Active Learning on Trees and Graphs

TL;DR

This paper studies active learning on trees and graphs, proposing efficient algorithms for minimizing mistakes through optimal query placement, and extends insights to general graphs with bounds on mistakes.

Contribution

It introduces an efficient query selection algorithm for active learning on trees and graphs, achieving near-optimal mistake minimization and trade-offs.

Findings

Optimal query placement characterized for trees

Efficient mincut classifier achieves minimal mistakes

Lower bounds established for general graphs

Abstract

We investigate the problem of active learning on a given tree whose nodes are assigned binary labels in an adversarial way. Inspired by recent results by Guillory and Bilmes, we characterize (up to constant factors) the optimal placement of queries so to minimize the mistakes made on the non-queried nodes. Our query selection algorithm is extremely efficient, and the optimal number of mistakes on the non-queried nodes is achieved by a simple and efficient mincut classifier. Through a simple modification of the query selection algorithm we also show optimality (up to constant factors) with respect to the trade-off between number of queries and number of mistakes on non-queried nodes. By using spanning trees, our algorithms can be efficiently applied to general graphs, although the problem of finding optimal and efficient active learning algorithms for general graphs remains open. Towards this end, we provide a lower bound on the number of mistakes made on arbitrary graphs by any active learning algorithm using a number of queries which is up to a constant fraction of the graph size.