Summary
# Summary
In this paper, the authors address the problem of inferring causal structures from subsampled time series data, where the frequency of measurement is much lower than that of causal influence. This presents challenges in identifying the causal structure, as hidden variables at unobserved time steps can induce bias. Existing methods that tackle this problem are limited to linear cases or fail to achieve identifiability.
The main contribution of this paper is a constraint-based algorithm that can identify the entire causal structure from subsampled time series without any parametric constraints. The authors propose a proxy-based causal discovery algorithm that leverages the temporal structure of time series data to remove the bias induced by hidden variables. The algorithm is nonparametric and can achieve full causal identification. Specifically, the author leverages the proxy variables to test the edge directions of the summary DAG from the uniquely identified MAG.
The authors demonstrate the theoretical advantages of their method and provide experiments on both synthetic and real-world data, showcasing improved performance over existing methods.
Strengths
# Originality
The paper presents a novel approach to causal discovery in subsampled time series data by proposing a constraint-based algorithm that leverages proxy variables to handle the challenges posed by hidden variables at unobserved time steps. The originality of the method lies in its ability to identify the entire causal structure without any parametric constraints, setting it apart from existing methods that are limited to linear cases or fail to achieve full identifiability. The authors draw inspiration from the recent progress in proximal causal discovery and adapt it to the subsampled time series setting.
# Quality
The quality of the paper is high, as it presents a well-formulated methodology with solid theoretical foundations. The authors provide rigorous proofs for their proposed algorithm's identifiability properties, ensuring that the algorithm is grounded in strong theoretical underpinnings. Although I have some questions regarding its generality and required assumptions, I will elaborate about them later.
As for the experiments, the author conduct 1 synthetic and 1 real-world experiment, which demonstrates its effectiveness against the baselines.
# Clarity
The paper is well-written and clear in its presentation. The methodogy is clear, thanks to the intuitive explanation provided by the authors. They also provide necessary background information on causal discovery and related literature.
# Significance
The problem that this paper aims to talks is significant in the field of tmeproal causal discovery. Although I don't think this paper fully addresses it, it made a reasonable progress towards the final destination.
Weaknesses
# Weakness
Although the paper provide a solid progress towards the final destination, here are some limitations I am a bit worried about:
## Assumptions are too strong:
One assumption is that only 1 step window is considered in this paper. However, is this true in practice? Is it possible that some factors has long-standing effect (higher-order Markovian) to the target variable? Can your method handle such scenario?
For summary DAG, does it has to be a DAG? Since from general full-time DAG, the summary graph may not be a DAG and can contain cycles. Does your method handle such cases? For example, A(1) -> B(2) and B(1) -> A(2), and the summary graph is A<->B.
What are the consequence if some variables are not self-caused? That means the proxy variables may not exists. In that case, full identifiablity cannot be establish, right? You may want to add something like to what extend of identifiability your method can establish without such assumption.
## Comparison with baselines
The author includes some of the well-known baselines. Surprisingly, Dynotears performes reasonably ok considering that it is a linear model (in its original form). However, after Dynotears, several state-of-the-art baselines are proposed, like Rhino [1]. Can you compare your method with this nonlinear model?
[1]Gong, Wenbo, et al. "Rhino: Deep Causal Temporal Relationship Learning With History-dependent Noise." arXiv preprint arXiv:2210.14706 (2022). Code at https://github.com/microsoft/causica/tree/v0.0.0
## Scalability
How expensive it is to run such algorithm, since you need to test every pair. For real-world experiment, you scale it to 90 variables, how long does it need to run it? If your method can be scaled to higher-order SVAR, how does it scales with the window size?
Questions
1. In figure 4 proxy model, do you mean $M(t_2)$?
Rating
6: Weak Accept: Technically solid, moderate-to-high impact paper, with no major concerns with respect to evaluation, resources, reproducibility, ethical considerations.
Confidence
4: You are confident in your assessment, but not absolutely certain. It is unlikely, but not impossible, that you did not understand some parts of the submission or that you are unfamiliar with some pieces of related work.
Limitations
The author did discuss its limitations but they only discuss the limitations of conditional independence test. Howver, in the weakness section, I have raised several improvements the author can consider. I suggest including these discussions in the limitations as well.