Convergence guarantees for response prediction for latent structure network time series

TL;DR

This paper introduces a semi-supervised method for predicting responses in network time series by leveraging latent low-dimensional structures, with theoretical guarantees and real-world biological applications.

Contribution

It presents a novel approach combining stress embedding with theoretical convergence guarantees for response prediction in growing network time series.

Findings

Method achieves consistent response prediction in simulated data.

Theoretical convergence guarantees are established.

Application to biological neural data demonstrates practical utility.

Abstract

In this article, we propose a technique to predict the response associated with an unlabeled time series of networks in a semisupervised setting. Our model involves a collection of time series of random networks of growing size, where some of the time series are associated with responses. Assuming that the collection of time series admits an unknown lower dimensional structure, our method exploits the underlying structure to consistently predict responses at the unlabeled time series of networks. Each time series represents a multilayer network on a common set of nodes, and raw stress embedding, a popular dimensionality reduction tool, is used for capturing the unknown latent low dimensional structure. Apart from establishing theoretical convergence guarantees and supporting them with numerical results, we demonstrate the use of our method in the analysis of real-world biological learning circuits of larval Drosophila.