This paper presents a graphical model that embeds two directional aligners into a single model.

We have presented a graphical model that combines two classical HMM-based alignment models.

This result is achieved by embedding two directional HMM-based alignment models into a larger bidirectional graphical model .

Our bidirectional model Q = (12,13) is a globally normalized, undirected graphical model of the word alignment for a fixed sentence pair (6, f Each vertex in the vertex set V corresponds to a model variable Vi, and each undirected edge in the edge set D corresponds to a pair of variables (W, Each vertex has an associated potential function w, that assigns a real-valued potential to each possible value v,- of 16.1 Likewise, each edge has an associated potential function gig-(vi, 213-) that scores pairs of values.

Figure l: The structure of our graphical model for a simple sentence pair.

In general, graphical models admit efficient, exact inference algorithms if they do not contain cycles.

While the entire graphical model has loops, there are two overlapping subgraphs that are cycle-free.

To describe a dual decomposition inference procedure for our model, we first restate the inference problem under our graphical model in terms of the two overlapping subgraphs that admit tractable inference.

Although differing in both model and inference, our work and theirs both find improvements from defining graphical models for alignment that do not admit exact polynomial-time inference algorithms.

To ensure a meaningful comparison with the joint model, our two baselines are both implemented in the same graphical model framework, and trained with the same machine-leaming algorithm.

The tagger is a graphical model with the WORD and TAG variables, connected by the local factors TAG-UNIGRAM, TAG-BIGRAM, and TAG-CONSISTENCY, all used in the joint model (§3).

To illustrate the effect, the graphical model of the sentence in Table 1, whose six words are all covered by the database, has 1,866 factors; without the benefit of the database, the full model would have 31,901 factors.

It will be presented as a graphical model,

Other previous work attempts to address some of the above concerns by mapping coreference to inference on an undirected graphical model (Culotta et al., 2007; Poon et al., 2008; Wellner et al., 2004; Wick et al., 2009a).

In this work we first distribute MCMC-based inference for the graphical model representation of coreference.

Our representation of the problem as an undirected graphical model , and performing distributed inference on it, provides a combination of advantages not available in any of these approaches.

In addition to representing features from all of the related work, graphical models can also use more complex entity-wide features (Culotta et al., 2007; Wick et al., 2009a), and parameters can be learned using supervised (Collins, 2002) or semi-supervised techniques (Mann and McCallum, 2008).

o MULTIR introduces a probabilistic, graphical model of multi-instance learning which handles overlapping relations.

We define an undirected graphical model that allows joint reasoning about aggregate (corpus-level) and sentence-level extraction decisions.

(2010), combine weak supervision and multi-instance learning in a more sophisticated manner, training a graphical model , which assumes only that at least one of the matches between the arguments of a Freebase fact and sentences in the corpus is a true relational mention.