also, they offered good observations of the comparison with baselines. This is a big plus to their contribution.
Weaknesses
Cons: 1. It's unclear what the unique theoretical contribution is to this switch variable since both types of interventions were proposed before. Could the author clarify the theoretical contribution? Especially regarding the original technical hardness compared to [1] and also [38]. 2. In the synthetic experiment, it seems that you use the linear decoder, which loses the purpose of training a neural network to handle non-linear issues. Did you try non-linear functions and see how it goes? Besides the switch variable utilizing interventional data, what is the difference between these settings and those classical linear unmixing methods (like linear ICA or its other assumption variants)? Some minor issues/recommendations: Line 161, the $e_i$ is not defined, if you mean causal variable, then you already have defined it as $Z_i$. Line 187, the ‘\s’ is not defined before but later in line 195.
Questions
I put my questions in my previous section.
Rating
4
Confidence
5
Soundness
2
Presentation
2
Contribution
2
Limitations
N/A
Thank you very much for providing clarifications in the detailed rebuttal. I will try to answer open points below. ## Diffeomorphic solution function deterministic mapping Do I undertand the rebuttal correctly, that you do use all exogenous variables in the solution function of the learned model? From that it follows that L136 is incorrect, but the implementation in the model is correct (since it uses all exogenous variables)? ## Sparse causal graphs Dense DAGS (ones with full upper triangular adjacency matrix) are perfectly consistent with the sparse mechanism shift (SMS) hypothesis. Sparse graphs therefore do not follow from it. The "sparse" in SMS refers to mechanisms, not edges. Hence, writing "As mentioned in [27, 25], causal graphs are sparse" is incorrect and implies a scientific consensus which is not backed up by the literature. You may argue or hypothesise that causal graphs are sparse and it may be reasonable. But then I think it should be clearly stated that this is an assumption or hypothesis that you make. Or if some literature also makes this assumption the relevant literature should be cited. ## Questions - L138: Then writing it as a map $\mathcal{E}\to\mathcal{Z}$ is a bit sloppy. This may be minor, but to help clarity of the mathematical formalisms things like this should be cleaned up. - L187: Why are they treated as parameters? This adds to the confusion. $s_i$ is a map that takes in all exogenous variables, omitting it from the set that it maps from makes it less clear. - L204: Ignoring in the linear regression example means setting it to zero, it wouldn't just disappear if you introduced it as a parameter argument of the function. Having consistent notation would help clarity. As a reader it would really help if the signature/number of arguments of a function doesn't change from one use to the next. - Assumption 3: Either you assume the decoder is linear, then it should be an equality. Or you don't assume the decoder is linear, then the approximation needs justification (it can be an arbitrarily bad approximation in general). You can't have it both ways.
- Do we use **all exogenous variables** in the solution function of the learned model? - Yes. We use all exogenous variables in the solution function of the learned model. - We will add this information to better clarify in L136. - **Sparsity of Causal Graphs** - The reviewer comment about the sparse mechanism shift (SMS) hypothesis is sound and correct. We will update relevant references [1], [2] which assume sparsity of causal graphs. [1] Jiaqi Zhang, Kristjan H. Greenewald, Chandler Squires, Akash Srivastava, Karthikeyan Shanmugam, and Caroline Uhler. Identifiability guarantees for causal disentanglement from soft interventions. In Advances in Neural Information Processing Systems 36: Annual Conference on Neural Information Processing Systems 2023, NeurIPS 2023, New Orleans, LA, USA, December 10 - 16, 2023, 2023. [2] Sébastien Lachapelle, Pau Rodríguez, Yash Sharma, Katie Everett, Rémi Le Priol, Alexandre Lacoste, and Simon Lacoste-Julien. Disentanglement via mechanism sparsity regularization: A new principle for nonlinear ICA. In 1st Conference on Causal Learning and Reasoning, CLeaR, volume 177 of Proceedings of Machine Learning Research, pages 428–484. PMLR, 2022. - L138: Writing: - We will clearly state that $\mathcal{S}$ is a set of functions of $s_i i=1, ..., n$ which are defined in L136. - L187: Why are they treated as parameters? - The other exogenous variables in $s_i$ ($e_{/i}$) are used as inputs of $loc$ and $scale$ networks (See Equation 6) which output a scalar. They can be seen as learnable parameters same as $b$ and $w_1$ in the linear regression example. Nevertheless, they are in the set of inputs that are mapped to $z_i$. - We will correct our definition in L136 to make this more clear. - L204: Ignoring in the linear regression example means setting it to zero ... - In the example in L205-L206 we have explained that ignoring $h_i(v_0)$ means setting it to zero. - We will revise the notation in L204 for more clarity. - Assumption 3: if the decoder is linear, then it should be an equality: - We will remove approximation and replace it by equality in Assumption 3 for linear decoders case to avoid confusion. - Assumption 3 is about observability of switch variable $V$. As a special case, we have explained that in the linear decoder case subtraction of $\tilde{X}$ and $x$ can contain information about $V$. In other nonlinear decoder cases, other augmentations may be used to obtain information about $V$.
