PASCAL - Pattern Analysis, Statistical Modelling and Computational Learning

Predicting the labels of an unknown graph via adaptive exploration
Nicolò Cesa-Bianchi, Claudio Gentile and Fabio Vitale
Theoretical Computer Science Volume 412, Number 19, pp. 1791-1804, 2011.


Motivated by a problem of targeted advertising in social networks, we introduce a new model of online learning on labeled graphs where the graph is initially unknown and the algorithm is free to choose which vertex to predict next. For this learning model, we define an appropriate measure of regularity of a graph labeling called the merging degree. In general, the merging degree is small when the vertices of the unknown graph can be partitioned into a few well-separated clusters within which labels are roughly constant. For the special case of binary labeled graphs, the merging degree is a more refined measure than the cutsize. After observing that natural nonadaptive exploration/prediction strategies, like depth-first with majority vote, do not behave satisfactorily on graphs with small merging degree, we introduce an efficiently implementable adaptive strategy whose cumulative loss is provably controlled by the merging degree. A matching lower bound shows that in the case of binary labels our analysis cannot be improved.

EPrint Type:Article
Project Keyword:Project Keyword UNSPECIFIED
Subjects:Theory & Algorithms
ID Code:7739
Deposited By:Nicolò Cesa-Bianchi
Deposited On:17 March 2011