Detecting causal associations in large nonlinear time series datasets (1702.07007v2)

Abstract: Identifying causal relationships from observational time series data is a key problem in disciplines such as climate science or neuroscience, where experiments are often not possible. Data-driven causal inference is challenging since datasets are often high-dimensional and nonlinear with limited sample sizes. Here we introduce a novel method that flexibly combines linear or nonlinear conditional independence tests with a causal discovery algorithm that allows to reconstruct causal networks from large-scale time series datasets. We validate the method on a well-established climatic teleconnection connecting the tropical Pacific with extra-tropical temperatures and using large-scale synthetic datasets mimicking the typical properties of real data. The experiments demonstrate that our method outperforms alternative techniques in detection power from small to large-scale datasets and opens up entirely new possibilities to discover causal networks from time series across a range of research fields.

• The paper presents PCMCI, a novel two-step method that uses condition selection with the PC₁ algorithm and momentary conditional independence testing.
• The approach significantly enhances detection power and maintains control over false positives even in autocorrelated, complex time series data.
• Validated using synthetic data and a climate case study, PCMCI outperforms traditional methods in reconstructing scalable, reliable causal networks.

Detecting Causal Associations in Large Nonlinear Time Series Datasets

In the paper by Runge et al., a methodological advancement is presented for detecting causal networks in high-dimensional, nonlinear time-series datasets. This research addresses a critical need in fields like climate science and neuroscience, where traditional experimental interventions are often impractical or impossible. These domains frequently encounter the challenge of discerning causal relationships from complex datasets characterized by nonlinear dependencies, high dimensionality, and limited sample sizes.

Overview of the Method

The authors introduce a novel two-step causal discovery method called PCMCI, which successfully mitigates the limitations of existing approaches, such as Granger causality and autoregressive models, which typically struggle in high-dimensional settings. The PCMCI method effectively integrates linear or nonlinear conditional independence tests with a causal discovery algorithm to reconstruct causal networks efficiently.

Key Innovations

1. Condition Selection with PC$_1$ Algorithm: The PCMCI method begins with the PC$_1$ algorithm, which performs a pre-selection of variables to identify the most relevant conditions for each target variable. This step aims to minimize the estimation dimension by intelligently dispensing with variables that do not significantly contribute to causal explanations.
2. Momentary Conditional Independence (MCI) Testing: The second phase implements the MCI test, which conditions on a reduced set of variables identified by PC$_1$. This reduction is crucial as it enhances the statistical power of the method to detect true causal links while maintaining control over false positives, even for highly autocorrelated time series.

Validation and Results

The efficacy of PCMCI is rigorously validated using both synthetic datasets, which mimic real-world challenges in time series analysis, and a well-documented climate teleconnection case. Compared to alternative methods, PCMCI displays superior performance across several dimensions:

• Higher Detection Power: PCMCI identifies true causal relationships with higher reliability across different scales of network sizes and complexities, outperforming methods like Lasso regression, which tend to suffer from overlooking critical causal links.
• Robustness to Autocorrelation: Unlike standalone PC algorithms, PCMCI correctly controls for false positives even in the presence of strong autocorrelations, making it more suitable for typical time series applications.
• Computational Efficiency: While the approach involves polynomial complexity, practical implementations and tests indicate that PCMCI is feasible for moderately large datasets under realistic computational constraints.

Implications and Future Directions

The implications of this research are twofold: from a theoretical standpoint, it contributes to the current understanding of causal inference in high-dimensional time series, and from a practical perspective, it opens new avenues for analyzing complex systems where causality must be inferred rather than experimentally determined.

Looking ahead, PCMCI's applicability could be enhanced by integrating contemporaneous causal discovery methods, especially since real-world systems often involve causal effects at zero lag. Additionally, the capability of PCMCI to accommodate multivariate and structured domain data through appropriate conditional independence tests suggests its potential utility in multilayer networks and other complex systems.

In conclusion, Runge et al.'s contribution provides a robust and scalable solution for causal network reconstruction in nonlinear time series, laying the groundwork for more credible and comprehensive causal analyses across a multitude of scientific fields.