Venue: UAI 2022 Workshop CRL

Reviews:

final_score: rating: 5: Marginally below acceptance threshold
review_content: This paper proposes a method to infer the time-delayed causal relationships from non-stationary time series, where the non-stationary behavior is modeled as stationarity conditioned on a set of state variables whose dynamics may be dependent on the observed sequence.

The reported experimental results show that the proposed method is much better than the previous ones. However, the evaluation is only on three-variable data set and only for linear causal relationship. It would be much more convincing if the authors could consider nonlinear causal relationships and more variables in the graph.

review_title: Experimental results are not enough

final_score: rating: 6: Marginally above acceptance threshold
review_content: This paper considers causal discovery from non-stationary time series data. The problem seems enough challenging and interesting.

They propose a solution that their model assumes their non-stationary time series are conditionally stationary. This means that the non-stationarity is a mixture of stationary time series, and the time series is stationary if a set of state variables are conditioned. This idea seems a reasonable choice. 

Then, they show the identifiability of their model, assuming no contemporaneous causal effects and state variables are observed. 
The appendix also says that they can include contemporaneous causal effects. Though the proof relies on the result of Peters et al. (2014) rather well, showing the identifiability of their proposed model would be an essential ingredient to make their paper more solid.

They further propose a VAE-based estimation method. They did not provide its consistency proof, but their experiments using artificial data imply the consistency. 
Their artificial data experiments also consider cases with unobserved state variables. Therefore, it implied that their approach might work for such unobserved state variable cases.

Though their model is nonlinear, their experiments seem to assume linearity. The number of variables in the experiments is relatively small, N=3. It was not clear to what extent their estimation method scales.

They also propose an idea that summarizes causal graphs for times series data into a single summary graph. I was unclear how we could use such a summary graph, though I appreciate such a visualization. E.g., can we choose a set of covariates to estimate intervention effects, or do we need to look at individual graphs after all?

review_title: The problem is interesting. The solution might not be so fresh but would be reasonable. The experiments would be necessary to be improved. 

Meta-review: metareview: While both reviewers agree that the experimental results could be strengthened, the problem was deemed challenging and interesting. As a suggestion, the authors may want to additionally comment on analogies and differences with previous work on nonlinear causal discovery under non-stationarity exploiting piece-wise stationarity, e.g., 

Monti, Ricardo Pio, Kun Zhang, and Aapo Hyvärinen. "Causal discovery with general non-linear relationships using non-linear ica." Uncertainty in artificial intelligence. PMLR, 2020.
confidence: 2: The area chair is not sure
Decision: Accept (Poster)