Science Advances

Supplementary Materials

This PDF file includes:

  • Section S1. Time series graphs
  • Section S2. Alternative methods
  • Section S3. Further PCMCI variants
  • Section S4. Conditional independence tests
  • Section S5. Theoretical properties of PCMCI
  • Section S6. Numerical experiments
  • Algorithm S1. Pseudo-code for condition selection algorithm.
  • Algorithm S2. Pseudo-code for MCI causal discovery stage.
  • Algorithm S3. Pseudo-code for adaptive Lasso regression.
  • Table S1. Overview of conditional independence tests.
  • Table S2. Model configurations for different experiments.
  • Table S3. Overview of methods compared in numerical experiments.
  • Table S4. Summarized ANOVA results for high-dimensionality ParCorr experiments.
  • Table S5. Summarized ANOVA results for high-density ParCorr experiments.
  • Table S6. Summarized ANOVA results for high-dimensionality GPDC and CMI experiments.
  • Table S7. Summarized ANOVA results for sample size experiments.
  • Table S8. Summarized ANOVA results for noise and nonstationarity experiments.
  • Table S9. ANCOVA results for FullCI.
  • Table S10. ANCOVA results for Lasso.
  • Table S11. ANCOVA results for PC.
  • Table S12. ANCOVA results for FullCI.
  • Fig. S1. Illustration of notation.
  • Fig. S2. Motivational climate example.
  • Fig. S3. Real climate and cardiovascular applications.
  • Fig. S4. Experiments for linear models with short time series length.
  • Fig. S5. Experiments for linear models with longer time series length.
  • Fig. S6. Experiments for dense linear models with short time series length.
  • Fig. S7. Experiments for dense linear models with longer time series length.
  • Fig. S8. Experiments for different method parameters.
  • Fig. S9. Experiments for linear methods with different sample sizes.
  • Fig. S10. Experiments for nonlinear models (part 1).
  • Fig. S11. Experiments for nonlinear models with different sample sizes (part 1).
  • Fig. S12. Experiments for nonlinear models (part 2).
  • Fig. S13. Experiments for nonlinear models with different sample sizes (part 2).
  • Fig. S14. Experiments for observational noise models.
  • Fig. S15. Experiments for nonstationary models.
  • Fig. S16. Runtimes for numerical experiments.
  • Fig. S17. ANCOVA interaction plots.
  • Fig. S18. Comparison of PCMCI and CCM on logistic maps.
  • References (6680)

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