Empirical stationary correlations for semi-supervised learning on graphs

TL;DR

This paper demonstrates that many semi-supervised graph learning methods are equivalent to kriging predictors and introduces a data-driven estimator to improve predictions by leveraging observed covariation.

Contribution

It establishes the equivalence of several semi-supervised methods to kriging and proposes a new data-driven correlation estimator for enhanced graph-based predictions.

Findings

Improved prediction accuracy with the new estimator

Equivalence of existing methods to kriging predictors

Effective use of observed covariation in predictions

Abstract

In semi-supervised learning on graphs, response variables observed at one node are used to estimate missing values at other nodes. The methods exploit correlations between nearby nodes in the graph. In this paper we prove that many such proposals are equivalent to kriging predictors based on a fixed covariance matrix driven by the link structure of the graph. We then propose a data-driven estimator of the correlation structure that exploits patterns among the observed response values. By incorporating even a small fraction of observed covariation into the predictions, we are able to obtain much improved prediction on two graph data sets.