Causal Temporal Representation Learning with Nonstationary Sparse Transition

Summary

Most existing causal temporal representation learning models either assume the domain variables to be observable, or have a Markov prior over them. This paper first comes up an identifiability theory for sequential data affected by non-stationary latent causal processes under unknown distributional shifts. In particular, a novel causal temporal representation learning method is developed to identify the latent causal variables with time-delayed causal relations. Moreover, without relying on prior knowledge on distributional shifts, the domain variables can be inferred from sequential observations. The final experiments on both synthetic and real-world action segmentation data, demonstrate the superior performance of the novel method in estimating domain variables and latent causal processes.

Strengths

Originality: It is the first attempt to develop causal temporal representational learning to identify both the domain variables and the latent causal processes from sequential observations, without relying on distributional or structural knowledge. Quality: The theorectical aspects of the paper look very sound, and absolutely pass the acceptance bar of the NeurIPS. Clarity: Overall, the paper is well written. Both the target problems and the main techniques are well presented! Significance: The developed identifiability theory for domain variables and latent causal processes from sequential observations under unknown distributional or structural prior knowledge, may have impacts for advancing the relevant causal representation learning methods.

Weaknesses

Throughout the paper, I did not find the details about how to set up the parameters of the neural nets for the novel CTRL framework, which could be crucial for the others to pick up the work.

Questions

Except the action segmentation tasks, can the authors provide more real applications including healthcare and finance, as mentioned in the boarder impacts.

Rating

6

Confidence

2

Soundness

3

Presentation

3

Contribution

3

Limitations

Yes, the paper discusses the potential negative societal impact of the work.

Summary

The paper focuses on causal temporal representation learning for non-stationary time series. It adopts a sparse transition assumption, aligned with intuitive human understanding, and presents identifiability results from a theoretical perspective. Based on the theoretical result, the authors introduce a novel framework, Causal Temporal Representation Learning with Nonstationary Sparse Transition (CtrlNS), designed to leverage the constraints on transition sparsity and conditional independence to reliably identify both distribution shifts and latent factors. Experiments on synthetic and real-world datasets demonstrate the effectiveness of the proposed method in recovering latent variables and domain indices.

Strengths

1.The paper focuses on the issue of causal discovery in nonstationary time series, which is a fascinating and significant area of research. 2.The authors claim to have proposed a method that establishes identifiability of nonstationary nonlinear ICA for general sequence data without prior knowledge of domain variables, which is an extremely challenging problem. 3.The authors have conducted experiments on both synthetic and real-world datasets, validating the effectiveness of the model, and have appropriately discussed the limitations of the model.

Weaknesses

1.The authors lack discussion of some existing work, for example, the paper [1] also demonstrates identifiability by clustering nonstationary spatiotemporal data into different domains without prior knowledge. It is essential for authors to further discuss the similarities and differences between the two papers and alleviate my concerns about the novelty of this work. 2.In lines 259-261 of this paper, the authors mention ensuring the invertibility of the modeled mixing function through reconstruction loss, which is insufficient. Invertible Neural Networks (INNs) should be employed to ensure invertibility, as there will inevitably be errors in the reconstruction process. [1] Zhao, Yu, et al. "Generative Causal Interpretation Model for Spatio-Temporal Representation Learning." Proceedings of the 29th ACM SIGKDD Conference on Knowledge Discovery and Data Mining. 2023.

Questions

Please see the Weaknesses.

Rating

5

Confidence

4

Soundness

3

Presentation

3

Contribution

2

Limitations

The authors have appropriately discussed the limitations and societal impacts of the model.

Summary

The paper focuses on temporally causal representation learning, where the goal is to recover a latent causal process from nonstationary observation sequences. Existing works represent the source of the nonstationarity by either known domain variables or (autocorrelated) unknown domain variables with Markov structure. The paper proposes a sparsity based constraint on the latent transitions to achieve the identifiability of the domain variables. Coupled with the identified domain variable, they make use of the sufficient variability assumption to identify the latent causal process. Based on this theoretical framework, they introduce a sequential VAE based model, which encourages the independent noise variables and the sparse transitions. They evaluate (i) the performance on the latent process identifiability on a synthetic dataset following their model definition, and (ii) the usefulness of their model on a weakly-supervised video action segmentation task on real-world datasets of daily actions and cooking.

Strengths

* Compared to the existing work, the paper tackles the identifiability of the domain variables from a new perspective: the domain variable's effect on the transition functions. This perspective is in line with seeing distribution shifts as interventions to the underlying system, and could be valuable in some related tasks such as learning causal relations by taking actions. * I appreciate the effort for the real-world experiment, though it only evaluates the prediction of the domain variable.

Weaknesses

* As is common in identifiability literature, the assumptions of the theoretical framework do not seem to be testable on a real-world setup. * Definition 6 (Weakly diverse lossy transitions) seems unrealistic and is not clear from the text: (i) The motivation for the “Lossy” is not clear to me, how is there a causal link between two variables, while changing the causal parent does not affect the effect variable? (ii) On the clarity of the definition: perhaps, some graphical model examples could help here. In addition, the assumption is not discussed in the main text, except stating in lines 227-228 that it is “a mild and realistic condition in the real-world scenarios, allowing for identical future latent states with differing past states”. Why is it mild and realistic? * It is not clear to me why having domain variables without a Markov structure is a better model of the real-world environments than domain variables with Markov structure. I don’t see why environments in the real-world would swap at random multiple times along a sequence of time points. For example, in the provided real-world experiment, ground-truth actions in the video in Figure S5 occur in blocks and they are autocorrelated. The weak-supervision of the action order used in this experiment also supports their autocorrelation. * According to the point above, the synthetic experimental setup seems unrealistic as it has randomly sampled domain variables. * I think the first contribution statement in Lines 59-61 is ambiguous: "this is the first identifiability result that handles nonstationary time-delayed causally related latent temporal processes without prior knowledge of the domain variables". What is meant by "without the prior knowledge of domain variables" is a bit vague, while the difference with the existing work [Song+23] seems to be the assumptions on the temporal dependence of the domain variables. [Song+23] assumes temporally-dependent domain variables and predicts the unknown domain variables with an HMM, while this work assumes temporally independent domain variables and predicts them from sequential observations. [Song+23]. Xiangchen Song, Weiran Yao, Yewen Fan, Xinshuai Dong, Guangyi Chen, Juan Carlos Niebles, Eric Xing, and Kun Zhang. "Temporally disentangled representation learning under unknown nonstationarity" Neurips, 2023.

