This repository holds implementations of the following four algorithms for causal structure learning for time series,

• SLARAC (Subsampled Linear Auto-Regression Absolute Coefficients),
• QRBS (Quantiles of Ridge regressed Bootstrap Samples),
• LASAR (LASso Auto-Regression),
• SELVAR (Selective auto-regressive model),

which came in first in 18 and close second in 13 out of the 34 competition categories in the Causality 4 Climate competition at the Conference on Neural Information Processing Systems 2019 (NeurIPS). For details on the competition tasks and the outcomes you may watch the recording of the NeurIPS session or consult the result slides. (Algorithm names map as follows between tidybench and our competition implementations: tidybench.slarac was varvar, tidybench.qrbs was ridge, tidybench.lasar was varvar(lasso=True), and tidybench.selvar was selvar.)

More details can be found in our accompanying paper and the respective well-documented code files.

Feel free to use our algorithms (AGPL-3.0 license). In fact, we encourage their use as baseline benchmarks and guidance of future algorithmic and methodological developments for structure learning from time series.

We kindly ask you to cite our accompanying paper in case you find our code useful:

@InProceedings{weichwald2020causal,
  title = {{Causal structure learning from time series: Large regression coefficients may predict causal links better in practice than small p-values}},
  author = {Weichwald, Sebastian and Jakobsen, Martin E. and Mogensen, Phillip B. and Petersen, Lasse and Thams, Nikolaj and Varando, Gherardo},
  publisher = {PMLR},
  series = {Proceedings of the NeurIPS 2019 Competition and Demonstration Track, Proceedings of Machine Learning Research},
  volume = {123},
  pages = {27--36},
  year = {2020},
  editor = {Hugo Jair Escalante and Raia Hadsell},
  pdf = {https://proceedings.mlr.press/v123/weichwald20a/weichwald20a.pdf},
  url = {https://proceedings.mlr.press/v123/weichwald20a.html},
}

Input: time series data (and some method-specific parameters)

Output: score matrix indicating which structural links are inferred likely to exist

All four algorithms take as input multivariate time series data in form of a T x d matrix of T time samples of d variables and output a d x d score/adjacency matrix A. The (i,j)th entry corresponds to an edge from the i-th to the j-th time series component, where higher values correspond to edges that are inferred to be more likely to exist, given the observed data.

At the moment, only a toy example is provided.

SLARAC, QRBS, and LASAR require numpy and sklearn. These requirements are listed in the requirements.txt and can be installed via pip install -r requirements.txt.

SELVAR requires lapack/blas installed and the compilation of selvarF.f with f2py (e.g. f2py -llapack -c -m selvarF selvarF.f).

We are a team of PhD students and Postdocs that formed at the Copenhagen Causality Lab (CoCaLa) of the University of Copenhagen (Martin E Jakobsen, Phillip B Mogensen, Lasse Petersen, Nikolaj Thams, Gherardo Varando, Sebastian Weichwald) to participate in the C4C competition.