Regret bounds for hierarchical classification with linear-threshold functions
Nicolò Cesa-Bianchi, Alex Conconi and Claudio Gentile
In: COLT 2004, 1-4 Jul 2004, Banff, Canada.
We study the problem of classifying data in a given taxonomy
when classifications associated with multiple and/or partial paths
are allowed. We introduce an incremental algorithm using a linear-threshold classifier at each node of the taxonomy. These classifiers are trained and evaluated in a hierarchical top-down fashion. We then define a hierachical and parametric data model and prove a bound on the probability that our algorithm guesses the wrong multilabel for a random instance compared to the same probability when the true model parameters are known. Our bound decreases exponentially with the number of training examples and depends in a detailed way on the interaction between the process parameters and the taxonomy structure. Preliminary experiments on real-world data provide support to our theoretical results.