Telling cause from effect in deterministic linear dynamical systems

By Naji Shajarisales, Dominik Janzing, Bernhard Schölkopf, Michel Besserve. 2015

52 citations recorded by the source corpus.

Telling a cause from its effect using observed time series data is a major challenge in natural and social sciences. Assuming the effect is generated by the cause through a linear system, we propose a new approach based on the hypothesis that nature chooses the "cause" and the "mechanism generating the effect from the cause" independently of each other. Specifically we postulate that the power spectrum of the "cause" time series is uncorrelated with the square of the frequency response of the linear filter (system) generating the effect. While most causal discovery methods for time series mainly rely on the noise, our method relies on asymmetries of the power spectral density properties that exist even in deterministic systems. We describe mathematical assumptions in a deterministic model under which the causal direction is identifiable. In particular, we show a scenario where the method works but Granger causality fails. Experiments show encouraging results on synthetic as well as real-world data. Overall, this suggests that the postulate of Independence of Cause and Mechanism is a promising principle for causal inference on observed time series.

Subfields: Artificial Intelligence, Cognitive Neuroscience, Molecular Biology, Causal Inference & Discovery

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Citations in the corpus

Toward Causal Representation Learning (2021, background): “10Other dependence measures have been proposed for highdimensional linear settings and time series [28], [119], [121], [122], [126], [226].”
Towards Causal Representation Learning (2021, background): “9Other dependence measures have been proposed for high-dimensional linear settings and time series [124, 226, 27, 122, 119, 125].”
A theory of independent mechanisms for extrapolation in generative models (2020, methodology): “2.6, that if a mechanism (here the generator) satisﬁes the principle of independent causal mechanisms, the inverse mechanism (here the encoder) will not (Shajarisales et al. 2015).”
Causality for Machine Learning (2019, background): “kin to assumptions of time-invariance of the laws of physics (Bohm, 1957). 9Other dependence measures have been proposed for high-dimensional linear settings and time series by Janzing et al. (2010); Shajarisales et al. (2015); Besserve et al. (2018a); Janzing and Schölkopf (2018), see also Janzing ”
Generalization in anti-causal learning (2018, neutral): “In causality, domain robustness of the causal mechanism is captured by the principle of the independence of cause and mechanism (ICM) (Daniusis et al., 2010; Schölkopf et al., 2012; Shajarisales et al., 2015).”
Group invariance principles for causal generative models (2017, methodology): “The main use of ICM postulates has been the development of several causal inference algorithms for cause-effect pairs (Janzing et al., 2010; Zscheischler et al., 2011; Daniusis et al., 2010; Janzing et al., 2012; Shajarisales et al., 2015; Sgouritsa et al., 2015); however, results in Schölkopf et al”
Intrinsic disentanglement: an invariance view for deep generative models (2018, methodology): “Shajarisales et al. (2015) introduce a specific formalization of ICM in the context of time series that will be suited to the study of convolutional layers in deep neural network.”