Response to the author
The review thanks the author for the clarification about the contribution regarding the implicit model. For the implicit model, does that mean you have a solution function to map exogenous variables to latent Z, but you don't have the learned and identifiable causal graph? The difference with classical methods: I agree that the CRL is different in the sense that latent Z is causally related, and that is the main difference from the first place. I should be more clear about the ICA and other variants. What I tried to ask is that let's say in the linear case, can your model be considered as a certain linear factor analysis model where we put extra constraint for the DAG (triangular matrix constraint in matrix factorization)? Since you want to triangular matrix to be unique, and also the mapping from Z to X to be unique.
- Do we have solution function to map exogenous variables to latent Z, but we do not have the learned and identifiable causal graph? - Yes, in implicit model we have a solution function to map exogenous variables to latent $Z$. We **do not learn a causal graph during training** but the causal graph's edges can be **inferred from solution functions after training** utilizing methods explained in [1]. [1] Johann Brehmer, Pim de Haan, Phillip Lippe, and Taco S. Cohen. Weakly supervised causal representation learning. In NeurIPS, 2022. - in the linear case, can our model be considered as a certain linear factor analysis model? where we put extra constraint for the DAG (triangular matrix constraint in matrix factorization)? - As the reviewer also confirmed, in CRL the latent $Z$ is causally related. - Our model can not be considered as a certain linear factor analysis model because in linear factor analysis models, the factors are assumed to be independent but in **causal representation learning the causal variables are dependent** and we must learn the causal relations as well. - For learning causal relations, we **did not use Directed Acyclic Graph (DAG)** but rather we used **solution functions in implicit causal representation learning**. - As opposed to explicit models, in implicit models we **do not use adjacency matrix to learn causal relations**, hence, we **do not apply constraints on matrices such as acyclicity constraint**. We use additional data such as **interventional data** and other assumptions including **diffeomorphism of solution functions** to learn the causal relations. - We wonder by **linear case**, the reviewer references the decoder function (mixing function). Please clarify otherwise. - Since in CRL we also need to take into account the causal relations, in linear decoder case, our model has solution functions to learn these relations where as in linear factor analysis there would be no such component. - In fact, **we want our latent causal models to be identifiable up to reparametrization**, so we proved it in theorem 3.5.
response to the author
The reviewer thanks the author for the clarification. The reviewer is monitoring the other discussion thread for re-considering the score at the end of the discussion period.
Thank you for the response
I thank the authors for the rebuttal. **Regarding Assumptions of a Diffeomorphic Causal Mechanism and Gaussianity Assumption of the Causal and Exogenous Variables** > We would like to add that CauCA [1] and dVAE [2] also assume diffeomorphic decoders in their theorems (see Table 2). 1. To clarify, my inquiry was not about "diffeomorphic decoders" but rather about the "diffeomorphic causal mechanisms." I recognize that diffeomorphic decoders are a common assumption in identifiability within causal representation learning, whereas diffeomorphic causal mechanisms are not. A thorough discussion on this distinction would significantly strengthen the paper. 2. Additionally, I noticed that the references for the two papers mentioned appear to be swapped in your rebuttal. Correcting this will help ensure clarity and accuracy in your citations. 3. As far as I am aware, Locatello et al. (2020) named their approach "Adaptive-Group-VAE (Ada-GVAE) and Adaptive-ML-VAE (Ada-ML-VAE)," rather than "dVAE." Accurately citing and referring to existing approaches is important for maintaining scholarly rigor. **Formal Mathematical Definition for "Sufficient Variability"** > Please refer to [4]. The reference to [4] for "sufficient variability" is somewhat unclear. First, [4] addresses a different setting within causal representation learning, involving both action and time, and second, there are multiple types of sufficient variability discussed within that work (e.g., sufficient time variability or sufficient action variability). Even when assumptions are similar to those in existing work, it is vital to clearly state them within the main theorem for improved readability and understanding. **Switch Variables Definition** > Switch variables are first introduced in line 180 and not before. In that paragraph, we have fully defined the switch variable. Would the reviewer clarify their comment? By "formal mathematical definition," I was looking for more detailed information, such as: Is this variable discrete or continuous? What is its domain? If it is a random variable, how is it distributed? Unfortunately, these details are not provided in the main text or the rebuttal. The authors only cited Schölkopf et al. (2019) upon first mentioning the causal switch variable. However, given the broad scope of that paper, a direct citation without further specifics does not adequately support the reader’s understanding of the key concept of causal switching variables. Overall, I believe that the mathematical formulation of the current manuscript lacks the necessary rigor and clarity required for publication at this time. These issues are fundamental and would require significant revision.
