Abstract
We address, in the context of time series, the problem of learning a summary causal graph from observations through a model with independent and additive noise. The main algorithm we propose is a hybrid method that combines the well-known constraint-based framework for causal graph discovery and the noise-based framework that gained much attention in recent years. Our method is divided into two steps. First, it uses a noise-based procedure to find the potential causes of each time series. Then, it uses a constraint-based approach to prune all unnecessary causes. A major contribution of this study is to extend the standard causation entropy measure to time series to handle lags bigger than one time step, and to rely on a lighter version of the faithfulness hypothesis, namely the adjacency faithfulness. Experiments conducted on both simulated and real-world time series show that our approach is fast and robust wrt to different causal structures and yields good results over all datasets, whereas previously proposed approaches tend to yield good results on only few datasets.
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Notes
- 1.
Two DAGs are Markov equivalent if and only if they have the same skeleton and the same v-structures [19].
- 2.
As motivated in [12], we use the partial correlation to measure the dependence, but one can use our procedure with any measure.
- 3.
Python code available at https://github.com/kassaad/causal_discovery_for_time_series.
- 4.
Python code available at https://github.com/jakobrunge/tigramite.
- 5.
Python code available at https://github.com/kassaad/causal_discovery_for_time_series.
- 6.
R code available at http://web.math.ku.dk/~peters/code.html.
- 7.
Python code available at https://github.com/cdt15/lingam.
- 8.
Matlab code available at https://github.com/SacklerCentre/MVGC1.
- 9.
Python code available at https://github.com/M-Nauta/TCDF.
- 10.
Data is available at https://webdav.tuebingen.mpg.de/cause-effect/.
- 11.
Data is available at http://future.aae.wisc.edu.
- 12.
Original data is available at https://www.fmrib.ox.ac.uk/datasets/netsim/index.html, a preprocessed version is available at https://github.com/M-Nauta/TCDF/tree/master/data/fMRI.
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Acknowledgements
This work has been partially supported by MIAI@Grenoble Alpes (ANR-19-P3IA-0003).
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Assaad, C.K., Devijver, E., Gaussier, E., Ait-Bachir, A. (2021). A Mixed Noise and Constraint-Based Approach to Causal Inference in Time Series. In: Oliver, N., Pérez-Cruz, F., Kramer, S., Read, J., Lozano, J.A. (eds) Machine Learning and Knowledge Discovery in Databases. Research Track. ECML PKDD 2021. Lecture Notes in Computer Science(), vol 12975. Springer, Cham. https://doi.org/10.1007/978-3-030-86486-6_28
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