Regret Bounds for Hierarchical Classification with Linear-Threshold Functions
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.