Questions

* Some assumptions are motivated in lines 219-224 as being aligned with human intuition: “separability states that if human observers cannot distinguish between two domains, it is unlikely that automated systems can achieve this distinction either. Secondly, variability requires that the transitions across domains are significant enough to be noticeable by humans, implying that there must be at least one altered edge in the causal graph across the domains.” I find it hard to follow this reasoning. Why are these the cases? * For both experiments, architectural details are missing. Besides, some information on the synthetic experimental setups is missing: what are the functions $\mathbf{m}$ and $\mathbf{g}$ used?, What is the train/val/test split?, What parts of the experiment change with the changing seed? * It is not clear to me what the model predicts on the action segmentation task. I think it predicts the action class per frame given the video frames and the action order. If so, why do you report MoF, IoU and IoD, instead of accuracy? How do you provide the weak-supervision information to the model? Why is the baseline NCTRL excluded from this task? Its generative model seems to fit the task well. * It is not clear what the sparsity loss is. In line 266, it is said to be the L2 norm of the parameter in the transition estimation functions. Which parameter is this?

Rating

4

Confidence

2

Soundness

2

Presentation

2

Contribution

1

Limitations

* The main limitation, the assumptions being untestable for a real-world setup, is not discussed in the main text.

Summary

The paper introduces CtrlNS, a causal temporal representation learning framework based on a sparse transition assumption to identify distribution shifts without strong prior knowledge of the domain variables. Theoretical and experimental results show CtrlNS effectively identifies distribution shifts and latent factors, outperforming existing methods.

Strengths

- Causal temporal representation learning under nonstationarity is an important problem. The paper replaces somewhat unrealistic and strong assumptions on the domain variable made by the prior works. - Theoretical analysis provides a rigorous foundation for the proposed framework. While I did not check the proofs in detail, the proof flows are convincing, and the results are intuitive and reasonable. - Another strength of the paper is its evaluation on realistic task setup (i.e., weakly supervised action segmentation). This illustrates the practical applicability of the proposed method. - Finally, the paper is well-written and well-organized.

Weaknesses

The authors argue that the paper derives identifiability results *“without prior knowledge of the domain variables”* (e.g., line 46, 61). However, this is an overstatement since CtrlNS still requires some prior knowledge or assumptions, such as the ground-truth number of different domains $U$. Moreover, while I understand it does not rely on Markov assumption of prior works (e.g., NCTRL), the proposed framework still requires a different set of assumptions such as weakly diverse lossy transition and mechanism sparsity. In fact, I am not sure whether the authors’ assumption can be claimed as “weaker” compared to prior works. Therefore, I feel those statements need to be toned down, and more discussion on the comparisons of those assumptions is suggested.

Questions

- It seems that the framework requires the prior knowledge of the number of environments $U$. This assumption should be made more explicit. Also, what happens under the misspecification of $U$? - For the mathematical rigor, the statements need to take measure-zero sets into account. For example, I think the conditions $p(S_{t, i, j})>0$ (line 136), $p(S_{t, i})>0$ and $p(S_{t, i, j}\setminus S_{t, i})>0$ (line 141) should be included, just to name a few. - The framework requires $U$ different transition networks, which could be a potential weakness, especially in terms of scalability. The discussion on this point would further strengthen the paper. For example, an efficient parameter sharing of networks [3] may alleviate such issues. - The proposed work assumes no contemporaneous causal relationships. (I know this is a common assumption in this line of work) How can this assumption be relaxed? With the interventional data, is it possible for the proposed framework to generalize to the existence of instantaneous effects, maybe similar to iCITIRS [1]? - A number of works in RL setting also consider the identifiability under the non-stationary process [2, 3]. For example, [3] considers the identifiability of both domain variables and causal structures. I suggest the authors include these related works in different areas. - The utilization of mechanism sparsity for identifiability is also explored in [4]. How is it different from the sparse transition assumption in CtrlNS? (minor) - Style file seems to be different from the official NeurIPS template (e.g., fonts). ***References*** [1] Lippe, Phillip, et al. "Causal Representation Learning for Instantaneous and Temporal Effects in Interactive Systems." *The Eleventh International Conference on Learning Representations*. [2] Feng, Fan, et al. "Factored adaptation for non-stationary reinforcement learning." *Advances in Neural Information Processing Systems* 35 (2022): 31957-31971. [3] Hwang, Inwoo, et al. "Fine-Grained Causal Dynamics Learning with Quantization for Improving Robustness in Reinforcement Learning." *International Conference on Machine Learning*. PMLR, 2024. [4] Xu, Danru, et al. "A Sparsity Principle for Partially Observable Causal Representation Learning." *International Conference on Machine Learning*. PMLR, 2024.

Rating

7

Confidence

3

Soundness

3

Presentation

3

Contribution

3

Limitations

.