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...s a key role in constructing efficient learning and inference procedures. Notable examples for structured label sets are graphs (in particular trees) and sequences (Collins, 2000; Altun et al., 2003; =-=Taskar et al., 2003-=-; Tsochantaridis et al., 2004). We now overview how the cost-sensitive learning algorithms described in the previous section can be adapted to structured output settings. For concreteness, we focus on...

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...dency trees, the loss of a tree is defined to be the number of words with incorrect parents relative to the correct tree. This is closely related to the Hamming loss that is often used for sequences (=-=Taskar et al., 2003-=-). For arbitrary inputs, there are typically exponentially many possible parses and thus exponentially many margin constraints in line 4 of Figure 4. 3.1 Single-best MIRA One solution for the exponent...

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...he multivariate SVM∆ multi be solved despite the huge number of constraints? This problem is a special case of the multivariate prediction formulations in (Tsochantaridis et al., 2004) as well as in (=-=Taskar et al., 2003-=-). The 3 http://svmlight.joachims.orgsA Support Vector Method for Multivariate Performance Measures Algorithm 1 Algorithm for solving quadratic program of multivariate SVM ∆ multi . 1: Input: ¯x = (x1...

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...icient history, their parsing algorithm must prune heuristically most of the possible parses. Taskar et al. (2004) formulate the parsing problem in the large-margin structured classification setting (=-=Taskar et al., 2003-=-), but are limited to parsing sentences of 15 words or less due to computation time. Though these approaches represent good first steps towards discriminatively-trained parsers, they have not yet been...

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...close as possible to the desired structures on the training instances. Following the lines of the recent work on maximum margin estimation for probabilistic models (Collins, 2002; Altun et al., 2003; =-=Taskar et al., 2003-=-), we present a discriminative estimation framework for structured models based on the large margin principle underlying support vector machines. The largemargin criterion provides an alternative to p...

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...ood of each node’s training data with respect to φi and ψ. In more detail, the algorithm is as follows. At iteration t, the goal is to minimize the negative log-likelihood of the training data. As in =-=[11]-=-, we consider the per-label loss (i.e., we use marginal probabilities), as opposed to requiring that the joint labeling be correct (as in Viterbi decoding). Hence the cost function to be minimized is ...

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...ough collective classification has gained attention only in the past five to seven years, initiated by the work of Jennifer Neville and David Jensen [44, 24, 25, 46] and the work of Ben Taskar et al. =-=[59, 17, 55, 58]-=-, the general problem of inference for structured output spaces has received attention for a considerably longer period of time from various research communities including computer vision, spatial sta...

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...bels have rich internal structure. Previous work in this area has focused on problems such as sequence learning, where y is a sequence of state labels (e.g., see (Lafferty, McCallum, & Pereira, 2001; =-=Taskar, Guestrin, & Koller, 2003-=-)), or natural language parsing, where y is a context-free parse tree for a sentence x (e.g., see Taskar et al. (2004)). In this paper we investigate a new type of structured classification problem, w...