We formulate dependency parsing as a graphical model with the novel ingredient of global constraints. We show how to apply loopy belief propagation (BP), a simple and effective tool for approximate learning and inference. As a parsing algorithm, BP is both asymptotically and empirically efficient. Even with second-order features or latent variables, which would make exact parsing considerably slower or NP-hard, BP needs only O(n3) time with a small constant factor. Furthermore, such features significantly improve parse accuracy over exact first-order methods. Incorporating additional features would increase the runtime additively rather than multiplicatively. 1

Log-linear and maximum-margin models are two commonly-used methods in supervised machine learning, and are frequently used in structured prediction problems. Efficient learning of parameters in these models is therefore an important problem, and becomes a key factor when learning from very large data sets. This paper describes exponentiated gradient (EG) algorithms for training such models, where EG updates are applied to the convex dual of either the log-linear or maxmargin objective function; the dual in both the log-linear and max-margin cases corresponds to minimizing a convex function with simplex constraints. We study both batch and online variants of the algorithm, and provide rates of convergence for both cases. In the max-margin case, O ( 1 ε) EG updates are required to reach a given accuracy ε in the dual; in contrast, for log-linear models only O(log (1/ε)) updates are required. For both the max-margin and log-linear cases, our bounds suggest that the online EG algorithm requires a factor of n less computation to reach a desired accuracy than the batch EG algorithm, where n is the number of training examples. Our experiments confirm that the online algorithms are much faster than the batch algorithms in practice. We describe how the EG updates factor in a convenient way for structured prediction problems, allowing the algorithms to be

This paper introduces algorithms for nonprojective parsing based on dual decomposition. We focus on parsing algorithms for nonprojective head automata, a generalization of head-automata models to non-projective structures. The dual decomposition algorithms are simple and efficient, relying on standard dynamic programming and minimum spanning tree algorithms. They provably solve an LP relaxation of the non-projective parsing problem. Empirically the LP relaxation is very often tight: for many languages, exact solutions are achieved on over 98 % of test sentences. The accuracy of our models is higher than previous work on a broad range of datasets. 1

In this paper we investigate several nonprojective parsing algorithms for dependency parsing, providing novel polynomial time solutions under the assumption that each dependency decision is independent of all the others, called here the edge-factored model. We also investigate algorithms for non-projective parsing that account for nonlocal information, and present several hardness results. This suggests that it is unlikely that exact non-projective dependency parsing is tractable for any model richer than the edge-factored model. 1

A notable gap in research on statistical dependency parsing is a proper conditional probability distribution over nonprojective dependency trees for a given sentence. We exploit the Matrix Tree Theorem (Tutte, 1984) to derive an algorithm that efficiently sums the scores of all nonprojective trees in a sentence, permitting the definition of a conditional log-linear model over trees. While discriminative methods, such as those presented in McDonald et al. (2005b), obtain very high accuracy on standard dependency parsing tasks and can be trained and applied without marginalization, “summing trees ” permits some alternative techniques of interest. Using the summing algorithm, we present competitive experimental results on four nonprojective languages, for maximum conditional likelihood estimation, minimum Bayes-risk parsing, and hidden variable training. 1

We develop an online algorithm called Component Hedge for learning structured concept classes when the loss of a structured concept sums over its components. Example classes include paths through a graph (composed of edges) and partial permutations (composed of assignments). The algorithm maintains a parameter vector with one non-negative weight per component, which always lies in the convex hull of the structured concept class. The algorithm predicts by decomposing the current parameter vector into a convex combination of concepts and choosing one of those concepts at random. The parameters are updated by first performing a multiplicative update and then projecting back into the convex hull. We show that Component Hedge has optimal regret bounds for a large variety of structured concept classes. 1

This paper describes an empirical study of high-performance dependency parsers based on a semi-supervised learning approach. We describe an extension of semisupervised structured conditional models (SS-SCMs) to the dependency parsing problem, whose framework is originally proposed in (Suzuki and Isozaki, 2008). Moreover, we introduce two extensions related to dependency parsing: The first extension is to combine SS-SCMs with another semi-supervised approach, described in (Koo et al., 2008). The second extension is to apply the approach to secondorder parsing models, such as those described in (Carreras, 2007), using a twostage semi-supervised learning approach. We demonstrate the effectiveness of our proposed methods on dependency parsing experiments using two widely used test collections: the Penn Treebank for English, and the Prague Dependency Treebank

One may need to build a statistical parser for a new language, using only a very small labeled treebank together with raw text. We argue that bootstrapping a parser is most promising when the model uses a rich set of redundant features, as in recent models for scoring dependency parses (McDonald et al., 2005). Drawing on Abney’s (2004) analysis of the Yarowsky algorithm, we perform bootstrapping by entropy regularization: we maximize a linear combination of conditional likelihood on labeled data and confidence (negative Rényi entropy) on unlabeled data. In initial experiments, this surpassed EM for training a simple feature-poor generative model, and also improved the performance of a feature-rich, conditionally estimated model where EM could not easily have been applied. For our models and training sets, more peaked measures of confidence, measured by Rényi entropy, outperformed smoother ones. We discuss how our feature set could be extended with cross-lingual or cross-domain features, to incorporate knowledge from parallel or comparable corpora during bootstrapping. 1

Virtually all methods of learning dynamic systems from data start from the same basic assumption: that the learning algorithm will be provided with a sequence, or trajectory, of data generated from the dynamic system. In this paper we consider the case where the data is not sequenced. The learning algorithm is presented a set of data points from the system’s operation but with no temporal ordering. The data are simply drawn as individual disconnected points. While making this assumption may seem absurd at first glance, we observe that many scientific modeling tasks have exactly this property. In this paper we restrict our attention to learning linear, discrete time models. We propose several algorithms for learning these models based on optimizing approximate likelihood functions and test the methods on several synthetic data sets. 1.

We propose a new algorithm for approximate MAP inference on factor graphs, by combining augmented Lagrangian optimization with the dual decomposition method. Each slave subproblem is given a quadratic penalty, which pushes toward faster consensus than in previous subgradient approaches. Our algorithm is provably convergent, parallelizable, and suitable for fine decompositions of the graph. We show how it can efficiently handle problems with (possibly global) structural constraints via simple sort operations. Experiments on synthetic and real-world data show that our approach compares favorably with the state-of-the-art. 1.