- **diffeomorphic causal mechanisms** - We have responded regarding the diffeomorphic decoder. - Since the same diffeomorphic causal mechanism assumption is made in [1] and in our paper we aimed to relax one of the assumption of [1] (availability of hard interventions). Therefore a **thorough addressing of the diffeomorphic causal mechanisms** falls out of scope of the current draft, however, we agreed with the reviewer that it is an important research topic so we will study it in details in our future works. - **Naming references** - [2] applied an averaging function to the posterior of their causal variables as a substitute to one of their constraints which is not applicable in our setting. Naming used in [2] is based on this averaging function. In [2] authors assumed independent causal variables. Following [1], we have also used the naming as disentangled VAE (dVAE). - Note that the code implementation of the dVAE is available through our submitted files. - **sufficient variability** - Since in our work we only have actions/interventions we did not distinguish between time and action sufficient variability. For more clarity, we will say that our assumption is similar to "sufficient action-variability" in [3]. - **formal mathematical definition of Switch Variable** - In **line 192 (Definition 3.2)**, we clearly defined the domain of the switch variable as well as if it is discrete or continuous, **We have mentioned that it is real valued, which shows it is a continuous variable.** - We do not have any assumption on the distribution of switch variable therefore we have not discussed it in line 180. - In **section 3.4 Training Objectives (L301-302)**, we clearly made an assumption of the switch variable for our experiment setup. - **Citing Schölkopf et al. (2019)** - We inspired the idea of using switch variable from Schölkopf et al. (2019), and we made our design and implementation based on that concept. - We would like to know what exactly the reviewer means by * further specifics*. For example please take a look at the Equations 6 and 7 of Schölkopf et al. (2019) where it mentions **"a random selector variable choosing from among a set of functions ..."**. Note that our usage of the concept is novel and specific to our paper. **References** - [1] J. Brehmer, P. De Haan, P. Lippe, and T. Cohen. Weakly supervised causal representation learning. In Advances in Neural Information Processing Systems, volume 35, pages 38319– 38331, 2022. - [2] Francesco Locatello, Ben Poole, Gunnar Rätsch, Bernhard Schölkopf, Olivier Bachem, and Michael Tschannen. Weakly-supervised disentanglement without compromises. In Proceedings of the 37th International Conference on Machine Learning,ICML, volume 119 of Proceedings of Machine Learning Research, pages 6348–6359. PMLR, 2020. - [3] Sébastien Lachapelle, Pau Rodríguez, Yash Sharma, Katie Everett, Rémi Le Priol, Alexandre Lacoste, and Simon Lacoste-Julien. Disentanglement via mechanism sparsity regularization: A new principle for nonlinear ICA. In 1st Conference on Causal Learning and Reasoning, CLeaR, volume 177 of Proceedings of Machine Learning Research, pages 428–484. PMLR, 2022
I appreciate the author's clarification. I will follow the other discussion thread to reassess the score once the discussion period concludes.
I thank the authors for their rebuttal. To further enhance the persuasiveness of the paper, I suggest the following improvements: 1. Strengthen experimental design: Conduct more comprehensive experiments, including tests under various datasets, with different numbers of variables, and with different data distributions, to evaluate the robustness of the proposed method. 2. Deepen theoretical analysis: Conduct a more in-depth theoretical analysis of the scalability issue, deriving the computational complexity and performance upper bound of the method under different conditions. I will review the other discussion thread and re-evaluate the score upon the conclusion of the discussion period.
We thank the reviewer for their suggestions. We would like to mention some points in the following: **Experiments** - In the current paper, we ran experiments using 3 datasets; A synthetic dataset and 2 realistic datasets (Causal-Triplet: Epic-Kitchen and ProcTHOR ). - In our experiments, we tried different number of causal variables; 4 for synthetic, 7 ProcTHOR and 20 for Epic-Kitchen. - Additionally for synthetic dataset we changed the causal variables from 4 to 10 (please see Figure A6). - Using different datasets would result in different data distributions. The data distributions of real-world datasets are unknown and therefore we did not make any assumption on them. **Scalability issue** - In this paper, we aim to relax one of the assumptions made in [1] regarding the availability of hard interventions. Our paper focuses on developing the theory and providing its proof. As also noted in [1], **scalability** remains a challenge (see Figure 8 in [1]). **Computational complexity and performance upper bound** - In our Ablation studies *Section 5.2: Factors Affecting Causal Disentanglement*, we have tried to study the impact of various factors affecting the upper bound of causal disentanglement. **More in-depth theoretical analysis** - In this paper we tried to bring implicit causal representation learning [1] one step closer to the real-world applications by relaxing hard interventions assumptions and proved identifiability theorem. However, as shown by the results in [1], there are other challenges remaining in this context including various factors affecting performance and scalability. We agree with the reviewer that these are important challenges and aim to address them in our future works. **References** - [1] J. Brehmer, P. De Haan, P. Lippe, and T. Cohen. Weakly supervised causal representation learning. In Advances in Neural Information Processing Systems, volume 35, pages 38319– 38331, 2022.
Decision
Reject