Discriminative training approaches like structural SVMs have shown much promise for building highly complex and accurate models in areas like natural language processing, protein structure prediction, and information retrieval. However, current training algorithms are computationally expensive or intractable on large datasets. To overcome this bottleneck, this paper explores how cutting-plane methods can provide fast training not only for classification SVMs, but also for structural SVMs. We show that for an equivalent "1-slack" reformulation of the linear SVM training problem, our cutting-plane method has time complexity linear in the number of training examples. In particular, the number of iterations does not depend on the number of training examples, and it is linear in the desired precision and the regularization parameter. Furthermore, we present an extensive empirical evaluation of the method applied to binary classification, multi-class classification, HMM sequence tagging, and CFG parsing. The experiments show that the cutting-plane algorithm is broadly applicable and fast in practice. On large datasets, it is typically several orders of magnitude faster than conventional training methods derived from decomposition methods like SVM-light, or conventional cutting-plane methods. Implementations of our methods are available at www.joachims.org.

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We explore an algorithm for training SVMs with Kernels that can represent the learned rule using arbitrary basis vectors, not just the support vectors (SVs) from the training set. This results in two benefits. First, the added flexibility makes it possible to find sparser solutions of good quality, substantially speeding-up prediction. Second, the improved sparsity can also make training of Kernel SVMs more efficient, especially for high-dimensional and sparse data (e.g. text classification). This has the potential to make training of Kernel SVMs tractable for large training sets, where conventional methods scale quadratically due to the linear growth of the number of SVs. In addition to a theoretical analysis of the algorithm, we also present an empirical evaluation.

Machine Learning today offers a broad repertoire of methods for classification and regression. But what if we need to predict complex objects like trees, orderings, or alignments? Such problems arise naturally in natural language processing, search engines, and bioinformatics. The following explores a generalization of Support Vector Machines (SVMs) for such complex prediction problems.

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