Venue: NeurIPS 2022 Conference

Reviews:

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: This paper considered establishing identifiability theories for nonparametric latent causal processes from their observed nonlinear mixtures. The authors proposed to recover time-delayed latent causal variables and identify their relations from measured temporal data, namely LiLY. The theoretical results were derived for both stationary environments and unknown distribution shifts, with promising results in real-world applications.
strengths_and_weaknesses: *Strengths:*

 - This paper handles an interesting problem in machine learning by considering the identifiability of causal dynamics in time series data. 
 - The theoretical analyses are sound with promising real data analysis results.
 - This paper is well written and organized.

*Weaknesses:*

- The theoretical performance of the proposed LiLY for learning latent causal dynamics was not derived and discussed. Can the authors provide any theoretical analysis on this?
- The partitioned latent subspace is pre-specified and limited to three components. Can the authors provide more justification for this?

questions: Please check the questions listed in the Weaknesses above. Any justifications are welcomed.
limitations: I didn't find any limitations discussed. Please correct me if I am missing anything.
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: This paper proposes a formulation to recover latent temporal processes from observed time series data. Assumptions for identifability of the latent processes relax the ones posited in previous works and now rely on linear independence of specific vectors of partial derivatives of the latent update function. Authors also consider the case with observations from different domains and with time varying causal effects between hidden processes. The authors then propose an architecture enforcing the specific linear independence assumption and show that they can identify the latent temporal processes for an artificially generated and cart pole dataset. 
strengths_and_weaknesses: Strengths :

- The problem addressed is important and builds upon solid previous work.
- The work relaxes distributional assumptions from previous works and provides identifiability proof.
- The reported performance are clearly above other compared methods.

Weaknesses : 

- There are some clarifications needed that I listed as questions below.
- Why didn’t you evaluate the MCC of other baselines on the cart pole dataset ? This seems a more informative experiment for comparing the methods than the synthetic data that exactly matches your data generating assumption.
- It would be great to have a formulation of the identifiability criteria for arbitrary lags. And understand how it impacts training.
- Overall I’m not really convinced by the causal taxonomy of the model. Some assumptions are posited but it does not guarantee any causal discovery mechanism. The model formulation doesn't also allow to draw any causal conclusion between observables. In particular, it feels that the action in the cart pole data is modelled as a different set of parameters which thus don’t really model the treatment effect in the observed process. 

Minor
- C is not shown on Figure 2
- Some typos : 
    - Line 49 : question arises *that* (does not sound really correct to me)
    - Line 185 : So *th* linear independence (« the » ?)


questions: - What are the exact conditions on g(.) ? Should it be an invertible function ? 
- Enforcing conditions of Eq 4. With prior model and KL loss. Use sampling to infer KL divergence. How do you make sure that this results in satisfying conditions of Eq.4 ? More generally, how do you make evaluate if your data and model satisfies your assumption in the end ? Was there any issue in the training and in getting the KL loss low ?
- How does the sampling for the KL loss impacts computational considerations. How does this scale for larger number of latents and number of lags?
- How do you divided the number of latents for each group (fixed,c,o) ? What happens when the number of latents is misspecified ? It seems you use n=8 in the cart pole but the true number of latents is 2. How do you select the right ones ?
limitations: I think the assumptions of the model are clear in general, except for the read-out function g(.) (see above).
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: This paper proposes a novel method for identifying causal variables from time-series data with time delayed effects. In order to do so, the authors consider data recorded from different distribution shifts/environments. The latent variables are grouped into three main parts: a dynamics part that is fixed across all environments, a dynamics part changing across environments, and finally global changes to the observation space. The paper discusses theoretical results and a practical implementation called LiLY, which outperforms previous methods on a set of synthetic and real-world inspired datasets.
strengths_and_weaknesses: ## Strengths

The paper proposes an interesting approach to identifying latent causal variables from temporal data. It covers more settings than previous work and supports different transition dynamics and observation noises. The overall approach towards identifiability is clear and closely follows previous works on non-linear ICA. I especially appreciate the thorough discussion in Section 3.1 of various settings which could be identified only with or without the linear independence condition. The theory seems sound, although I have not checked the proofs in the Appendix in detail. The proposed implementation model supposedly supports non-trivial distributions by using Normalizing Flows in the VAE prior. Finally, the experiments cover several settings well in which the proposed model is compared to a set of relevant baselines and shows to outperform previous methods.

