On Causal Discovery With Convergent Cross Mapping

Convergent cross mapping is a principled causal discovery technique for signals, but its efficacy depends on a number of assumptions about the systems that generated the signals. In this work, we present a self-contained introduction to the theory of causality in state-spaces, Takens' theorem, and cross maps, and we propose conditions to check if a signal is appropriate for cross mapping. Further, we propose simple analyses based on Gaussian processes to test for these conditions in data. We show that our proposed techniques detect when convergent cross mapping may conclude erroneous results using several examples from the literature, and we comment on other considerations that are important when applying methods such as convergent cross mapping.

Automated summary

Convergent cross mapping is a causal discovery technique for signals that relies on certain assumptions about the underlying systems. This study provides an introduction to the theory of causality, Takens' theorem, and cross maps, and proposes conditions to assess the suitability of a signal for cross mapping. The authors also propose analyses using Gaussian processes to test these conditions in data and demonstrate the detection of potential erroneous results using examples from the literature. They also discuss important considerations when applying convergent cross mapping.