Adaptive filtering for hidden node detection and tracking in networks

Abstract

The identification of network connectivity from noisy time series is of great interest in the study of network dynamics. This connectivity estimation problem becomes more complicated when we consider the possibility of hidden nodes within the network. These hidden nodes act as unknown drivers on our network and their presence can lead to the identification of false connections, resulting in incorrect network inference. Detecting the parts of the network they are acting on is thus critical. Here, we propose a novel method for hidden node detection based on an adaptive filtering framework with specific application to neuronal networks. We consider the hidden node as a problem of missing variables when model fitting and show that the estimated system noise covariance provided by the adaptive filter can be used to localize the influence of the hidden nodes and distinguish the effects of different hidden nodes. Additionally, we show that the sequential nature of our algorithm allows for tracking changes in the hidden node influence over time.

Detecting Hidden Units and Network Size from Perceptible Dynamics

“…Previous approaches to detect hidden nodes are capable of detecting a single hidden node in an otherwise completely perceptible network: Some [45] employ nonlinear Kalman filters to fit the parameters of a given model and use the covariance matrix of the fitting error;…”

“…Previous approaches to detect hidden nodes are capable of detecting a single hidden node in an otherwise completely perceptible network: Some [45] employ nonlinear Kalman filters to fit the parameters of a given model and use the covariance matrix of the fitting error; others first approximate the dynamics via differential equations and then determine the existence and location of the hidden unit through heuristic methods [30][31][32]. Our theory instead reliably captures many hidden units, is data-driven, relies on sampled time series and thereby requires no model a priori.…”