## Weaknesses

The clarity of the paper is adversely affected by a confusing notation in several places. Specifically, the following notation was not fully introduced before usage:
* In lines 155-159, the latent space $z$ is indexed by $k$, which had been introduced in Section 2 as a number over domains ($k=1,...,K$) and index of $u$. However, here it seems to be running over different values without explanation.
* Eq 1: the variable "$\tau$" is undefined
* Line 168: the variable "$n$" is undefined
* Between line 224-225 (line numbering issue): the index $r$ as well as Eq. 11 are not in the main text
* Between line 224-225: it is unclear why the different environments are now indexed with $1,...,m$ while previously used $1,...,K$
* Line 225: $\eta_{kt}$ had been defined as $\log p(z_{k,t}|z_{t-1})$, unclear how it is now a function of $u$
* Line 256-260: "$k$" is here again used for domains instead of latent variables
It is strongly recommended to keep the notation consistent throughout the paper, since it is currently difficult to fully understand all statements when the notation is unclear.

A second weakness of the paper is that the comparison to one of the most related works, [Huang et al., 2022] (cited as [33] in the paper), is very sparse. Section 2 beings with 'Following [32,33], ...'. It is unclear what parts are taken from [Huang et al., 2022], and which parts are own definitions/setting descriptions. A more direct discussions of the similarities between this work and [Huang et al., 2022] should be stated. Furthermore, I would have expected a similar discussion in the model part, Section 4, since both follow a similar strategy with an observation setting $\theta^{\text{obs}}$ and dynamics setting $\theta^{\text{dyn}}$.

Another weakness of this work is that it does not discuss the limitations of the work, despite the authors stating so in the paper checklist. Every work on identifiability has its limitations, since certain assumptions need to be taken. However, it is important to address when these assumptions might hold in a realistic setting, and what pre-knowledge was used in creating the models. For instance, Section 4 suggests that in order to obtain identifiability, one needs to exactly know how many variables there are for all three parts: static dynamics, changing dynamics, and observation. This seems quite limiting, since one likely can only estimate those in a real-world setup. How sensitive is the method to this? What happens when too large sets are used? How sensitive is the model to hyperparameters? A fair discussion of other limitations would also be needed. For example, in a real-world system where we do not know the causal variables, how can one ensure that the assumption of Theorem 1 holds (i.e. the $2n$ vector functions being linearly independent)? 

Finally, while the experiments cover a decent range of settings, all of them have a rather simple observation space. To strengthen the paper, it is beneficial to include an experiment on a visually complex dataset, for example, Causal3DIdent [von Kügelgen et al., 2021; Zimmermann et al., 2021], more specifically its extension to temporally data [Lippe et al., 2022]. This would highlight the method's capability of identifying causal variables in complex settings.


### Minor points

* Figure 2: the noise variables of the observation, $\hat{\epsilon}\_{i,t}$, are labeled as time-delayed information, although they have the same index and are likely not delayed information.
* The paragraph about the factor representation (line 280-283) comes a bit late, since these have been already used in the previous paragraphs. It would be easier to state this up front.

### Typos

* Line 101: space before comma - "...domains , ..."
* Line 112: "Let u denote the..." (no s)
* Line 184: dot after 1 - "k=1.,2,..."
* Line 185: incomplete word - "So th linear..."
* Line 232: time index $t$ missing - $z_{-1}$
* Line 268: ")" too much
* Line 296: capital "We" within the sentence

### Conclusion

The proposed method is interesting and potentially relevant for researchers in causal representation learning. The current version lacks a bit in clarity and misses a fair discussion of its limitations. Still, I believe that these points can be addressed in a revised version/the rebuttal. Hence, my current score is "Weak Accept".

### References

[Huang et al., 2022] Huang, Biwei, Fan Feng, Chaochao Lu, Sara Magliacane, and Kun Zhang. 2022. AdaRL: What, where, and how to adapt in transfer reinforcement learning. International Conference on Learning Representation (ICLR).

[von Kügelgen et al., 2021] Julius von Kügelgen, Yash Sharma, Luigi Gresele, Wieland Brendel, Bernhard Schölkopf, Michel Besserve, and Francesco Locatello. 2021. Self-Supervised Learning with Data Augmentations Provably Isolates Content from Style. In Thirty-Fifth Conference on Neural Information Processing Systems.

[Zimmermann et al., 2021] Roland S. Zimmermann, Yash Sharma, Steffen Schneider, Matthias Bethge, and Wieland Brendel. 2021. Contrastive Learning Inverts the Data Generating Process. In Proceedings of the 38th International Conference on Machine Learning.

