Robust and highly scalable estimation of directional couplings from time-shifted signals

TL;DR

This paper introduces a scalable variational Bayes method for estimating directed couplings from time-shifted signals, effectively handling unknown delays and outperforming existing techniques.

Contribution

It presents a hybrid variational inference approach that marginalizes delay uncertainties, providing reliable coupling estimates in complex networks.

Findings

Reliable and conservative coupling estimates achieved

Outperforms regression DCM in experiments

Handles unknown delays effectively

Abstract

The estimation of directed couplings between the nodes of a network from indirect measurements is a central methodological challenge in scientific fields such as neuroscience, systems biology and economics. Unfortunately, the problem is generally ill-posed due to the possible presence of unknown delays in the measurements. In this paper, we offer a solution of this problem by using a variational Bayes framework, where the uncertainty over the delays is marginalized in order to obtain conservative coupling estimates. To overcome the well-known overconfidence of classical variational methods, we use a hybrid-VI scheme where the (possibly flat or multimodal) posterior over the measurement parameters is estimated using a forward KL loss while the (nearly convex) conditional posterior over the couplings is estimated using the highly scalable gradient-based VI. In our ground-truth experiments, we show that the network provides reliable and conservative estimates of the couplings, greatly outperforming similar methods such as regression DCM.