mlsanityData to 14 Oct 2026

Learning Multiscale Non-stationary Causal Structures

arXiv 2208.14989 ↗First posted 31 Aug 2022cs.LG stat.ME stat.MLcited by 3

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Abstract (arXiv)

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.

Key facts. Cited by 3 papers in the map (data through 14 Oct 2026). Builds on 26 of its 71 references that are in the map. First posted on arXiv 31 Aug 2022.

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26 of 71 references.

References · 26

  1. 2019PyTorch: An Imperative Style, High-Performance Deep Learning Librarycited by 20,305
  2. 2013Auto-Encoding Variational Bayescited by 4,053
  3. 2016Variational Inference: A Review for Statisticianscited by 1,472
  4. 2018GPyTorch: Blackbox Matrix-Matrix Gaussian Process Inference with GPU Accelerationcited by 609
  5. 2018Pyro: Deep Universal Probabilistic Programmingcited by 380
  6. 2013Causal Discovery with Continuous Additive Noise Modelscited by 255
  7. 2014Scalable Variational Gaussian Process Classificationcited by 228
  8. 2020On the Role of Sparsity and DAG Constraints for Learning Linear DAGscited by 191
  9. 2013Learning Bayesian Networks: The Combination of Knowledge and Statistical Datacited by 187
  10. 2013CAM: Causal additive models, high-dimensional order search and penalized regressioncited by 178
  11. 2019Causal Discovery from Heterogeneous/Nonstationary Data with Independent Changescited by 166
  12. 2014Neural Variational Inference and Learning in Belief Networkscited by 117
14 more
  1. 2019Learning Neural Causal Models from Unknown Interventionscited by 113
  2. 2022Amortized Inference for Causal Structure Learningcited by 90
  3. 2019Masked Gradient-Based Causal Structure Learningcited by 89
  4. 2013High-dimensional learning of linear causal networks via inverse covariance estimationcited by 87
  5. 2016Understanding Probabilistic Sparse Gaussian Process Approximationscited by 68
  6. 2021BCD Nets: Scalable Variational Approaches for Bayesian Causal Discoverycited by 68
  7. 2021gCastle: A Python Toolbox for Causal Discoverycited by 61
  8. 2022Causal Discovery in Heterogeneous Environments Under the Sparse Mechanism Shift Hypothesiscited by 55
  9. 2022Differentiable DAG Samplingcited by 47
  10. 2021Variational Causal Networks: Approximate Bayesian Inference over Causal Structurescited by 43
  11. 2019Low-variance Black-box Gradient Estimates for the Plackett-Luce Distributioncited by 11
  12. 2019Causal Discovery with a Mixture of DAGscited by 7
  13. 2022Multiscale Causal Structure Learningcited by 7
  14. 2021The Evolving Causal Structure of Equity Risk Factorscited by 3

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Citing papers per year: 2023: 1; 2024: 1; 2025: 1.

3 papers.

  1. 2025The Relativity of Causal Knowledgecited by 2
  2. 2023Learning Multi-Frequency Partial Correlation Graphscited by 1
  3. 2024Towards Causal Relationship in Indefinite Data: Baseline Model and New Datasetscited by 0