We present a kernel-based algorithm for hierarchical text classification where the documents are allowed to belong to more than one category at a time. The classification model is a variant of the Maximum Margin Markov Network framework, where the classification hierarchy is represented as a Markov tree equipped with an exponential family defined on the edges. We present an efficient optimization algorithm based on incremental conditional gradient ascent in single-example subspaces spanned by

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... e marginal dual variables. Experiments show that the algorithm can feasibly optimize training sets of thousands of examples and classification hierarchies consisting of hundreds of nodes. The algorithm's predictive accuracy is competitive with other recently introduced hierarchical multi-category or multilabel classification learning algorithms.