Keywords: non-linear dynamical systems, selection bias, vector autoregressive models, neuroscience, time-inhomogenous models
TL;DR: We exhibit sample selection bias when inferring the mechanisms underlying transient phenomena in dynamical systems, and provide a bias correction approach for it.
Abstract: Many important dynamical phenomena emerging in complex systems such as storms, stock market crashes, or reactivations of memory engrams in the mammalian brain are transient in nature. We consider the problem of learning accurate models of such phenomena based only on data gathered by detecting such transient events, and analyzing their peri-event dynamics. This approach is widely used to analyze spontaneous activity in brain recording, as it focuses on emerging events of particular significance to brain function. We show, however, that such an approach may misrepresent the properties of the system under study due to the event detection procedure that entails a selection bias. We develop the Debiased Snapshot (DeSnap) approach to de-bias the time-varying properties of the system estimated from such peri-event data and demonstrate its benefits in recovering state-dependent transient dynamics in toy examples and neural time series.