Active learning on trees and graphs
Nicolò Cesa-Bianchi, Claudio Gentile, Fabio Vitale and Giovanni Zappella
In: Colt 2010, Haifa, Israel(2010).
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.