Learning Multiscale Non-stationary Causal Structures
Abstract: This paper addresses a gap in the current state of the art by providing a solution for modeling causal relationships that evolve over time and occur at different time scales. Specifically, we introduce the multiscale non-stationary directed acyclic graph (MN-DAG), a framework for modeling multivariate time series data. Our contribution is twofold. Firstly, we expose a probabilistic generative model by leveraging results from spectral and causality theories. Our model allows sampling an MN-DAG according to user-specified priors on the time-dependence and multiscale properties of the causal graph. Secondly, we devise a Bayesian method named Multiscale Non-stationary Causal Structure Learner (MN-CASTLE) that uses stochastic variational inference to estimate MN-DAGs. The method also exploits information from the local partial correlation between time series over different time resolutions. The data generated from an MN-DAG reproduces well-known features of time series in different domains, such as volatility clustering and serial correlation. Additionally, we show the superior performance of MN-CASTLE on synthetic data with different multiscale and non-stationary properties compared to baseline models. Finally, we apply MN-CASTLE to identify the drivers of the natural gas prices in the US market. Causal relationships have strengthened during the COVID-19 outbreak and the Russian invasion of Ukraine, a fact that baseline methods fail to capture. MN-CASTLE identifies the causal impact of critical economic drivers on natural gas prices, such as seasonal factors, economic uncertainty, oil prices, and gas storage deviations.
Submission Length: Long submission (more than 12 pages of main content)
Previous TMLR Submission Url: https://openreview.net/forum?id=jlE1439nwL
Changes Since Last Submission: Dear AE and reviewers,
Thanks to the insightful comments by the reviewers of our previous manuscript, we have substantially improved the quality of our work, which we are delighted to submit to Transaction on Machine Learning Research.
The new manuscript, which also has a new title, addresses all the issues raised by the reviewers of the previous submission, as we explain in the rest of this letter.
Firstly, we have improved the proposed inference method, thus overcoming the difficulties encountered in the inference of graphs with a larger number of nodes, as confirmed by our new experiments presented in Section 6.2. The new version of the algorithm leverages the results presented in Lemma 4.2 and Proposition 4.3 of our paper, and uses information from the partial correlation between time series to estimate causal relationships.
We have also introduced a fourth experimental setting to study the performance of our method in the presence of violations of the model assumptions. Specifically, we violate the assumption of Gaussianity of the latent noise $\mathbf{z}_{j,k}$ and apply our model to subsampled data, i.e., in the presence of overlapping temporal resolutions that cannot be distinguished given the frequency of observation of the data. We have provided the results for this new experimental setting in Figure 8c and Figure 10.
Furthermore, we have replaced the previous application on real data with a study of natural gas prices in the US market, described in Section 7. Given the presence of different temporal scales, it was possible to estimate multiscale causal relationships, thus demonstrating the relevance of the proposed method and motivating its use. Also, we have provided comprehensive information regarding the data sources, time series pre-processing, and the inference process in Appendix K.
Finally, we have streamlined the structure of the article by moving the mathematical background to the Appendices A-D, and report only what constitutes the novelty of our work in the main body. In addition, some of the plots have been moved to the Appendices H and J to improve the readability of the article.
We hope you appreciate our new manuscript.
Sincerely,
The Authors.
Assigned Action Editor: ~Sinead_Williamson1
License: Creative Commons Attribution 4.0 International (CC BY 4.0)
Submission Number: 1017
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