A note on kernel methods for multiscale systems with critical transitions

Boumediene Hamzi, Christian Kuehn, Sameh Mohamed

Research output: Contribution to journalArticlepeer-review

7 Scopus citations


We study the maximum mean discrepancy (MMD) in the context of critical transitions modelled by fast-slow stochastic dynamical systems. We establish a new link between the dynamical theory of critical transitions with the statistical aspects of the MMD. In particular, we show that a formal approximation of the MMD near fast subsystem bifurcation points can be computed to leading order. This leading order approximation shows that the MMD depends intricately on the fast-slow systems parameters, which can influence the detection of potential early-warning signs before critical transitions. However, the MMD turns out to be an excellent binary classifier to detect the change-point location induced by the critical transition. We cross-validate our results by numerical simulations for a van der Pol-type model.

Original languageEnglish
Pages (from-to)907-917
Number of pages11
JournalMathematical Methods in the Applied Sciences
Issue number3
StatePublished - 1 Feb 2019
Externally publishedYes


  • bifurcation
  • critical transition
  • kernel methods
  • maximum mean discrepancy
  • multiscale system
  • time series
  • tipping point


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