Inferring collective dynamical states from widely unobserved systems

TL;DR

This paper introduces a subsampling-invariant estimator that accurately infers the stability and infectiousness of complex systems from limited observations, with applications in epidemiology and neuroscience.

Contribution

The authors develop a novel estimator that corrects for spatial subsampling biases, enabling reliable analysis of dynamical states in partially observed systems.

Findings

Estimator accurately infers disease infectiousness under subsampling

Reveals mixed asynchronous and critical states in brain activity across species

Enables new insights into neural reverberation and stability

Abstract

When assessing spatially-extended complex systems, one can rarely sample the states of all components. We show that this spatial subsampling typically leads to severe underestimation of the risk of instability in systems with propagating events. We derive a subsampling-invariant estimator, and demonstrate that it correctly infers the infectiousness of various diseases under subsampling, making it particularly useful in countries with unreliable case reports. In neuroscience, recordings are strongly limited by subsampling. Here, the subsampling-invariant estimator allows to revisit two prominent hypotheses about the brain's collective spiking dynamics: asynchronous-irregular or critical. We identify consistently for rat, cat and monkey a state that combines features of both and allows input to reverberate in the network for hundreds of milliseconds. Overall, owing to its ready applicability, the novel estimator paves the way to novel insight for the study of spatially-extended dynamical systems.