Poisson Reweighted Laplacian Uncertainty Sampling for Graph-based Active Learning

TL;DR

This paper demonstrates that uncertainty sampling, when aligned with the model's uncertainty measure, effectively balances exploration and exploitation in graph-based active learning, using a novel Poisson Reweighted Laplace Learning approach.

Contribution

It introduces a new acquisition function for PWLL that identifies unexplored regions and analyzes the method's theoretical properties through a continuum limit.

Findings

Effective exploration-exploitation tradeoff control via diagonal perturbation.

Theoretical analysis confirms the method's well-posedness and localization.

Experimental results on image classification validate the approach.

Abstract

We show that uncertainty sampling is sufficient to achieve exploration versus exploitation in graph-based active learning, as long as the measure of uncertainty properly aligns with the underlying model and the model properly reflects uncertainty in unexplored regions. In particular, we use a recently developed algorithm, Poisson ReWeighted Laplace Learning (PWLL) for the classifier and we introduce an acquisition function designed to measure uncertainty in this graph-based classifier that identifies unexplored regions of the data. We introduce a diagonal perturbation in PWLL which produces exponential localization of solutions, and controls the exploration versus exploitation tradeoff in active learning. We use the well-posed continuum limit of PWLL to rigorously analyze our method, and present experimental results on a number of graph-based image classification problems.