[Lippe et al., 2022] Phillip Lippe, Sara Magliacane, Sindy Löwe, Yuki M. Asano, Taco Cohen, and Efstratios Gavves. 2022. CITRIS: Causal Identifiability from Temporal Intervened Sequences. In Proceedings of the 39th International Conference on Machine Learning.
questions: * Can you provide a clearer comparison of your method to [Huang et al., 2022]?
* What are the limitations of your method from your perspective?
limitations: As mentioned in the "Weakness" section, no limitations have been discussed, as well as no potential negative social impacts.
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 proposes a new framework for nonlinear Independent Component Analysis, LiLY, which recovers time-delayed latent causal variables from temporal data under stationary environments and under different distribution shifts. The authors provide proofs for the identifiability of the causal variables in the settings under consideration and show experimentally that their approach achieves improved performance on data that matches their assumptions.
strengths_and_weaknesses: # Strengths
- The proposed framework consideres a novel setting for nonlinear ICA and provides convincing identiability results in terms of theory and practice. 

- Overall, the paper follows a coherent structure and uses clear formulations for all theoretical and experimental settings.

- Table 1 gives a great overview that summarizes the novelty of the proposed framework compared to existing research.

# Weaknesses
1) In my eyes, the biggest weakness of this paper is that it does not provide any convincing motivation for the proposed approach. In the current form, the paper argues that existing approaches have a certain set of assumptions and that the proposed approach uses different assumptions. However, this is not really an argument in itself. What I would like to know is: why do these assumptions matter; how are existing approaches limited by the assumptions that they use and what new applications do you enable with your new approach? To embed these answers into the paper, I would propose a rewrite of the introduction. Additionally, it would be nice to include a discussion on the assumptions in section 3.1, i.e. why they are needed and how restrictive they are in practice. Besides this, the paper is also missing a discussion on the proposed separation of distribution changes into three types. Why did you choose these three types; are there any alternative separations that you considered and why is the proposed solution the best; are there any distribution changes that these types cannot (jointly) represent? Finally, a discussion on the limitations of the proposed approach is missing. Overall, this makes it very difficult to judge the significance of this work.

2) The connection between this method and causal discovery seems somewhat hand-wavy. The abstract claims that the proposed framework recovers latent variables and identifies their relations. While the experiments and theoretical results support the former claim, the latter seems to be missing from the paper, effectively removing the connection to causal discovery. Additionally, "causal dynamics" are mentioned throughout the paper without ever being defined.

3) According to l.297, all evaluations were conducted on the validation datasets. This is not appropriate according to standard machine learning practice. For convincing results, these experiments need to be repeated on the test datasets.

4) The paper's clarity could be improved in certain regards. For example, I found it confusing which variables and functions are estimated by the model and which ones are ground-truth factors. Does the model use the ground-truth transition functions, or does it estimate them? Does the model work with unknown distribution shifts as claimed in the abstract and intro, or does it require a domain index (l. 281) as input? 



## Others
- Currently, the introduction also functions as a related works section. I would prefer a separation of these two sections. For one, this would allow the introduction to focus on the motivation for the proposed approach, as mentioned above. Additionally, a separate related work section could discuss existing work in more detail and provide an embedding of the proposed work into the existing research landscape - an aspect that is largely missing in the current form.

- There are grammatical errors and spelling mistakes throughout the paper that a standard spell checker should be able to catch.

- Personally, I am not a big fan of the name of the method, as well as the resulting acronym. The name "Learning latent causal dynamics" is too general, could be applied to a whole range of methods and does not describe the essence of the proposed method, and the acronym is gathering scattered letters with non-matching capitalization.

questions: A number of questions regarding this paper are embedded in the "Strengths and Weaknesses" section above. Besides these questions, I would be interested in a more concrete connection between the proposed approach and causal discovery. If the authors can answer these points convincingly, as well as outline how and where they would embed their answers into the paper, I will consider raising my score.
limitations: I could not find any discussion on the limitations of the proposed method, and would appreciate if the authors could highlight some limitations in their rebuttal.

**Given the author's reply and revised version of the paper, I have increased my rating for this paper.**
review_title: null

Meta-review: metareview: Decision: Accept

This paper presents identifiability results of causal relationships in non-stationary time series under the assumption of latent dynamics with non-linear mixtures. The authors also propose an implementation of the assumed causal model as a sequential deep generative model. Experiments compare the proposed method with existing causal ML methods on time series & sequential VAE and obtained better results.

Reviewers commended the paper as well motivated and agreed that the paper's assumptions are more practical than existing causal ML work on time series data. There were questions on the assumptions & technical results from some reviewers, which were largely addressed in author feedback. I'd also encourage the authors to include some of the replies in author feedback to the camera ready, as this will help clarifying the approach further.

As a side note, some reviewers are not very comfortable with the paper title "Causal Disentanglement for Time Series", as they think the title is perhaps "too ambitious and general to reflect this paper's main focus and disappoints audiences who imagine something else". I'd encourage the authors to consider this comment from the reviewers.
confidence: Certain
Decision: Accept