Detecting and quantifying causal associations in large nonlinear time series datasets

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. X 1 X 2 X 3 X 4 linear nonlinear X 1 X 2 X 3 spurious associations causal links X 4 1 2 1 B Causal discovery A Large-scale time series dataset C FULLCI E time lags Figure 1. Causal discovery problem. Consider a large-scale time series dataset (panel A) from a complex system such as the Earth system of which we try to reconstruct the underlying causal dependencies (panel B), accounting for linear and nonlinear dependencies and including their time lags (link labels). Pairwise correlations yield spurious associations due to common drivers (e.g., X 1 ← X 2 → X 3 ) or transitive indirect paths (e.g., X 2 → X 3 → X 4 ). Causal discovery aims to unveil such spurious associations leading to reconstructed causal networks that are, therefore, much sparser than correlation networks.leads to a dilemma that has limited applications of Granger causality mostly to bivariate analyses that cannot, however, account for indirect links and common drivers. There are methods that can cope with high-dimensionality such as regularized regression techniques 11, 12 , but mainly in the context of prediction and not causal discovery where assessing the significance of causal links is more important. An exception is Lasso regression 11 which also allows to discover active variables. Another approach with some recent applications in climate research 13-15 are algorithms aimed specifically at causal discovery [16][17][18] , which remove redundant or irrelevant variables utilizing iterative independence and conditional independence testing. However, both regularized regression and recent implementations of causal discovery algorithms do not deal well with the strong interdependencies due to the spatiotemporal nature of the variables as we show here. In particular, controlling false positives at a desired level is difficult for such methods 19-21 , and becomes even more challenging for nonlinear estimators. In summary, these problems lead to brittle causal network reconstructions and a more reliable methodology is required.We present a causal discovery m...

Causal Interactions between Southern Ocean Polynyas and High-Latitude Atmosphere–Ocean Variability

“…5. Other causal inference techniques are better adapted to connecting larger numbers of variables in a single model (Runge et al 2019) and our bivariate approach offers the advantage of simple, straightforward interpretability. VAR model analysis requires stationary time series.…”

Debates—Does Information Theory Provide a New Paradigm for Earth Science? Causality, Interaction, and Feedback

“…• HERMES (Niso et al, 2013) is a toolbox that includes IT-based and cross-correlation measures for time series data sets. • TIGRAMITE (Runge et al, 2017) is a Python module for causal inference in time series data sets. • causeme.net (Runge et al, 2019) is a causality benchmarking platform that compares several types of IT-based and other measures.…”

Tropical and mid-latitude teleconnections interacting with the Indian summer monsoon rainfall: A Theory-Guided Causal Effect Network approach

“…In the MCI-step, the partial correlation between an actor and its set of parents is calculated again but conditioned simultaneously on both the sets of parents of the i th actor and the sets of parents of each of the parents of the i th actor. Those parents that pass the MCI test will then form the final set of parents for the i th actor (Runge et al, 2017). A numerical example of these steps is given in the SI, Text S1.…”