# Learning Multiscale Non-stationary Causal Structures

arXiv: https://arxiv.org/abs/2208.14989 · HTML: https://mlsanity.com/paper/2208.14989/

## 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.

## Builds on (most cited first, 26 of 26)

- [PyTorch: An Imperative Style, High-Performance Deep Learning Library](https://mlsanity.com/paper/1912.01703/) (2019)
- [Auto-Encoding Variational Bayes](https://mlsanity.com/paper/1312.6114/) (2013)
- [Variational Inference: A Review for Statisticians](https://mlsanity.com/paper/1601.00670/) (2016)
- [GPyTorch: Blackbox Matrix-Matrix Gaussian Process Inference with GPU Acceleration](https://mlsanity.com/paper/1809.11165/) (2018)
- [Pyro: Deep Universal Probabilistic Programming](https://mlsanity.com/paper/1810.09538/) (2018)
- [Causal Discovery with Continuous Additive Noise Models](https://mlsanity.com/paper/1309.6779/) (2013)
- [Scalable Variational Gaussian Process Classification](https://mlsanity.com/paper/1411.2005/) (2014)
- [On the Role of Sparsity and DAG Constraints for Learning Linear DAGs](https://mlsanity.com/paper/2006.10201/) (2020)
- [Learning Bayesian Networks: The Combination of Knowledge and Statistical Data](https://mlsanity.com/paper/1302.6815/) (2013)
- [CAM: Causal additive models, high-dimensional order search and penalized regression](https://mlsanity.com/paper/1310.1533/) (2013)
- [Causal Discovery from Heterogeneous/Nonstationary Data with Independent Changes](https://mlsanity.com/paper/1903.01672/) (2019)
- [Neural Variational Inference and Learning in Belief Networks](https://mlsanity.com/paper/1402.0030/) (2014)
- [Learning Neural Causal Models from Unknown Interventions](https://mlsanity.com/paper/1910.01075/) (2019)
- [Amortized Inference for Causal Structure Learning](https://mlsanity.com/paper/2205.12934/) (2022)
- [Masked Gradient-Based Causal Structure Learning](https://mlsanity.com/paper/1910.08527/) (2019)
- [High-dimensional learning of linear causal networks via inverse covariance estimation](https://mlsanity.com/paper/1311.3492/) (2013)
- [Understanding Probabilistic Sparse Gaussian Process Approximations](https://mlsanity.com/paper/1606.04820/) (2016)
- [BCD Nets: Scalable Variational Approaches for Bayesian Causal Discovery](https://mlsanity.com/paper/2112.02761/) (2021)
- [gCastle: A Python Toolbox for Causal Discovery](https://mlsanity.com/paper/2111.15155/) (2021)
- [Causal Discovery in Heterogeneous Environments Under the Sparse Mechanism Shift Hypothesis](https://mlsanity.com/paper/2206.02013/) (2022)
- [Differentiable DAG Sampling](https://mlsanity.com/paper/2203.08509/) (2022)
- [Variational Causal Networks: Approximate Bayesian Inference over Causal Structures](https://mlsanity.com/paper/2106.07635/) (2021)
- [Low-variance Black-box Gradient Estimates for the Plackett-Luce Distribution](https://mlsanity.com/paper/1911.10036/) (2019)
- [Causal Discovery with a Mixture of DAGs](https://mlsanity.com/paper/1901.09475/) (2019)
- [Multiscale Causal Structure Learning](https://mlsanity.com/paper/2207.07908/) (2022)
- [The Evolving Causal Structure of Equity Risk Factors](https://mlsanity.com/paper/2111.05072/) (2021)

## Built on by (most cited first, 3 of 3)

- [The Relativity of Causal Knowledge](https://mlsanity.com/paper/2503.11718/) (2025)
- [Learning Multi-Frequency Partial Correlation Graphs](https://mlsanity.com/paper/2311.15756/) (2023)
- [Towards Causal Relationship in Indefinite Data: Baseline Model and New Datasets](https://mlsanity.com/paper/2401.08221/) (2024)

## 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.