Support vector machines (SVMs) were originally designed for binary classification. How to effectively extend it for multiclass classification is still an ongoing research issue. Several methods have been proposed where typically we construct a multiclass classifier by combining several binary classifiers. Some authors also proposed methods that consider all classes at once. As it is computationally more expensive to solve multiclass problems, comparisons of these methods using large-scale problems have not been seriously conducted. Especially for methods solving multiclass SVM in one step, a much larger optimization problem is required so up to now experiments are limited to small data sets. In this paper we give decomposition implementations for two such “all-together” methods. We then compare their performance with three methods based on binary classifications: “one-against-all,” “one-against-one,” and directed acyclic graph SVM (DAGSVM). Our experiments indicate that the “one-against-one” and DAG methods are more suitable for practical use than the other methods. Results also show that for large problems methods by considering all data at once in general need fewer support vectors.

We present a family of margin based online learning algorithms for various prediction tasks. In particular we derive and analyze algorithms for binary and multiclass categorization, regression, uniclass prediction and sequence prediction. The update steps of our different algorithms are all based on analytical solutions to simple constrained optimization problems. This unified view allows us to prove worst-case loss bounds for the different algorithms and for the various decision problems based on a single lemma. Our bounds on the cumulative loss of the algorithms are relative to the smallest loss that can be attained by any fixed hypothesis, and as such are applicable to both realizable and unrealizable settings. We demonstrate some of the merits of the proposed algorithms in a series of experiments with synthetic and real data sets.

We formalize weighted dependency parsing as searching for maximum spanning trees (MSTs) in directed graphs. Using this representation, the parsing algorithm of Eisner (1996) is sufficient for searching over all projective trees in O(n 3) time. More surprisingly, the representation is extended naturally to non-projective parsing using Chu-Liu-Edmonds (Chu and Liu, 1965; Edmonds, 1967) MST algorithm, yielding an O(n 2) parsing algorithm. We evaluate these methods on the Prague Dependency Treebank using online large-margin learning techniques (Crammer et al., 2003; McDonald et al., 2005) and show that MST parsing increases efficiency and accuracy for languages with non-projective dependencies. 1

We present an effective training algorithm for linearly-scored dependency parsers that implements online largemargin multi-class training (Crammer and Singer, 2003; Crammer et al., 2003) on top of efficient parsing techniques for dependency trees (Eisner, 1996). The trained parsers achieve a competitive dependency accuracy for both English and Czech with no language specific enhancements. 1

We discuss the problem of ranking instances. In our framework each instance is associated with a rank or a rating, which is an integer from 1 to k. Our goal is to find a rank-prediction rule that assigns each instance a rank which is as close as possible to the instance's true rank. We describe a simple and efficient online algorithm, analyze its performance in the mistake bound model, and prove its correctness. We describe two sets of experiments, with synthetic data and with the EachMovie dataset for collaborative filtering. In the experiments we performed, our algorithm outperforms online algorithms for regression and classification applied to ranking.

In this paper we extend the maximum spanning tree (MST) dependency parsing framework of McDonald et al. (2005c) to incorporate higher-order feature representations and allow dependency structures with multiple parents per word. We show that those extensions can make the MST framework computationally intractable, but that the intractability can be circumvented with new approximate parsing algorithms. We conclude with experiments showing that discriminative online learning using those approximate algorithms achieves the best reported parsing accuracy for Czech and Danish. 1

Very high dimensional learning systems become theoretically possible when training examples are abundant. The computing cost then becomes the limiting factor. Any efficient learning algorithm should at least take a brief look at each example. But should all examples be given equal attention? This contribution proposes an empirical answer. We first present an online SVM algorithm based on this premise. LASVM yields competitive misclassification rates after a single pass over the training examples, outspeeding state-of-the-art SVM solvers. Then we show how active example selection can yield faster training, higher accuracies, and simpler models, using only a fraction of the training example labels.

We present a simple and effective semisupervised method for training dependency parsers. We focus on the problem of lexical representation, introducing features that incorporate word clusters derived from a large unannotated corpus. We demonstrate the effectiveness of the approach in a series of dependency parsing experiments on the Penn Treebank and Prague Dependency Treebank, and we show that the cluster-based features yield substantial gains in performance across a wide range of conditions. For example, in the case of English unlabeled second-order parsing, we improve from a baseline accuracy of 92.02 % to 93.16%, and in the case of Czech unlabeled second-order parsing, we improve from a baseline accuracy of 86.13% to 87.13%. In addition, we demonstrate that our method also improves performance when small amounts of training data are available, and can roughly halve the amount of supervised data required to reach a desired level of performance. 1

We introduce constraint classification, a framework capturing many flavors of multiclass classification including multilabel classification and ranking, and present a meta-algorithm for learning in this framework. We provide generalization bounds when using a collection of k linear functions to represent each hypothesis. We also present empirical and theoretical evidence that constraint classification is more powerful than existing methods of multiclass classification. 1

We describe a new family of topic-ranking algorithms for multi-labeled documents. The motivation for the algorithms stem from recent advances in online learning algorithms. The algorithms are simple to implement and are also time and memory efficient. We provide a unified analysis of the family of algorithms in the mistake bound model. We then discuss experiments with the proposed family of topic-ranking algorithms on the Reuters-21578 corpus and the new corpus released by Reuters in 2000. On both corpora, the algorithms we present achieve state-of-the-art results and outperforms topic-ranking adaptations of Rocchio's algorithm and of the Perceptron algorithm.