Transfer Learning for Latent Variable Network Models

TL;DR

This paper develops an efficient transfer learning method for latent variable network models, enabling accurate estimation of target networks using limited target data and source network information, without assuming parametric forms.

Contribution

It introduces a novel algorithm leveraging graph distances for transfer learning in latent variable models, achieving vanishing error without parametric assumptions and providing minimax bounds for stochastic block models.

Findings

Algorithm achieves $o(1)$ error in transfer learning.

No parametric assumptions needed for the method.

Empirical results on real and simulated data demonstrate effectiveness.

Abstract

We study transfer learning for estimation in latent variable network models. In our setting, the conditional edge probability matrices given the latent variables are represented by $P$ for the source and $Q$ for the target. We wish to estimate $Q$ given two kinds of data: (1) edge data from a subgraph induced by an $o(1)$ fraction of the nodes of $Q$, and (2) edge data from all of $P$. If the source $P$ has no relation to the target $Q$, the estimation error must be $\Omega(1)$. However, we show that if the latent variables are shared, then vanishing error is possible. We give an efficient algorithm that utilizes the ordering of a suitably defined graph distance. Our algorithm achieves $o(1)$ error and does not assume a parametric form on the source or target networks. Next, for the specific case of Stochastic Block Models we prove a minimax lower bound and show that a simple algorithm achieves this rate. Finally, we empirically demonstrate our algorithm's use on real-world and simulated graph transfer problems.