The anticipation of bifurcation-induced transitions in dynamical systems has
gained relevance in various fields of the natural, social, and economic
sciences. When approaching a co-dimension 1 bifurcation, the feedbacks that
stabilise the initial state weaken and eventually vanish; a process referred to
as critical slowing down (CSD). This motivates the use of variance and lag-1
autocorrelation as indicators of CSD. Both indicators rely on linearising the
system's restoring rate. Additionally, the use of variance is limited to time-
and state-independent driving noise, strongly constraining the generality of
CSD. Here, we propose a data-driven approach based on deriving a Langevin
equation to detect local stability changes and anticipate bifurcation-induced
transitions in systems with generally time- and state-dependent noise. Our
approach substantially generalizes the conditions underlying existing early
warning indicators, which we showcase in different examples. Changes in
deterministic dynamics can be clearly discriminated from changes in the driving
noise. This reduces the risk of false and missed alarms of conventional CSD
indicators significantly in settings with time-dependent or multiplicative
noise. In multi-dimensional systems, our method can greatly advance the
understanding of the coupling between system components and can avoid risks of
missing CSD due to dimension reduction, which existing approaches suffer from