Tigramite – Causal inference for time series datasets

Overview

• ➡️ GitHub Repository
• ➡️ Documentation
• ➡️ Tutorials

It's best to start with our Overview/review paper: Causal inference for time series.

🆕 Update: Tigramite now has a new CausalEffects class that allows to estimate (conditional) causal effects and mediation based on assuming a causal graph. Have a look at the tutorial.

Further, Tigramite provides several causal discovery methods that can be used under different sets of assumptions. An application always consists of a method and a chosen conditional independence test, e.g. PCMCIplus together with ParCorr. The following two tables give an overview of the assumptions involved:

Method	Assumptions	Output
	(in addition to Causal Markov Condition and Faithfulness)
PCMCI	Causal stationarity, no contemporaneous causal links, no hidden variables	Directed lagged links, undirected contemporaneous links (for tau_min=0)
PCMCIplus	Causal stationarity, no hidden variables	Directed lagged links, directed and undirected contemp. links (Time series CPDAG)
LPCMCI	Causal stationarity	Time series PAG
RPCMCI	No contemporaneous causal links, no hidden variables	Regime-variable and causal graphs for each regime with directed lagged links, undirected contemporaneous links (for tau_min=0)
J-PCMCI+	Multiple datasets, causal stationarity, no hidden system confounding, except if context-related	Directed lagged links, directed and undirected contemp. links (Joint time series CPDAG)

Conditional independence test	Assumptions
ParCorr	univariate, continuous variables with linear dependencies and Gaussian noise
RobustParCorr	univariate, continuous variables with linear dependencies, robust for different marginal distributions
ParCorrWLS	univariate, continuous variables with linear dependencies, can account for heteroskedastic data
GPDC / GPDCtorch	univariate, continuous variables with additive dependencies
CMIknn	multivariate, continuous variables with more general dependencies (permutation-based test)
Gsquared	univariate discrete/categorical variables
CMIsymb	multivariate discrete/categorical variables (permutation-based test)
RegressionCI	mixed datasets with univariate discrete/categorical and (linear) continuous variables

Remark: With the conditional independence test wrapper class PairwiseMultCI you can turn every univariate test into a multivariate test.

General Notes

Tigramite is a causal inference for time series python package. It allows to efficiently estimate causal graphs from high-dimensional time series datasets (causal discovery) and to use graphs for robust forecasting and the estimation and prediction of direct, total, and mediated effects. Causal discovery is based on linear as well as non-parametric conditional independence tests applicable to discrete or continuously-valued time series. Also includes functions for high-quality plots of the results. Please cite the following papers depending on which method you use:

• Overview: Runge, J., Gerhardus, A., Varando, G. et al. Causal inference for time series. Nat Rev Earth Environ (2023). https://doi.org/10.1038/s43017-023-00431-y

• PCMCI: J. Runge, P. Nowack, M. Kretschmer, S. Flaxman, D. Sejdinovic, Detecting and quantifying causal associations in large nonlinear time series datasets. Sci. Adv. 5, eaau4996 (2019). https://advances.sciencemag.org/content/5/11/eaau4996

• PCMCI+: J. Runge (2020): Discovering contemporaneous and lagged causal relations in autocorrelated nonlinear time series datasets. Proceedings of the 36th Conference on Uncertainty in Artificial Intelligence, UAI 2020,Toronto, Canada, 2019, AUAI Press, 2020. http://auai.org/uai2020/proceedings/579_main_paper.pdf

• LPCMCI: Gerhardus, A. & Runge, J. High-recall causal discovery for autocorrelated time series with latent confounders Advances in Neural Information Processing Systems, 2020, 33. https://proceedings.neurips.cc/paper/2020/hash/94e70705efae423efda1088614128d0b-Abstract.html

• RPCMCI: Elena Saggioro, Jana de Wiljes, Marlene Kretschmer, Jakob Runge; Reconstructing regime-dependent causal relationships from observational time series. Chaos 1 November 2020; 30 (11): 113115. https://doi.org/10.1063/5.0020538

• Generally: J. Runge (2018): Causal Network Reconstruction from Time Series: From Theoretical Assumptions to Practical Estimation. Chaos: An Interdisciplinary Journal of Nonlinear Science 28 (7): 075310. https://aip.scitation.org/doi/10.1063/1.5025050

• Nature Communications Perspective paper: https://www.nature.com/articles/s41467-019-10105-3

• Mediation class: J. Runge et al. (2015): Identifying causal gateways and mediators in complex spatio-temporal systems. Nature Communications, 6, 8502. http://doi.org/10.1038/ncomms9502

• Mediation class: J. Runge (2015): Quantifying information transfer and mediation along causal pathways in complex systems. Phys. Rev. E, 92(6), 62829. http://doi.org/10.1103/PhysRevE.92.062829

• CMIknn: J. Runge (2018): Conditional Independence Testing Based on a Nearest-Neighbor Estimator of Conditional Mutual Information. In Proceedings of the 21st International Conference on Artificial Intelligence and Statistics. http://proceedings.mlr.press/v84/runge18a.html

• CausalEffects: J. Runge, Necessary and sufficient graphical conditions for optimal adjustment sets in causal graphical models with hidden variables, Advances in Neural Information Processing Systems, 2021, 34. https://proceedings.neurips.cc/paper/2021/hash/8485ae387a981d783f8764e508151cd9-Abstract.html

Features

• flexible conditional independence test statistics adapted to continuously-valued, discrete and mixed data, and different assumptions about linear or nonlinear dependencies
• handling of missing values and masks
• p-value correction and (bootstrap) confidence interval estimation
• causal effect class to non-parametrically estimate (conditional) causal effects and also linear mediated causal effects
• prediction class based on sklearn models including causal feature selection

Minimum requirements

• Python 3.8, 3.9, 3.10, 3.11
• numpy, scipy, numba

Optional packages depending on used functions

• scikit-learn for Gaussian Process (GP) Regression
• matplotlib for Plotting
• seaborn for Plotting
• networkx for Plotting
• torch for GPDC pytorch version
• gpytorch for GPDC gpytorch version
• dcor for GPDC distance correlation version
• joblib for CMIsymb shuffle parallelization
• ortools for RPCMCI

Installation

To install from PyPI, you can use pip:

pip install tigramite

This will install tigramite in your path.

To install from source, you can use the following commands:

git clone https://github.com/jakobrunge/tigramite.git
cd tigramite
pip install .

For development purposes, use PDM to install the dependencies from the pdm.lock file:

pdm sync

To use just the ParCorr, CMIknn, and CMIsymb independence tests, only numpy/numba and scipy are required. For other independence tests more packages are required:

• GPDC: scikit-learn is required for Gaussian Process regression and dcor for distance correlation
• GPDCtorch: gpytorch is required for Gaussian Process regression

Note: Due to incompatibility issues between numba and numpy, we currently enforce soft dependencies on the versions.

User Agreement

By downloading TIGRAMITE you agree with the following points: TIGRAMITE is provided without any warranty or conditions of any kind. We assume no responsibility for errors or omissions in the results and interpretations following from application of TIGRAMITE.

You commit to cite above papers in your reports or publications.

License

Copyright (C) 2014-2024 Jakob Runge.

See the LICENSE file for full text.

TIGRAMITE is free software; you can redistribute it and/or modify it under the terms of the GNU General Public License as published by the Free Software Foundation; either version 3 of the License, or (at your option) any later version. TIGRAMITE is distributed in the hope that it will be useful, but WITHOUT ANY WARRANTY; without even the implied warranty of MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the GNU General Public License for more details.