Inferring causal networks of dynamical systems through transient dynamics and perturbation.

@article{Stepaniants2020InferringCN,
  title={Inferring causal networks of dynamical systems through transient dynamics and perturbation.},
  author={George Stepaniants and Bingni W. Brunton and J. Nathan Kutz},
  journal={Physical review. E},
  year={2020},
  volume={102 4-1},
  pages={
          042309
        }
}
Inferring causal relations from time series measurements is an ill-posed mathematical problem, where typically an infinite number of potential solutions can reproduce the given data. We explore in depth a strategy to disambiguate between possible underlying causal networks by perturbing the network, where the forcings are either targeted or applied at random. The resulting transient dynamics provide the critical information necessary to infer causality. Two methods are shown to provide accurate… 

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References

SHOWING 1-10 OF 53 REFERENCES

Inferring connectivity in networked dynamical systems: Challenges using Granger causality.

The results show a significant systematic disparity between the original and inferred network, unless the true structure is extremely sparse or dense, and advocate the need to perform comparisons with any network inference method since the inferred connectivity results appear to have very little to do with the ground truth system.

Network inference using directed information: The deterministic limit

This paper proposes a remedy called restricted directed information (RDI), and shows that, RDI recovers the graph correctly in all instances, deterministic or stochastic, where there is enough information to recover the graph uniquely.

Advances to Bayesian network inference for generating causal networks from observational biological data

A novel influence score for DBNs is developed that attempts to estimate both the sign (activation or repression) and relative magnitude of interactions among variables and reduces a significant portion of false positive interactions in the recovered networks.

Detecting Causality in Complex Ecosystems

A new method, based on nonlinear state space reconstruction, that can distinguish causality from correlation is introduced, and extends to nonseparable weakly connected dynamic systems (cases not covered by the current Granger causality paradigm).

Systematic errors in connectivity inferred from activity in strongly recurrent networks

It is demonstrated that strongly recurrent circuits inferred from neural activity, even with unlimited data from every neuron, are biased and Synapses are inferred between unconnected but correlated neurons.

Revealing network connectivity from response dynamics.

  • M. Timme
  • Mathematics
    Physical review letters
  • 2007
This work considers networks of coupled phase oscillators and explicitly study their long-term stationary response to temporally constant driving, finding good predictions of the actual connectivity even for formally underdetermined problems.

Methods for causal inference from gene perturbation experiments and validation

The results suggest that prediction and prioritization of future experimental interventions, such as gene deletions, can be improved by using the statistical inference techniques used in this work.
...